ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D...

109

Transcript of ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D...

Page 1: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� ������������ ���������������������� �!���"#�$�#%&�'�(*) �+�-,��/.102� 34����5�6��879���!��:����� �!;

<�= �!�>�>?@�>A < �B���C�>�D�E�D���F;HG��

I�JLK+MONQPRN�S4T�MUNQMOVCW�MOX

YBZ

[ MU\]V�^_T�X`IaX�^cbdSe\]bfMUTg^cV+h

JLK+MjikMUlm^_TQWQbfMOVCWH\]n"o4pRMOq:WQT�PRqO^cp�^cV+X8rL\]bsl�tuW�MUT�o/V+v]PRV+MUMUT�PRV+v

PRV�lm^_TQW�PR^cp>nwt+p-x�pRp-bfMOVCWH\]n�W�K+MyTQMOz{t+PFT�MObfMOVCW�Nnw\cT�W�K+MjX+MOvcT�MOMj\]n

| ^cN}W�MUT�\]n�~{qOPRMUV+qOM

PRV�WQK+Mjx�MOp-X`\]n

� P-MOpRX+NU���5^��CMONU�^cV+X��al+W�P-qON

� \cTQW�K+MO^cN�W�MUT�V��aV+P-�CMUT�N�P-W Z� \]N}W�\]V>� | ^cNQN�^cqgKBt+N�MUWQW�N

| ^ Z��]� �����]� �

Page 2: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

Iaq � V+\��Hp-MOX+v]bfMOVCW�N

JLK+PRN1TQMONQM#^_T�qgKDl+T�\��}MOqUW qO\]t+p-X V+\cW1K�^��CM Y MUMOV qO^_TQT�PRMUX�\]tuW���P-WQK+\]tuW1W�K+M9K+MOpFl \]nb9^cV Z P-V+X+P-�uP-X+t�^cpRN�����\]t+p-X p-P � M9W�\8M��{l+T�MONQN b Z vcTg^_W�PFW�t+X+M9W�\ ^cpRp�\]n W�K+M N�Wg^� *^_W W�K+M� t�^cV WQt+b o/pRMUqUWQT�\]V+P-qON��kT�\]tul�� � \]n [ P-V+qO\]pRV [ ^ Y \cTg^_W�\cT Z nw\cTkMOV�^ Y pRP-V+v bfM1W�\fl@M:T�nw\cT�bb Z M��ul@M:T�PRbfMUV W��uJ!\]b��]M Z NLnw\cT�^cpRp-\���PRV+v b M2W�\ N�Wg^ Z nw\cT NQ\ pR\]V+v����]M� ��y\cT�V�nw\cTLK+MUp-l�PRV+vbfM��HPFW�KfW�K+Map ^cN�MUT ^cV+X MU�CMUT Z W�K+PRV+v MOp-NQMaPRV9W�K+MapR^ Y � | Z T�\]V | ^cq�� V+V+PRN�nw\cTLK+P-NL^cNQNQP-N�Wg^cV+qOMP-VfW�K+M2b9^cP-V W�MUV�^cV+qOM2\]n W�K+MapR^cNQMUT�^cV+X�nw\cT4W�K+MaqO\]V+N�W�T�t+qUW�P-\]V9\]n�^ pRP-v]K W Y ^_T�T�PRMUT��uJ��! "� � ^cVnw\cT W�K+M I2TQv]\]V�p ^cN�MUT��m^cV+X`S/K+P-p [ ^cqU\ �_^_Tg^ nw\cT W�K+Mjl�K+\cWQ\]b t+pFW�P-l�p-PRMUTLW�t Y M#�

�$��\]t+pRX9^cp-NQ\1pRP � M�W�\ ^cq � V+\��Hp-MOX+v]MHW�K+M2N�tul+l@\cTQW�WQK�^_W%��T�MOqUMOP-�CMOX&��K+PRp-M2^_W�rLK�^_TQpRMON~BWg^_T � iaTg^_l MUT [ ^ Y \cTg^_W�\cT Z �'�}V+q�� | Z W�K�^cV � N v]\�\]tuWsW�\ WQK+M�nw\]pRp-\���PRV+v l@MO\cl�p-M#()�aT�MOvrL^_l+l�PRMOp-pR\anw\cT�l+T�\��uP-X+PRV+v2W�K+MLbf\]V+\Bq6KuTQ\]b9^_W�\cT!^cV+X ^cp-NQ\anw\cTEK+PRNeb9^cV Z K+MOpFl�nwt+p+PRX+M#^cN�� � \ Yiy^cK+pRvcTQMOV nw\cT�l+T�\ �{PRX+P-V+v WQK+MyK+P-v]K9�C\]p-Wg^cv]M2N�tul+l�p Z ��*�\ Y | ^cK+M:TH^cV+X � T�MOV+X�^sr�\]pRMUWQWQP nw\cT^cNQN�PRN�W�P-V+v bfM+��P-W�K x Y M:T�N��^cV+X � ^_TQK�^cX-,k^ � PRbfP@nw\cT�NQt+v]v]MON}W�PRV+v W�K+Mjt+N�M \]n�WQK+M � X.(! /I/�pR^cNQMUT��4~Bl@MUqOP ^cp WQK�^cV � N�W�\�*�PRq � J!t+b bfPRV+MOp-pRP�nw\cT�l+T�\��uP-X+PRV+v W�K+M Z W�W�MUT Y P-t+b10 MUT Y PRt+b x Y MUT�N^cV+X5nw\cT K+P-N1K+MOp-l�nwt+p/X+PRNQqOt+N�NQPR\]V+N��2����\]t+p-XD^cpRNQ\�p-P � M W�\�M��ul+TQMONQN N�l MOqOP ^cpEW�K�^cV � NjW�\�b ZNQtul MUTQ�{PRNQ\cT3�]\]K+V4,a\cl+l�N�nw\cT N�tul+l@\cTQW�P-V+v b M`PRV W�K+PRNfTQMONQM#^_T�qgK*l+T�\��}MOqUW n T�\]b N�W�^_TQWfW�\x�V+P-NQK.�

ILW � \cT�W�K+M#^cN�W�M:T�V5�.��\]t+pRX p-P � M�W�\2M��{l+T�MONQN"WQK�^cV � N�WQ\k~BW�MU�CM | q��yV+PRv]KCW�nw\cT"K+MUp-l�PRV+vW�\ ^_T�Tg^cV+v]MHW�K+MaqO\]VCWg^cqUW6�HPFW�K J!MOX | \cT�NQMk^_W � TQ\���V9�aV+P-�CMUTQNQP-W Z ^cV+X nw\cT�WQK+MaNQt Y NQMOzBt+MOV W^cqOzBt+PRNQPFW�PR\]V \]n�MUT Y P-t+b x Y MUT��7�y^cb ^cp-NQ\��CMUT Z vcTg^_WQMOnwt+peW�\�~{qO\cW�W [ PRV+X Y M:T�v`nw\cT1K+MUp-l�PRV+vbfM X+MOqUP-l�K+MUTfJ o'8 ^cV+X v]M:WQW�PRV+v8W�K+M�b9^cV t+NQqUT�PFl+W \]tuW \]V WQPRbfM#� � PRV�^cpRp Z ���\]t+p-X p-P � MW�\�M��{l+T�MONQNyb Z vcTg^_W�PFW�t+X+M W�\�b Z ^cXu�{PRNQ\cT r�KBt+q � ikP | ^_T�hOP-\���2\���M W�K+M NQt+qOqOMON�N \]n4WQK+PRNl+T�\��}MOq:WHW�\ K+PRN�b9^cN�W�MUTQnwt+p�P-V+NQPRv]KCWH^cV+X`qO\]VCW�PRV t+PRV+vfv]t+P-X�^cV+qOM \��CMUT W�K+MONQMylm^cN�W2nwM�� Z MO^_T�N��

JLK+PRN�T�MUNQM#^_T�qgK-��^cN�NQtul+l@\cTQWQMOX�t+V+X+MUTH^ rLK�^_TQpRMON�~BWg^_T � ikT�^_l@MUT [ ^ Y \cTg^_W�\cT Z MOX+t90q#^_WQPR\]V�qU\]V WQT�^cqUW���P-WQK � \cTQW�K+MO^cN�W�MUT�V��aV+P-�CMUT�N�P-W Z �

[ MO\]V�^_T�X�I��+Se\]bfMUTg^cV+h

�]� | ^ Z ���]� �

Page 3: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

I Y N�W�Tg^cqUW

~{zBt+MOMOhOMUX1N�Wg^_W�MUN�\]n W�K+M/MOp-MOqUWQTQ\]b9^cv]V+MUW�P-q�x�MUpRX K�^#�CM Y MOMOV N�W�t+X+PRMUX1nw\cT!bf^cV ZaZ M#^_TQN���aV+p Z T�MOqOMOVCW�p Z K�^cN2W�K+P-NHl�tuT�MOp Z z{t�^cVCW�t+b l�K+MUV+\]bfMOV+\]V Y MOMUV q:T�M#^_W�MOX8P-V`W�K+M1p ^ Y � � \��W�K+M:T�M�P-N ^�T�MOV+M���MOX PRVCW�MUT�MUN�WfP-V X+MU�CMOp-\cl�PRV+v \cl+W�PRq#^cpLX+MU�{PRqOMUN"��K+PRqgK ��PRp-p�t+NQM�NQzBt+MOMOhOMUXp-PRv]KCW4x�MOp-X+N4W�\jPRb l+TQ\ �CM bfM#^cNQtuTQMObfMOVCW�^cqUqOtuTg^cq Z ��JLK+M�x Y MUT�\cl+W�P-qHv Z T�\]NQqO\cl M�P-N/\]V+M NQt+qgKX+MU�{PRqOMyW�K�^_W ��\]t+pRX�lm^_TQW�PRqUt+p ^_T�p Z9Y MOV+MUx+WHn T�\]b t+NQM \]n"N�z{t+MOMOhUMOX`pRP-v]K W��

JLK+PRN4T�MONQM#^_TQq6K lm^_l@M:T�PRVC�CMON�W�P-vC^_W�MON�V+\]V+p-PRV+M#^_T�M� @MOq:W�N�W�K�^_W�\BqOqOtuTLPRV9K+P-v]K+p Z X+\cl@MOX\cl+W�P-q#^cpLx Y MUT�N�� � \]V+p-PRV+M#^_Tfl+TQ\{qOMON�NQMON ^_T�M`t+N�MOX W�\�l+T�\BX+t+qOM�NQz{t+MUMOhOMOX N�Wg^_WQMONf\]napRP-v]K W��IaV�MOV+K�^cV+qOMOX V+\]V+pRP-V+M#^_T�PFW Z qUTQM#^_W�MOX P-V W�K+MON�M�x Y MUTQN�qO\]t+p-X l+T�\��uPRX+M�^ bf\cTQM M � qOPRMUV WbfM:W�K+\{X�W�\ v]MOV+MUT�^_W�M NQz{t+MOMUhOMOX�N}Wg^_W�MON�� J K+P-NabfMUW�K+\BX)��\]t+pRX Y M X+P-TQMOqUW�p Z ^_l+l�pRP-q#^ Y pRM W�\W�K+Mav Z T�\]NQqO\cl M#��IaV \ �CMUT��uPRM�� \]n�NQz{t+MUMOhOMOX�N�Wg^_W�MUN�PRN�l+T�MON�MOV WQMOX.��JLK+MaV+\]V+pRPRV+MO^_T�l+T�\{qOMUNQNO�W�K+PFT�XfK�^_T�b \]V+PRqHv]MUV+MUTg^_W�P-\]V9PRV9^cV9\cl+W�P-q#^cp+x Y MUTO�uPRN/^cV�^cp Z hUMOX ^cV+X9bfMONQtuTQMObfMOVCW�N/\]n@WQK+P-T�X\cT�X+M:T2NQt+NQqUMUl+W�P Y P-pRPFW Z ^_T�Myb9^cX+My\]V�NQM:�CMUTg^cp�x Y MUT�N W�\ qU\]b lm^_T�M��HPFW�K�l+TQMOX+PRqUWQMOX`�c^cp-t+MON��

Page 4: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

J"^ Y pRMy\]n�r�\]V WQMOV WQN

SET�MOn ^cqOM

����������� �������������������������� �"!#���$��%&�'�(�#��)���* �

� �R� �$� V WQTQ\{X+t+qUW�P-\]V

� � � � [ P-v]K W � PRMUpRX�~BW�^_W�PRN�WQPRqON

� �,+ �4rL\]K+M:T�MOVCWk~BWg^_W�MUN

� �.-�� � t�^cVCW�P-hOPRV+v WQK+M � P-MOpRX#/ NHo/V+M:T�v Z

� �109� � t�^cVCW�P-hOPRV+v WQK+M � P-MOpRX

� �,2 ��S/K�^cNQM1~Blm^cqOM*�MUl+T�MON�MOV W�^_W�PR\]V

� �139�4~{z{t+MOMUhOMOX ~BWg^_W�MUN

�����������546�"!#���$��%7�8�:96�8�<;=��>?��@* A�B

� �R� �%�yMOV+M:Tg^_W�PRV+v9~{z{t+MOMOhUMOX ~BWg^_W�MON

� � � ��ikMUW�MOqUWQPR\]V�\]ne~{z{t+MOMOhUPRV+v

� �,+ �4~{z{t+MOMUhOPRV+v7��P-WQK`^cV��2l+W�P-q#^cp � P Y MUT | MOX+PRt+b

� �.-���S/K�^cNQM | M#^cNQtuT�MOb MOV WQN

� �109� � P Y MUTa�2l+W�P-q�� Z T�\]NQqO\cl M

� �,2 � | M#^cNQtuT�MOb MOV WHS/P-qUW�tuT�M

� �139� � t�^cXuT�^_W�tuT�M ~{MUpRMOqUWQPR\]V

�����������CAED����FG�IHJG���$LKM����N8�����$�O@�P�RQ S�T

+ �R� � � P Y MUT�N

+ � � � � P Y MUT � \]V+p-PRV+M#^_TQP-W�P-MON

+ �,+ �4~{MUW�tul`WQ\ X+MUW�M:T�bfPRV+MVU?WYX[Z��c^cp-t+Mj\]ne^ x Y MUTHN�^cb l�p-M

Page 5: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

+ �.-�� � \]V+pRP-V+M#^_Ta�aNQqOP-pRpR^_W�\cT o/z{t�^_WQPR\]V�N�\]p-�CMOX�t+NQPRV+vfSeM:TQW�tuT Y ^_W�P-\]V

+ �109� � \]V+pRP-V+M#^_THSe\]pR^_T�PRhO^_W�PR\]V

+ �,2 ��o/p-MOqUWQT�P-q1~{t+N�qOMUl+W�P Y PRpRPFW Z

+ �139��iaT�P-�CMOV��D^#�CM o/zBt�^_W�PR\]V

+ � � ��ikP-T�MOq:W | M#^cNQtuTQMObfMOVCW2o �ul@M:T�PRbfMUV W

�����������JT � ���O* ������E�����5��Q"* ���� � �'* �F9 � ���

-��R� � *HMON�M#^_T�qgK�S4T�\]vcTQMONQN

-�� � �4~{MObfP-qOp ^cNQN�PRq#^cp�JLK+MO\cT Z

-��,+ �4~ Z N�WQMObdiyMUNQPRv]V

-��.-��4~ Z N�WQMOb ~{MOV+NQP-WQP-�uPFW Z

-��109�4r ^cp-qOt+p ^_WQPR\]V�\]n"SeM#^ � Se\���MUT

-��,2 �EJ K+PFT�X ,k^_TQbf\]V+PRqjr�\]V �CMUTQNQPR\]V

-��139���kPRNQP Y PRp-P-W Z [ PRbfPFW

-�� � �4~ Z N�WQMOb ~{MOV+NQP-WQP-�uPFW Z ^cV+X`rL\]bslm^_T�PRNQ\]V3�HPFW�K �yV+\��HV��/^cpRt+MUN

�����������5S � ���O* ������E�����J�� KM����N��8���$��G�P�RQ 4

09�R� ��o'�{l@MUT�P-bfMOVCW

09� � � *HMON�t+p-W�N

09�,+ �4rL\]V+qUpRt+NQP-\]V+N

�5���?�'����� ������� �)���� N�����* �OA

� �� ����'��� �'* ��

Page 6: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

�V@�� ��� �

JLK+M \ Y �}MOqUWy\]neW�K+PRNabf^cN�W�MUT�N2WQK+MONQPRNaP-N2W�\9l+T�MONQMUV Wj^cV ^_l+l+T�\C^cqgK WQ\ WQK+M1l+Tg^cqUW�P-q#^cpv]MOV+M:Tg^_W�PR\]V \]nkNQzBt+MOMOhOMOX*N�Wg^_WQMON9\]ny^cV*\cl+WQPRq#^cp x�MOpRX.� JLK+M�t+V+X+MUT�p Z PRV+vD\ Y �}MOqUW�PF�CM`W�K�^_WX+MU�CMUpR\cl@MUXsP-V W�\aW�K+P-N"l+T�MONQMUV W'��\cT � ��^cN�^kiaTg^_l MUT [ ^ Y PRV+PFW�P ^_WQP-�CM4WQ\yP-V �CMUN�W�PRvC^_WQM�v]t+PRX�^cV+qOMX+MU�{PRqOMUNsW�K�^_W"��MUT�M�q#^_lm^ Y pRM�\]nH\cl@M:Tg^_W�PRV+v ^_W NQt Y z{t�^cVCW�t+b pRPRb P-W�N���JLK+M�T�MUNQM#^_T�qgK �L^cNWg^_TQv]MUW�MOX ^_WeP-V �CMON}W�PRvC^_W�P-\]V \]n+W�K+M�z{t�^cVCW�t+b�bfMUq6K�^cV+P-q#^cp{l�K+MOV+\]b MOV+\]V \]nmN�z{t+MOMOhUMOX N�W�^_W�MON\]n�^cV MOpRMOq:WQT�\]b9^cv]V+MUWQPRq2x�MOp-X�^cV+X�bf\cT�MaX+PFT�MOqUW�p Z ^_W X+MObf\]V+N�W�Tg^_W�PRV+v p-PRV+M���PRXuWQK�T�MUX+t+qUW�PR\]V\]n�^ N�MObfPRqU\]V+X+t+qUW�\cT�pR^cNQMUT�W�KuTQ\]t+v]K9v]MOV+MUTg^_W�P-\]V9\]n>NQz{t+MUMOhOMOX�N�Wg^_W�MUN�\]n@W�K+M2pR^cNQMUT / N�\cl+W�PRqO^cpx�MOp-X.�

�2�CMUT�W�K+MLqO\]tuT�N�M�\]n�W�K+MLT�MONQM#^_TQq6K W�K+MLv]\C^cpRNe\]n�W�K+MLl+T�\��}MOqUWEqgK�^cV+v]MOX.�EJ K+M NQz{t+MUMOh�0P-V+v2M��ul MUT�P-bfMOVCW �L^cN�MU�CMOVCW�t�^cpRp Z XuT�\cl+l MOX��HK+MUV P-W �L^cN"pRMO^_T�V+MOX K+\�� vcTQM#^_We^�TQMOz{t+PFT�MObfMOVCWPFW5��\]t+pRX Y M9PRV5T�MON�M#^_T�qgK5W�PRbfMf^cV+X5MOz{t+PFl�bfMOVCW nwt+V+X+N��8J K+P-N1NQK+\]t+p-X N�WQPRpRp�T�MObf^cPRVD^cN ^nwtuW�tuTQMHv]\C^cp Y MUq#^ct+NQMHW�K+M PRN�NQt+MON/\]nz{t�^cVCW�t+b \cl+W�PRqON ��PRpRp Y MOqO\]bfM bf\cT�MLP-b l@\cTQW�^cV W�P-V W�K+MW�MUq6K+V+\]p-\]v]PRq#^cp�^cXu�_^cV+qOMON�\]n!W�K+MyqO\]bfPRV+v Z M#^_T�N��

~{zBt+MOMOhOP-V+v�TQMOz{t+PFT�MON9V+\]V+pRP-V+M#^_T�\cl+W�PRqO^cp�l+T�\BqOMONQNQMUN�� JLK+MUT�MUnw\cT�M WQK+MUT�M8PRN ^5V+MOMOXW�\Dt+V+X+MUTQN�Wg^cV+X V+\]V+p-PRV+M#^_T�\cl+W�P-qON9PRV x Y M:T�N�� J K+P-N Y MOq#^cbfM`WQK+M8l+TQPRV+qOPFl�pRM8v]\C^cp � JLK+PRNX+\BqOt+bfMOVCWHqU\]V Wg^cP-V+N2^ N�W�t+X Z \]ne^sV+\]V+p-PRV+M#^_T lm^_Tg^cbfMUWQMUT#�+W�K+MkW�K+P-T�X�\cT�X+MUT2N�t+NQqOMUl+W�P Y PRp-P-W Z� U?W X[Z��:�C\]nN�MU�CMUTg^cp+\cl+W�P-q#^cp{x Y MUT�N��EJLK+PRN�X�^_Wg^aq#^cV Y MLt+NQMOXsWQ\jNQtul+l \cTQWEnwtuW�tuT�M ��\cT � \]V W�K+MX+MU�CMUpR\cl�bfMOVCW�\]n>\cl+WQPRq#^cp���NQz{t+MUMOhOMUT�N����5J!\1^_TQT�P-�CMH^_W/W�K+P-N4l \]PRVCW#�Bl+T�MUpRPRb PRV�^_T Z X+MUT�PF�c^_WQPR\]V+N��M:T�M q#^_T�T�PRMOX�\]tuW2\]V�V+\]V+pRPRV+MO^_T2\cl+W�P-q#^cp@l+T�\{qUMONQNQMON��

JLK+M qO\]V WQMOV WQN \]n4WQK+PRNaW�K+MONQP-N ^_TQMs\cT�vC^cV+P-hOMOX PRV�qgKuT�\]V+\]p-\]v]PRq#^cpe\cTQX+MUT�� JLK+M Z T�MUl 0T�MUNQMOVCW ^�NQM:T�PRMON \]n�pR\]v]P-q#^cpeN�W�MUl�N q#^_TQT�P-MOX \]tuW1X+tuTQPRV+v�W�K+M T�MONQMO^_T�qgK+PRV+v�\]n/W�K+MsNQz{t+MUMOhOPRV+vl+T�\BqOMONQN��HJLK+M V+\]V+pRP-V+M#^_T2l+T�\BqOMONQNaP-NHMONQN�MOV WQP ^cp"nw\cTazBt�^cXuTg^_W�tuT�M NQz{t+MOMUhOPRV+v ^cV+X8V+\]V+pRP-V+M#^_Tx Y MUT/T�MUNQM#^_T�qgKfP-N/^ypR\]v]PRqO^cpuN�W�MUlfPRVsWQK+M�X+MU�CMUpR\cl�bfMOVCW4\]n@^jN�z{t+MOMOhUMUT�nw\cT/^yx Y MUT�\cl+W�P-q�v Z T�\\cTy\cW�K+MUTyX+MU�{PRqOM��� V lm^_TQWQPRqOt+pR^_T���MsK Z l \cW�K+MONQP-hOM WQK�^_W ^9K+P-v]K+p Z X+\cl@MUX x Y M:T t+NQMUX ��P-W�KNQ\]tuTQqOMON�^_W�W�K+Mal+T�\cl@M:T ��^��CMOp-MOV+vcW�K �HP-pRpml+T�\ �{PRX+My^1�CMUT Z M � qOP-MOV W bfMUX+PRt+b&nw\cT V+\]V+pRP-V+M#^_Tl+T�\BqOMONQN�MON��6� V�lm^_T�W�PRqOt+pR^_T���M X+MObf\]V+N}WQTg^_W�MkW�K�^_W x Y MUT�N�X+\cl@MOX-�HPFW�K`^ K+M#^�� Z qU\]V+qOMOVCWQTg^ 0W�P-\]V \]n�o4T Y PRt+b P-\]V+N l+T�\��uP-X+M ^�p ^_T�v]MsW�K+P-T�X5\cTQX+MUT NQt+NQqUMUl+W�P Y P-pRPFW Z �HK+MUVDl�t+bsl@MOX Y Z ^N�W�T�\]V+v�N�\]tuT�qOM ^_W��&���.+u���� �� X+t+M W�\ T�MONQ\]V�^cVCWyb t+pFW�P-l�K+\cWQ\]V ^ Y N�\cTQl+W�PR\]V.�jJLK+PRNkNQt+v�0v]MON}W�N�W�K�^_W W�K+MON�Mjx Y M:T�N/��\]t+p-X Y MjM � qUPRMOVCWHl+T�\BX+t+qOMUT�NH\]n"NQz{t+MUMOhOMOX�N�W�^_W�MON��{P ^ W�K+MjWQK+P-T�X\cT�X+M:THl+T�\BqOMONQN�\]n!nw\]tuT 0 �L^��CM bfP �uPRV+v PRV�x Y MUT�N��

Page 7: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����� ���m�� A2�!, ���F�H� �C� <�= �!�>�>?@�>A < �B���C�>�

���8��� � ���@������� ���F���

JLK+M p ^cNQMUTyP-Njt+NQMUX PRV b9^cV Z ^_l+l�pRPRqO^_W�PR\]V+NaW�\BX�^ Z � [ ^cNQMUTQN K�^#�CMsnw\]t+V+X W�K+MOP-T��L^ ZP-V W�\`^cpRp�b9^ �}\cT P-V+X+t+N�WQT�P-MON ^cV+X5^_T�M t+NQMOX5PRV ^cpRbf\]N�W ^cpRp�K+P-v]K W�MOqgK+V+\]pR\]v Z T�MONQMO^_T�qgK�pR^ Y 0\cTg^_WQ\cT�PRMONs^_T�\]t+V+X WQK+M-��\cT�p-X.� JLK+M�qO\]K+M:T�MOVCW9V�^_W�tuT�M�^cV+X N�lm^_W�P ^cp�l�tuTQP-W Z \]n�W�K+M�pR^cNQMUT^_T�MfWQK+M W ��\�l+T�\cl MUTQW�P-MON W�K�^_W b9^ � MfPFW ^cV�PRX+M#^cp/WQ\{\]p/nw\cT qU\]bfb t+V+PRq#^_W�P-\]V+N ^cV+X�NQMOV+NQ\cT^_l+l�p-PRq#^_W�P-\]V+N��

� \yb9^_WQWQMUT$�HK�^_WEW�K+M M���^cq:W/^_l+l�p-PRq#^_WQPR\]V PRNO�B^cpRp+MOp-MOqUWQTQ\�0 \cl+W�P-q�N Z N�W�MOb NEN�t @MUT/n T�\]bV+\]P-NQM#�EJ K+M:T�My^cp �L^ Z N�M��uPRN�WQN�^cV \]tuWQl�tuWLNQPRv]V�^cp �HK+P-q6K �_^_T�PRMON�T�^cV+X+\]bfp Z �HPFW�K V+\ T�MOp ^_WQPR\]VW�\ W�K+M�PRVul�tuWfN�PRv]V�^cp � � \]PRN�M�p-PRbfPFW�N X+MUW�MOqUWQPR\]V \]n���M#^ � NQPRv]V�^cp-NsV+\�b9^_WQW�MUT K+\��db t+q6K^cb l�p-P-x�q#^_WQPR\]V WQK+MUT�M`P-N�� �}V bf^cV Z ^_l+l�pRP-q#^_W�PR\]V+NsMU�CMOV W�K+M�NQpRP-v]K W�MUN�W9V+\]PRN�M`NQPRv]V�^cp-N q#^cVNQM:�CMUT�MOp Z X+MOvcTg^cX+MaW�K+MaN Z N�W�MOb / N/l MUT�nw\cT�b9^cV+qUM#�'� n>W�K+MaNQP-v]V�^cp l@\���MUTLP-N�pRMON�N�W�K�^cV>�u\cTLMU�CMOV^_l+l+T�\C^cqgK+P-V+v+�{W�K+M2V+\]P-NQMapRMU�CMUpP-VfW�K+MabfM#^cNQtuTQMObfMOVCW Y ^cV+X ��PRXuW�K>�uWQK+M2bfM#^cNQtuTQMObfMOVCW�N6��PRp-pK�^#�CM pR^_T�v]MkMUTQT�\cT�N�� � \]PRN�MyT�MUX+t+qUW�PR\]V�PRNLW�K+MUT�MOnw\cTQM1^sqU\]V+N�Wg^cVCW2b9^_WQWQMUT \]n!T�MONQMO^_T�qgK.�

� \]P-NQM�qO^cV v]MOV+MUTg^cp-p ZDY M Y T�\ � MOV X+\��HV P-V WQ\ NQMU�CMUT�^cp W Z l MONO��P-V+qOpRt+X+P-V+v�W�K+MUT�bf^cp� ^cp-NQ\ q#^cp-pRMOX �]\]K+V+NQ\]V ��V+\]P-NQMD^cV+X NQK+\cW � ^cpRNQ\ q#^cp-pRMOX zBt�^cV WQt+b ��V+\]P-NQM#� �2W�K+MUT`V+\]PRNQMNQ\]tuTQqOMON M��+P-N�W Y tuW9qO^cV Y M`WQTg^cqOMUX WQ\D^ q#^ct+NQM`T�\B\cW�MOX PRV NQ\]b MUW�K+PRV+v�\cW�K+MUT9W�K�^cV nwt+V90X�^cbfMUV Wg^cp@l�K Z N�PRqON����kV+p Z WQK+MUT�b9^cp�^cV+X�NQK+\cW2V+\]P-NQM ��PRp-p Y MyqO\]V+NQPRX+M:T�MOX�K+MUT�M��

JLK+MUT�bf^cp/V+\]PRN�M9PRN v]MOV+MUT�^_W�MOX�PRV�^cV Z T�MONQP-N�W�P-�CM MOp-MObfMOVCW PRV�^`N Z N�W�MOb �)*2^cV+X+\]bbf\cWQPR\]V \]n�n T�MOMsq6K�^_TQv]MON��P-W�K+P-V�W�K+M MUpRMObfMUV W ^_T�M qO^ct+NQMOX Y Z W�K+M:T�b9^cp�^cv]P-W�^_W�PR\]V>��K+MOV+qOMW�K+MaV�^cb M#��J K+MaTg^cV+X+\]b V�^_W�tuT�Ma\]n>W�K+PRN/bf\cW�PR\]VsT�MONQt+pFW�NLPRV ^���t+qUW�t�^_W�P-V+v �C\]p-Wg^cv]MH^cqUT�\]NQNW�K+MyMOp-MObfMOVCW��

I�TQMOp ^_W�P-\]V+NQK+P-l8nw\cTHW�K+MUT�b9^cp�V+\]PRN�M q#^cV Y M X+MUTQP-�CMOX ^cN2nw\]p-pR\��HN���S/pR^cV+q � / N2pR^�� nw\cTY pR^cq �BY \BX Z T�^cX+P ^_W�P-\]V�z{t�^cVCW�P-hOMOX�W�K+M Tg^cX+P ^_WQPR\]V x�MUpRX Y Z ^cNQN�t+bfPRV+v�l@MUT�b P-WQW�MUX�MOV+MUTQv]PRMON\]n�W�K+M9nw\cTQb�� � ������� �

��� ��K+MUT�M � PRN1^8V+\]V+V+MUvC^_W�P-�CMfP-V WQMOv]MUT�� � n�W�K+Mf�_^_T�PR^ Y pRM �P-N�P-V W�M:TQl+T�MUW�MUX�^cNH^ z{t�^cVCWg^ \]n�lm^_TQW�P-qOpRMUN � l�K+\cWQ\]V+N�\cT�MOpRMUqUWQT�\]V+N ��l@M:T2bf\BX+My\]n�Tg^cX+P ^_WQPR\]V��P-W�K�n T�MOzBt+MOV+q Z�� W�K+MOV�WQK+Myl+T�\ Y ^ Y P-pRPFW Z W�K�^_W � l�K+\cWQ\]V+N2^_T�MyM��+qUP-W�MOX�PRV�^ bf\{X+MkP-N

� � � � ��� ��� � � ����� !�"$# ��� � �� � ���� %

&

Page 8: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��K+MUT�M W�K+M VBt+b MUTg^_W�\cT qO\]VCWg^cPRV+N � \]p-W�hUb9^cV+V#/ N1n ^cq:W�\cTs^cV+X W�K+M�X+MOV+\]bfP-V�^_W�\cT PRN ^8v]MO\�0bfM:WQT�PRqO^cp>NQMUT�P-MON���K+PRqgK�T�MUX+t+qOMONHW�\

�� � ��� ��� � � ���� %

NQ\ � � � � � � � � � � � � ������ ��� � � � � ���� �

JLK+M1^#�CMUTg^cv]Mk�c^cp-t+Mjnw\cT � �+v]P-�CMOV � � � �:�+PRN

� � !�"$# � � � � � %^cV+X�WQKBt+N W�K+M ^#�CMUTg^cv]MjVBt+b Y MUTH\]n�lm^_TQW�PRqUpRMON PRV�^sbf\BX+MjP-N

� �

� � � � ���� � ��

JLK+PRNLPRN � V+\���V�^cN�W�K+MkS4p ^cV+q � X+PRN}WQT�P Y tuWQPR\]V�^cV+X�^cp-NQ\ ^cN�WQK+M � \]NQM�0 o/P-V+N�W�MOP-V�n ^cqUWQ\cT��EJ K+M^#�CMUTg^cv]MyMOV+MUT�v Z l@M:THbf\BX+MjP-N

� � � � � � �� � � ��� �

��� � � ���� � �� �

��� �JLK+MUT�b9^cp@l \���MUT2nw\cT2^ Tg^cX+PR^_W�PR\]V�bf\{X+Mk\]n Y ^cV+X ��PRXuWQK��8PRNLW�K+MOV

� � � ��� �

��� � � ���� � �� �

� � �� V�WQK+M pR\�� n T�MOzBt+MOV+q Z pRP-bfP-W � � �� ��� �6�

��������������� ��� � �JLK+MUT�b9^cp/V+\]PRNQM9l@\���MUTsPRN bf\]N}W PRb l \cTQWg^cVCW ^_W pR\�� q#^_TQT�P-MUT n T�MOzBt+MOV+qOPRMUN � �� � �"!�#%$'& �Y MOq#^ct+NQM � P-NHpR^_T�v]M#��ILWHp-\�� n T�MOzBt+MOV+qOP-MONy^_l+l+T�\cl+T�P ^_WQM qO\B\]pRPRV+vsq#^cV�pRP-bfP-WLW�K+M V+\]PRNQM#� � \cT\cl+W�P-q#^cp�N Z N}W�MObfN�W�K+MHqO^_TQT�PRM:T�n T�MOzBt+MOV+qOP-MONL^_T�MHP-VsW�K+M W�MUTg^cK+M:TQW�hc� W�K+M�W�K+M:T�b9^cp�V+\]PRNQM l@\���MUTK�^cN�XuT�\cl+l MOX�\# ��I W/W�K+MONQMan T�MUz{t+MOV+qOP-MON�W�K+\]t+v]K>��^1V+M�� V+\]PRNQMaMOVCW�MUTQN�^cN/NQK+\���V�PRVfx�v]tuT�M� �

JLK+PRN V+M��&V+\]P-NQMfPRNjW�K+MfNQMOqU\]V+X�W Z l Mc�"zBt�^cV W�t+b V+\]PRNQM#��JLK+PRN V+\]PRN�Mfb9^ Z Y MfX+M�0NQq:T�P Y MOX�^cN�T�MONQt+pFW�PRV+v n T�\]b WQK+M vcT�\]t+V+X8N�Wg^_W�M qO\]VCWQT�P Y tuW�PR\]V8P-V`W�K+M z{t�^cVCW�PRhUMOX MUV+MUT�v Z \]nW�K+M�T�^cX+P ^_W�P-\]V bf\{X+M#�!J K+MLM��uPRN�WQMOV+qOM�\]n�z{t�^cVCW�t+b�V+\]P-NQM�PRN"T�MUp ^_W�MOX W�\2WQK+M�l+T�\{qOMUNQNe\]n�pRPRv]KCW(

Page 9: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

������������ ��������������������

X+MUWQMOqUW�P-\]V.����K+MOV9l�K+\cW�\]V+N�N}WQT�P � M2^ X+MUW�MOq:W�\cT�MOp-MOqUWQT�\]V+NL^_TQMHn T�MOMUX � \cTL^cN/P-V9NQMObfP-qO\]V+X+t+q�0W�\cTQNO�CMOpRMOq:WQT�\]V90 K+\]p-M lm^cPFT�N4^_T�MLqUT�M#^_W�MUX � Y Z W�K+M�l�K+\cW�\{MOp-MOqUWQTQPRq M� @MOq:W��"� K+MUV9^yqU\]V W�P-VBt+\]t+NN�W�T�M#^cb \]nEMOpRMOq:WQT�\]V+NkPRNal+T�\BX+t+qOMOX5^cV+X nw\cT�qOMOX W�\ bf\��CM1W�K+MUT�M �HP-pRp Y M ^9T�^cV+X+\]bfV+MONQNyPRVW�K+MjqO\]b Y PRV+MOX�qOtuTQT�MOVCW��/J K+P-NHX+MUW�MUqUW�\cT2qUtuTQT�MOVCWaPRNLW�K t+NH�_^_T�PRMOX YBZ V+\]PRN�M � t+NQt�^cp-p Z q#^cp-pRMOXNQK+\cW�V+\]PRN�M ���

� t�^cVCW�t+b V+\]PRNQM9Wg^ � MON W�K+M nw\cT�b \]n NQK+\cWsV+\]PRNQM P-V�l�K+\cW�\BX+MUW�MOq:W�\cT�N Y tuW PRN t+p-W�P 0b9^_WQMOp Z X+MUW�MUT�b PRV+MOX YBZ W�K+M bfM#^cN�tuT�PRV+v9l+T�\BqOMONQN��5� V \cW�K+MUT���\cT�X+NkW�K+MUT�M PRNy^cV PRV+K+MUT�MUV Wt+V+qOM:TQWg^cPRVCW Z PRV8^cV Z b M#^cNQtuT�MOb MOV W2\]V8^fz{t�^cVCW�PRhOMUX8x�MUpRX8PRV�zBt�^cV W�t+b bfMOqgK�^cV+PRqUN��aJLK+PRNP-N ��K Z W�K+MjV+\]PRNQMjPRN q#^cpRp-MOX�zBt�^cV WQt+b V+\]P-NQM#�

~{K+\cWLV+\]P-NQMkPRNLX+MUT�PF�CMOX�n T�\]b&W�K+M2l�K+\cW�\BqOtuTQT�MOVCW#���Q�u\]n�^1l�K+\cW�\{X+M:W�MOqUW�\cT q#^ct+N�MOX Y Z^ pRPRv]KCW�NQPRv]V�^cp �4JLK+M V+\]P-NQM K�^cN�^cV�T�b NL�_^cpRt+M � N�Wg^cV+X�^_TQX�X+MU�{P ^_W�P-\]V �

� � "! � � ��� �JLK+Msb M#^cV�NQzBt�^_T�M �c^cp-t+Ms\]nEW�K+Msl�K+\cW�\BqOtuTQT�MUV W ��t+qUW�t�^_W�P-\]V�PRNkl+T�\cl \cTQW�PR\]V�^cp"WQ\�W�K+M ijrqO\]bsl@\]V+MOVCW \]nyWQK+M�qOtuTQT�MOVCW#�HWQK+M�q6K�^_TQv]M \]nj^cV MOpRMUqUWQT�\]V>�H^cV+X WQK+M Y ^cV+X ��PRXuWQK�\]nkW�K+M

#

Page 10: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

qOtuT�T�MOVCW��%� V�W�M:T�bfNL\]n"V+\]PRN�Myl \���M:T

� � � � ��� � � # � � � �%��K+MUT�M

� l�K+\cW�\{qOtuT�T�MOVCW

� � �,2�� � ��� !�yqU\]t+pR\]b Y N � MOpRMOq:WQT�\]V`qgK�^_T�v]M �� Y ^cV+X �HP-XuW�K`\��CMUT���K+PRqgK���t+q:W�t�^_W�PR\]V+N�\{qOqUtuT��

JLK+MUT�M8P-N ^DX+P @MUTQMOV+qOM Y MUW ��MOMUV�W�K+M�N�W�^_W�PRN�WQPRqON9\]naW�K+M�l�K+\cW�\]V+N9W�K�^_W N�W�T�P � M8^cV\cl+W�P-q#^cpLX+MUW�MOq:W�\cT ^cV+X W�K+M�N�Wg^_W�P-N�W�PRqUNs\]nHWQK+M`MOpRMUqUWQT�\]V+N W�K�^_W W�K+M�X+MUW�MOq:W�\cT9MObfPFW�N�� J K+MbfMO^cV`^cV+X�N}Wg^cV+X�^_T�X`X+MU�{P ^_W�P-\]V�\]n�W�K+M X+P-N�WQT�P Y tuW�PR\]V�\]n�l�K+\cW�\]V+NH^_T�M

�� � � � � ! � ������ � �� � � � � ! � � ������ %NQ\ W�K+M N�PRv]V�^cp>W�\ V+\]PRNQMyTg^_W�PR\ PRN M��{l+T�MONQNQMUX8^cN

� ���� � � � � ! � � #������ #!������ � ������ �

� \cTHMUpRMOqUW�T�\]V+NO�

� � ��� � � � ! � � ������ � ��� � � � � � ! � � � ������ %NQ\ W�K+M N�PRv]V�^cp>W�\ V+\]PRNQMyTg^_W�PR\ PRN M��{l+T�MONQNQMUX8^cN

� !� � � ��� � � � ! � � ������ �

JLKBt+N�W�K+M�X+P MUT�MOV+qUM Y MUW ��MUMOV \cl+W�PRq#^cp ^cV+X MOp-MOqUWQTQPRq#^cp N�Wg^_W�P-N�W�P-qON�P-N�W�K+M/z{t�^cVCW�t+b M � qOP-MOV+q Zn ^cqUWQ\cT � �$� WLPRN�V+\cW�MOX W�K�^_WLP-n�WQK+Mkl�K+\cWQ\]V+NL^_T�MkSe\]PRNQNQ\]V X+P-N�WQT�P Y tuW�MOX W�K+MkMOpRMOq:WQT�\]V+N ^_T�Mk^cN��MUpRp �4JLK+MjbfMO^cV��_^cpRt+Mc��K+\���MU�CMUT#�mnw\cT W�K+M MOp-MOqUWQTQ\]V`X+PRN�W�T�P Y tuW�P-\]V�P-N T�MUX+t+qOMOX.�

JLK+M�l�K+\cW�\BqOtuTQT�MOVCW ��t+qUW�t�^_WQPR\]V+N�^_T�M�q#^ct+N�MOX Y Z WQK+M�l�K+\cW�\{qOtuT�T�MOVCW�P-W�NQMUpRn � � V \cW�K+MUT��\cTQX+N WQK+M9z{t�^cVCW�t+b V+\]PRNQM9l+T�\BX+t+qOMOX YBZ ^`l�K+\cW�\BX+MUW�MOq:W�\cT PRN ^`l+T�\cl@M:TQW Z \]n WQK+M9pRPRv]KCWx�MOp-X WQK�^_WkP-WkX+MUW�MUqUW�N�� ~{K+\cWyV+\]PRNQM PRN2TQMOp ^_W�MUX W�\fWQK+M T�^cV+X+\]bfV+MONQNk\]n�l�K+\cW�\]V+Ny^cV+X W�K+MUP-T^cNQN�\{qOPR^_W�MOX`qO\]t+VCW�P-V+vfN�Wg^_W�P-N�W�P-qON��/IaV Z pRPRv]KCW x�MOpRX`qO^cV Y Mjq6K�^_T�^cqUW�MUT�P-hOMOX Y Z PFW�NH\���V���t+q�0W�t�^_WQPR\]V+N�� � � �� qU\]t+V W�P-V+v9N�Wg^_W�P-N�W�P-qON���JLK+M ��t+q:W�t�^_W�PR\]V+NHPRV�qU\]K+MUT�MOVCWaNQ\]tuT�qUMON � p ^cN�MUT�NO��MUW�q�� �^_T�MsNQb9^cp-pRMUTkW�K�^cV�WQK+MUT�b9^cp�V+\]PRN�M NQ\]tuT�qUMON�� JLKBt+N1zBt�^cV WQt+b ��t+qUWQt�^_W�PR\]V+N ^_TQMsW�K+MspR\���MUTp-PRbfPFWL\]n!V+\]PRN�M PRV�^cV Z N Z N�W�MOb �/JLK+Mj\]V+p Z �L^ Z W�\ T�MOX+t+qOMjW�K+MjzBt�^cV WQt+b V+\]P-NQMjP-N�W�\

� ��t+V+X+MUT�N�Wg^cV+X�V+\]P-NQMyN�Wg^_W�P-N�W�PRqUN�\]n"p-PRv]KCW#��^cV+X"

Page 11: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� � x�V+X1^ ��^ Z W�\�b9^cV+P-l�t+pR^_W�MepRP-v]K W�x�MOp-Xjl+T�\cl MUTQW�P-MON�N�\�W�K+MEpRM#^cN}W�V+\]P-NQM4TQMONQt+p-WQN��

JLK+PRN��{PRM�� l@\]P-V W ��PRp-p@t+p-WQPRb9^_W�MUp Z pRM#^cX W�\ W�K+MkpRP-v]K W�x�MOp-X�\]n�NQzBt+MOMOhOMOX�N�Wg^_W�MUN��EJ K+Mt+NQMj\]n!NQzBt+MOMOhOMUX�N�Wg^_W�MON �HP-pRp@T�MUX+t+qOM W�K+Myz{t�^cVCW�t+b V+\]PRNQMjPRV�MUpRMOqUW�T�\�0 \cl+W�P-qjN Z N�W�MUbfN��

���F4 � � ��9����C;=����N8� �#��)����* ���8�&*

JLK+M zBt�^cV WQt+b V�^_W�tuTQMj\]n"p-PRv]KCW�TQMON�l@\]V+N�P Y pRM nw\cTHzBt�^cV W�t+b V+\]PRN�M Y MUqO\]bfMON t+V+X+MUT 0N�W�^cV+X�^ Y pRM Y Z qO\]V+X+t+qUW�P-V+v l�K+\cWQ\]V qO\]t+VCW�P-V+v M��ul@M:T�PRbfMUV W�N�� � \cT \]tuT l�tuT�l@\]NQMON ��M&��PRp-pp-\{\ � ^_W9W�K+M qO\]t+VCW�PRV+v�N�Wg^_WQPRN�W�P-qON \]nyW ��\DW Z l MON�\]nypRP-v]K WO�HpRP-v]K W n TQ\]b WQK+MUT�b9^cp2N�\]tuT�qOMON� P-V+qO\]K+MUT�MUV W � ^cV+X`pRP-v]K W n T�\]b ^ l MUT�nwMOq:W2p ^cN�MUT � qU\]K+MUT�MOVCW ���

JLK+M l�K+\cW�\]V�qO\]t+V WQPRV+v�M��{l@MUT�P-bfMOVCW��PRp-pEt+N�M W�K+MONQMsW ��\�NQ\]tuT�qOMON1^cV+X5X+MUW�MUT�b PRV+MW�K+M l+T�\ Y ^ Y PRp-P-W Z X+PRN�WQTQP Y tuW�P-\]Vfnwt+V+qUW�P-\]V+N�\]n W�K+MOPFT�p-PRv]KCW��EJ K+P-N/pRP-v]K W'��PRpRp Y M2X+MUW�MOq:W�MOX&��P-W�K^9l�K+\cW�\{X+P-\{X+M���P-W�K8t+V+P-WyzBt�^cV W�t+b M � qOPRMUV+q Z �1JLK+M l�K+\cWQ\{MOp-MOqUWQT�\]V+NkMOb P-WQW�MUX P-V�^9W�P-bfMP-V W�M:TQ�c^cp�� �HP-pRp Y M qO\]t+VCW�MOX.�kJLK+PRN2M��ul@M:T�PRbfMUV W ��PRp-p Y M1T�MUl M#^_W�MOX8b9^cV Z WQPRbfMONHNQ\fW�K�^_Wk^X+P-N�WQT�P Y tuW�PR\]V qOtuTQ�CM q#^cV Y M Y t+P-p-Wjtul �sJLK+PRNyqOtuTQ�CM ��PRpRp"WQMOpRpeK+\�� b9^cV Z W�PRbfMUNk^�qOMUT�Wg^cPRVl�K+\cW�\]V V t+b Y MUT � � � �L^cN9qO\]t+VCW�MOX.� r ^cp-p WQK+PRNf�_^cpRt+M � � � ��� � n M��ul@M:T�PRbfMUV W�N1��MUT�MqO\]V+X+t+q:W�MOX>� � � � � �� � ����� � � � � � ���K+MOV l@M:T�nw\cT�bfP-V+v�W�K+M qU\]t+V W�P-V+v�M��ul MUT�P-bfMOVCW ��P-W�K ^�W�K+MUT�bf^cpEN�\]tuT�qOMf\]n/T�^cX+P ^_W�P-\]V ��Mq#^cV1l+TQ\{qOMOMUX5�HPFW�K W�K+M�NQ^cbfM�^_T�v]t+b MOV WQN!t+NQMOX P-V1S/pR^cV+q � / N Y p ^cq �{Y \{X Z Tg^cX+P ^_W�P-\]V ^cV�^cp Z NQPRN��

� ML^cX+XuT�MONQN�PRV+qU\]K+MUT�MOVCWEpRPRv]KCW"x+T�N}W�(�r�\]V+NQPRX+MUT4^2qO\]p-t+bfV \]n+Tg^cX+P ^_WQPR\]V \]n�pRMOV+vcWQK��� \cT�T�^cX+P ^_W�P-\]V�W�K�^_W l+T�\clm^cvC^_W�MUNHPRV�^ �_^cqOt+t+b� �����4Iap-p�l�K+\cWQ\]V+NHPRV�W�K+PRN qO\]p-t+bfV-��PRp-pT�MO^cq6K W�K+MaX+MUWQMOqUW�\cTLP-V WQK+MyqU\]t+V W�P-V+v PRVCW�MUTQ�_^cp �EJLK+Mkl+TQ\ Y ^ Y PRpRPFW Z \]n>x�V+X+PRV+v � l�K+\cW�\]V+NLPRV\]V+MyTg^cX+P ^_W�P-\]V�b \{X+MkPRV�WQK+PRN qO\]pRt+bfV�PRN� � � � � � � � � ��� � ���� � ��� ��� � � ���� �

JLK+M ^#�CMUTg^cv]M MOV+M:T�v Z \]n"W�K+M1x�MUpRX8PRNHTQMOp ^_W�MUX`W�\fW�K+M ^#�CMUTg^cv]M l�K+\cWQ\]V qU\]t+V W � Y Z� � � � � � TQ\]bdWQK+Myl+T�M:�uPR\]t+N�NQMOqUWQPR\]V�PFW���^cN�NQK+\���V`W�K�^_W� � � � � � �� � � ��� �

��� � � ���� � �� �

��� �� W q#^cV V+\�� Y M�N�^cPRX�W�K�^_W W�K+M�^#�CMUTg^cv]M�V t+b Y MUTs\]n�l�K+\cW�\]V+NsPRV \]V+M�bf\BX+M�\]n W�K+MUT�bf^cpTg^cX+PR^_W�PR\]V�PRN ��� �

��� � � ���� � �

Page 12: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

\cT T�M#^_TQT�^cV+v]MOX

��� � � ���� � � �� �JLK+Mjl+T�\ Y ^ Y P-pRPFW Z qO^cV Y MkT�M�� T�P-W�W�MOV

� � � � � �� � � � �� � � �� � ! � !

� � � � � ! � ! �JLK+PRN PRN W�K+M � \]NQM�0 o/P-V+N�W�MOP-V�l+T�\ Y ^ Y P-pRP-W Z X+P-N�WQT�P Y tuW�PR\]V.�

����������� � ��� ���� �� ���� ��� ����� ��� � � � � ��� �

� \cT W�K+PRN X+PRN�W�T�P Y tuW�P-\]V�W�K+MjN�Wg^_W�P-N�W�P-qON ^_T�M#(

� bfM#^cV � �

� N�Wg^cV+X�^_T�X`X+M:�uP ^_WQPR\]V � � � ��^cV+X

� ~ � * �� � � �

Page 13: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+MUT�bf^cp+NQ\]tuT�qOMON4l+T�\{X+t+qOMHpRPRv]KCW'�HPFW�K � \]NQM�0 o/P-V+N�W�MOP-Vsl�K+\cW�\]VfqU\]t+V W�P-V+v1N�Wg^_WQPRN�W�P-qON^cNaNQK+\���V�PRV�x�v]tuT�M � �yJ K+M l+T�\ Y ^ Y P-pRPFW Z X+PRN�WQTQP Y tuW�P-\]V \]n�l�K+\cW�\]V VBt+b Y MUTyPRNy^9nwt+V+qUW�PR\]V��K+PRqgK�X+MOqUT�M#^cN�MON ��P-WQK�P-V+qUT�M#^cN�PRV+v VBt+b Y M:T#�uT�MOvC^_T�X+p-MONQNL\]n�P-W�N�b M#^cV9�c^cp-t+M#� � \cW�M2W�K�^_W ^cNW�K+Mab M#^cV9VBt+b Y MUTLPRV+qUTQM#^cNQMON � ^#�CMUTg^cv]M2V t+b Y MUTL\]n>l�K+\cW�\]V+N�l MUTLbf\BX+M �EW�K+MaX+P-N�WQT�P Y tuW�PR\]VW�MUV+X+NjW�\��L^_T�X�^�qO\]V+N�W�^cV W NQK�^_l@MsPRV+X+MUl MOV+X+MOVCW \]n/W�K+M bfM#^cV VBt+b Y M:T��sIaNj^�TQMONQt+p-WjW�K+MTg^_WQPR\ \]n!W�K+M N}Wg^cV+X�^_T�X`X+MU�{P ^_W�P-\]V�W�\ W�K+M b M#^cV � �� !� ��W�MUV+X+N�W�\��L^_T�X�^ �c^cp-t+M \]n"t+V+PFW Z �JLK+PRNfP-V+qO\]K+MUT�MUV W p-PRv]KCW&�HP-pRp K�^��CM`^��c^_T Z PRV+v�x�MUpRX ��P-W�K ^ *H^ Z pRMOP-v]K ^cb l�pRPFW�t+X+M�^cV+X ^t+V+P-nw\cT�b l�K�^cNQM#�EJLK+M�P-TQT�^cX+P ^cV+qOML\]n+W�K+M�NQ\]tuT�qUM K�^cN�^aV+MOvC^_WQP-�CM�M��{l@\]V+MOVCW�PR^cpuX+PRN�W�T�P Y tuW�P-\]V.�

JLK+MkpRP-v]K W�N�\]tuT�qOMynw\cT�W�K+MkV+M��uWLqO\]t+VCW�P-V+vsM��{l@MUTQPRbfMOVCWLPRNL^1l�tuT�MyqO\]K+MUTQMOV W NQ\]tuTQqOM#�� VsWQK+MHqOpR^cNQNQPRqO^cpmN�MOV+NQMHW�K+P-N4P-N/^cVsPRX+M#^cp�NQP-V+M��L^#�CM#� � � � � � � � ���e�aV+p-P � MLW�K+M�pR^cN�W4NQ\]tuT�qOM��K+PRqgK K�^cX�^9�c^_T Z PRV+v � *2^ Z pRMUPRv]K ��x�MOp-X W�K+P-Nax�MOpRX PRNaqO\]V+N}Wg^cV WjPRV ^cb l�p-P-W�t+X+M ^cV+X8l�K�^cNQM^cV+X NQ\�P-W9^cp-NQ\ K�^cN9^ qU\]V+N�Wg^cVCW9P-TQT�^cX+P ^cV+qOM#� � \cT W�K+P-NfNQ\]tuT�qUM�W�K+MUT�M�PRNfV+\ qU\cTQT�MOpR^_W�PR\]VY MUW ��MOMOV l�K+\cW�\]V+N��fJLK+Msl+T�\ Y ^ Y P-pRP-W Z \]n�^ l�K+\cW�\]V5^_TQTQP-�uP-V+v�K�^cNjV+\`PRV ��t+MUV+qOMfn T�\]b W�K+MN Z N�W�MOb / N2lm^cN�W�� ,aMUT�M W�K+M qO\]t+VCW�PRV+v�N�Wg^_W�P-N�W�P-qONk^_T�M nw\]t+V+X Y Z M���^cb PRV+PRV+v ��K�^_WkK�^_l+l@MOV+N��K+MOV�W�K+MjPRVCW�MUTQ�_^cp ��PRN PRV+q:T�M#^cNQMOX Y Z�� ���

JLK+Mjl+TQ\ Y ^ Y PRpRPFW Z \]n � � �jl�K+\cW�\]V+NH^_TQT�P-�{PRV+v PRV�W�K+M P-V W�M:TQ�c^cp � ��� ��P-N

� � � � �%� ��� � � � � � %

� � � � �% �� � � � � � � �

%� � � � �

% �� �%��K+MUT�M � � �

% �� �% � � �

% �� � ^_T�M PRV+X+MUl MOV+X+MOVCW \]n � � � %

� ���5�}n � � ��� �% �� � ��^cN � ��� �

W�K+MUV � � �% �� � � � � � �

% �� �%��K+MUT�M � � �

% �� � � � ���� � � � %JLK+PRN PRN W�K+M9l+T�\ Y ^ Y P-pRP-W Z \]nLx�V+X+PRV+v \]V+M9l�K+\cW�\]V.� � PRN W�K+M�NQ\]tuT�qOM�PRVCW�MOV+NQPFW Z ��K+PRqgK PRN

qO\]V+N}Wg^cV W�^cV+X� PRN�WQK+MyV t+b Y MUTL\]n>l�K+\cW�\]V+N � ���� ���4JLK+M2W�\cl T�MOpR^_W�PR\]V P-N ��\cT � MOX \]tuWt+NQP-V+v W�K+Mynw\]pRp-\���PRV+vsNQt Y N�W�PFW�tuW�PR\]V+N��

� � � � �%� � � � � � � � %

� �� � � � � � � � �%� ���F� � � ���� � � � �

%� ��� � � � � � � %

� �� � � � � � � � �%� � � � � ��� �

%� �� � � ��� � � � �

%� ��� � � � � � � � �

%� � �� � � � %

� � � � � � � �%� ���� � �

� � � ��� �%� � �� � � � %

� � � � � � � �%� ���� � �

�� � � � � � � � �� � � � � � � � � � � ������

Page 14: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

I X+P @M:T�MOVCW�P ^cp�MOzBt�^_W�PR\]V�q#^cV Y Mynw\cT�bfMUX.�

�� � � � � � � � � � � � � � � � � � � � �

JLK+M Y \]t+V+X�^_T Z qO\]V+X+P-W�P-\]V+Nfnw\cT9W�K+P-NfMOz{t�^_WQPR\]V ^_T�M � � � � � � NQ\ � � � � � � � � ^cV+X� � � � � � �� � � � � ��K+MUT�M � � PRN2W�K+M ^#�CMUTg^cv]M V t+b Y MUTk\]nel�K+\cW�\]V+NkP-V`W�PRbfM ���2J K+MNQ\]p-tuW�PR\]V�PRN � � � � � � � � � � � �NQ\ � � � � �� � � � � � � ���!

� � � � � � � � � � � #��� � ���! �

� \cT2^cV Z�� � � � � � � !��� � ���! �JLK+PRN�PRN�W�K+M/Se\]P-NQNQ\]V l+T�\ Y ^ Y P-pRPFW Z X+P-N�WQT�P Y tuW�PR\]V>�_^cN!PRN�NQK+\��HV1P-V x�v]tuT�M + �eJ K+P-N!X+P-N�WQT�P Y tuW�PR\]VN�W�^_W�MON�WQK�^_W�W�K+MEl+T�\ Y ^ Y PRp-P-W Z \]n{x�V+X+PRV+v � l�K+\cW�\]V+N!nw\cT!NQb9^cp-p]PRVCW�MUTQ�_^cpRN � W�K+MUT�MUnw\cT�M/NQbf^cpRp � ���PRp-puX+MOqUT�MO^cNQM���P-W�K � � ,a\���MU�CMUTO�Bnw\cTEp ^_TQv]MLWQPRbfM�P-V W�M:TQ�c^cp-N � W�K t+N4pR^_T�v]M�� �!W�K+M l+TQ\ Y ^ Y PRpRPFW ZX+P-N�WQT�P Y tuW�PR\]V K�^cN ^ b9^ �+P-b t+b V+M#^_T�� ��^cV+X W�K+MsqUtuTQ�CM Y MOK�^#�CMON b t+qgK�p-P � Ms^ �y^ct+NQNQP ^cVX+P-N�WQT�P Y tuW�PR\]V.�

� \cT W�K+PRN X+PRN�W�T�P Y tuW�P-\]V�W�K+MjN�Wg^_W�P-N�W�P-qON ^_T�M#(

� bfM#^cV � �

� N�Wg^cV+X�^_T�X`X+M:�uP ^_WQPR\]V � �m^cV+X

� ~ � * � �� \cT�W�K+MkSe\]P-NQNQ\]V X+PRN�W�T�P Y tuW�P-\]V�WQK+MaN�Wg^cV+X�^_T�X�X+MU�uPR^_W�PR\]V P-N�W�K+MaNQz{t�^_TQMkTQ\{\cW�\]n�W�K+M

bfMO^cV.�

� M qO\]b lm^_T�M1W�K+M1W ��\ NQ\]tuTQqOMON�/>qO\]t+VCW�P-V+v�N�W�^_W�PRN�WQPRqON Y Z qO\]b lm^_TQPRV+vfW�K+MOPFTkNQPRv]V�^cp 0W�\�0 V+\]PRNQM2T�^_W�PR\]N�\cT/W�K+MOP-TLV+\]P-NQM�0'W�\�0 NQP-v]V�^cp Tg^_W�P-\]N�^cN�PRV9x�v]tuT�M -��EJLK+MaN�Wg^cV+X�^_T�X�X+MU�{P ^_W�P-\]V>���K+PRqgK W�MOpRp-N"W�K+ML^#�CMUTg^cv]ML^cbf\]t+VCW�\]n ��t+qUW�t�^_W�P-\]VsP-V WQK+M N�PRv]V�^cp'�]P-NeNQb9^cp-pRMUTenw\cTeWQK+M Se\]P-NQNQ\]VX+P-N�WQT�P Y tuW�PR\]V7��P-WQK W�K+MHNQ^cbfM � �EJLKBt+N�^ qO\]K+MUT�MUV WLp-PRv]KCW/NQ\]tuTQqOMHl+T�\��uP-X+MON�^ Y MUWQW�MUT/NQPRv]V�^cp 0W�\�0 V+\]PRNQM Tg^_W�P-\�WQK�^cV ^cV�P-V+qO\]K+MUT�MUV W NQ\]tuT�qOM#�sJLK+PRNyX+P @M:T�MOV+qOMsPRNypRMONQN ^_WypR\�� pRPRv]KCWypRMU�CMUpRN^cV+X`vcTQM#^_W�MUTH^_WHK+P-v]K�\]V+MON��

Page 15: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��������� � � ��� � ���� � ��� ��� � � � � ��� �

��� A � � � �:����'���L�#��)��'*

JLK+MfqO\]K+M:T�MOVCW1x�MOpRX5K�^cX WQK+M Y M:WQW�MUT NQPRv]V�^cp 0 W�\�0 V+\]PRNQM T�^_W�PR\�PRV�W�K+M NQMObfP 0 qOpR^cNQNQPRqO^cpW�K+MU\cT Z ^_l+l�p-PRMOX ^ Y \ �CM��4J�\ NQK+\���WQK�^_W�^cV9MU�CMOV Y MUWQW�M:T�NQP-v]V�^cp 0 WQ\�0 V+\]PRN�MHTg^_W�P-\ M��uPRN�W�NU�Bl�tuT�MzBt�^cV W�t+b W�K+MU\cT Z b t+N}W Y M4t+NQMUX.� � P-T�N�W�W�K+MEqOp ^cN�NQPRq#^cpCNQP-V+M'��^��CM'�HP-pRp Y MEz{t�^cVCW�P-hOMOX W�\ NQK+\��W�K�^_W"PRV W�K+M�z{t�^cVCW�t+b p-PRbfPFW!PFW"T�MUl+T�MUNQMOVCW�MOX Y Z ^2qO\]K+MUTQMOV WEN�W�^_W�M �HK+P-qgK l \]NQNQMONQN�MON4Se\]P-NQNQ\]VqO\]t+VCW�P-V+v N�Wg^_WQPRN�W�P-qON�� � T�\]b ^cV�t+V+X+MUT�N�Wg^cV+X+P-V+v \]nkW�K+M qU\]K+MUT�MOVCW`N�W�^_W�Mc��WQK+M NQzBt+MOMOhOMUXN�W�^_W�Maq#^cV Y MaP-V WQTQ\{X+t+qOMOX.�4JLK+PRN�N�Wg^_WQM �HP-pRp Y MaNQK+\��HV W�\ K�^#�CMyp-MONQN�t+V+qOM:TQWg^cPRVCW Z W�K�^cV W�K+MqO\]K+M:T�MOVCW2N�Wg^_WQM#�

JLK+M nw\]p-pR\��HP-V+v NQMUqUW�PR\]V�qO\]V W�^cPRV+Na^ N�Wg^cV+X�^_T�X�X+MUTQP-�_^_W�PR\]V�nw\cTHW�K+Mjz{t�^cVCW�PRh#^_WQPR\]V`\]n^cV`MUpRMOqUW�T�\]b9^cv]V+MUW�P-qyx�MUpRX.�LJLK+M \cT�P-v]PRV�^cp�NQ\]tuT�qOMjT�MOnwMUT�MUV+qOMOX nw\cT2bf\]N�W�\]n!W�K+P-NHX+MUTQP-�_^_W�PR\]VP-N W�K+M���\cT � \]n ��� ��� � ��� ��� � � ��IaX+X+P-WQPR\]V�^cp>NQtul+l \cTQW/�L^cN�\ Y Wg^cPRV+MUX�W�KuT�\]t+v]K�W�K+M���\cT �\]n � ��� ��������� ����� ��^cV+X � � � � �� ��� � � �

� V ^cV Z WQT�M#^_W�b MOV W�\]n1z{t�^cVCW�t+b bfMOqgK�^cV+PRqON�W�K+M�qOpR^cNQNQP-q MOpRMUqUWQT�\]b9^cv]V+M:W�PRq8x�MOpRX�

Page 16: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��������� � ����� ��� ����� � � � � � ��� � � � �����

P-N z{t�^cVCW�P-hOMOX P-V W�K+M`b9^cV+V+M:TfNQP-bfPRpR^_T WQ\ W�K+M`zBt�^cV WQPRh#^_W�P-\]V \]nHWQK+M`qOp ^cN�NQPRq#^cp K�^_T�bf\]V+P-q\]NQqUPRpRpR^_W�\cT���JLK+MjT�MUNQt+p-W�\]n�W�K+Mkl+T�\BqOMONQN�PRNLW�K+M ^_l+l M#^_Tg^cV+qOMj\]n�l�K+\cW�\]V+NLW�K�^_W X+MONQq:T�P Y M W�K+MMOV+M:T�v Z \]n!W�K+Mkx�MOpRX.�

JLK+M qOp ^cNQN�PRq#^cp�MOp-MOqUWQT�\]bf^cv]V+MUW�PRq�x�MOp-X9^_l+l@MO^_T�N�^cN4^yl�tuT�M�NQPRV+M �L^#�CM���P-W�K qO\]V+N�W�^cV W^cb l�p-P-W�t+X+My^cV+X�l�K�^cN�M#��~BWg^_T�W���P-W�K | ^ � ��MOp-p / N�MOzBt�^_W�PR\]V+N�(

� �� � i ii �� � �� � � �� � � �� ����� � � � ��� � � �� �3,,, �+i ii� � %W�K+MyqO\]V+N�WQP-W�tuW�PF�CMyTQMOp ^_W�P-\]V+N

� �� � , ,, i ii �� � � �� � � � � � %^cV+X�WQK+M Y \]t+V+X�^_T Z qU\]V+X+P-W�P-\]V�nw\cT2MUV+MUT�v Z

� ���

� � � � � � � �� # � � , ,, # ����� �&��

Page 17: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+M ^ Y \��CM pRMO^cX+NHW�\fW�K+M��^��CM1MUz{t�^_W�P-\]V.�HJLK+PRNaMOzBt�^_W�PR\]V>�mNQK+\��HV8P-V�\]V+M X+PRbfMOV+N�PR\]V�nw\cTNQP-b l�pRP-qOP-W Z �uv]MUV+MUTg^_W�MON l�p ^cV+M��L^#�CMON � ��K+PRqgK`N�^_WQPRNQn Z

� # �� � # � � # �� # � � # %^cV+X�WQK+M Y \]t+V+X�^_T Z qU\]V+X+P-W�P-\]V � �

� � � � � � # � � �JLK+M NQ\]p-tuW�PR\]V�PRN�^ l�pR^cV+M��L^#�CM \]n��CMOpR\BqOP-W Z �aPRV�X+P-T�MOq:W�PR\]V �� � � � � � � � � � � � � �� \cTy^9q#^��{P-W Z \]nEpRMOV+vcWQK �� � � � �

�yJ K+P-NkqOp ^cNQN�PRq#^cp"x�MOp-X P-NaV+M��uW�� T�P-W�W�MOV)�HPFW�K ^9V+M��

�_^_T�P ^ Y p-Mc�uW�K+MjqO\]b l�pRM���^cb l�pRPFW�t+X+M��m�uW�\ K+MUp-l`W�K+MkWQTg^cV+N�P-W�P-\]V�PRVCW�\ W�K+M zBt�^cV W�t+b T�MO^cpRb2�

�aN�t�^cpRp Z W�K+M�x�MOpRX9P-N�NQMUlm^_Tg^_WQMOX9PRVCW�\ W ��\ NQP-V+M/�L^#�CMON/W�K�^_W�^_T�M2V+P-V+MUW Z X+MOvcTQMOMON�\]tuW\]n�l�K�^cNQM��P-W�K�M#^cqgK`\cW�K+MUT��4JLK+MONQM1^_TQMjW�K+Myz{t�^cXuTg^_WQtuT�MON��

� � � � ��� � � � � � � � � � � � � � � � � � � � � ��� � � � � � � �� M��{WLW�K+MONQM WQMUT�bfN ^_T�MyNQPRbsl�pRP-x�MUX�W�KuT�\]t+v]K�W�K+Mj�_^_T�P ^ Y p-MON

� � �� ��� � � � � � � � � � � � � � � � �

NQ\ � � � � � � � � � � � � ��� � � � � � %^cV+X�WQK+M Y \]t+V+X�^_T Z qU\]V+X+P-W�P-\]V Y MUqO\]bfMON

� � � � � � # � # � � # � �~{P-b l�pRP-n Z \]V+qOM bf\cTQM���P-WQK�W�K+MON�Mj�_^_T�P ^ Y p-MON��

� ! � � � � ! � � � �� \�� PRVCWQT�\BX+t+qOMjW�K+MyqO\]b l�p-M���^cb l�pRPFW�t+X+Ma�c^_TQP ^ Y pRMUN

� � � � � � � � � � � � ��� �

� � � � � � � � � � %��K+MUT�M S/pR^cV+q � / NkqO\]V+N}Wg^cV WyK�^cN Y MUMOV�P-V+qOpRt+X+MOX nw\cTyt+NQM p ^_W�MUTkX+tuTQPRV+v�zBt�^cV WQPRh#^_W�P-\]V.�yJ K+MqO\]bsl�pRM���^cbsl�pRP-WQt+X+MON ^_T�MjqU\]V �}t+vC^_W�MON \]n!M#^cqgK�\cWQK+MUT��4J K+M Y \]t+V+X�^_T Z qU\]V+X+P-W�P-\]V � MOV+M:T�v ZqO\]V+X+PFW�PR\]V ��q#^cV Y MyTQM���TQP-WQW�MUV`^cN2^ l+T�\{X+t+q:W2\]n!qU\]b l�pRM���qU\]V �}t+vC^_W�MON��

� �� � � # � # � � # � �

� � � � � � � � � � � � � � � �& &

Page 18: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+PRNHl+TQ\{X+t+qUWaqO^cV Y M T�M:l�p ^cqOMOX)��P-W�K�W�K+M1qO\]b l�p-M��`^cb l�pRPFW�t+X+MON�� � W2P-N2PRb l \cTQWg^cVCW�WQ\fNQMOMW�K�^_WeWQK+M qU\]b l�pRM�� ^cb l�pRPFW�t+X+MONeK�^#�CM Y MOMOVsX+MUx�V+MOX W�\aT�M:l+T�MONQMOVCW/WQK+M Y \]t+V+X�^_T Z qO\]V+X+PFW�PR\]V^cV+X�^cp-NQ\ W�K+Mjx�MOp-X.�/�aNQP-V+v o4t+pRMUT / N�P-X+MOVCW�P-W Z

� ��� � � � � � � � ��� � � � � ��� � � � � � � � � � � � ��� � � � � ���W�K+Mkx�MOp-X`q#^cV Y MjT�M�� T�PFWQW�MOV�^cN

� ! � � � � � � � ��� � � � � ���� � � � � � ��� � � � � ���

� � �

� � � � � � � � � � � � ��� � � � � � � � � � � ��� � � � � �

� � � � ��� � � � ��� � � � � ��� � %��K+MUT�MyW�K+M Y \]t+V+X�^_T Z qO\]V+X+P-W�P-\]V�P-N

� � � � � �� \�� WQK�^_W W�K+M�x�MUpRX�PRN1T�M�� T�PFWQW�MOV�P-W P-N TQM#^cX Z W�\ Y M z{t�^cVCW�P-hOMOX.� JLK+M N�Wg^cV+X�^_T�X

V+\cWg^_WQPR\]V PRV ^cpRp{lm^_l MUT�NEPRVsWQK+MLx�MUpRX \]nz{t�^cVCW�t+b�l�K Z NQP-qON/P-N�WQK�^_W4\]nmikP-Tg^cq���J K+P-N4V+\cWg^_WQPR\]V^cp-pR\��HN4\]V+M2W�\ qUT�M#^_WQMa^1nw\cT�b9^cp-PRNQb \]n�z{t�^cVCW�t+b bfMUq6K�^cV+P-qON Y ^cNQMOX \]VfW�K+M+,aP-p Y MUTQW�N}lm^cqOM#�JLK+PRNe^ Y N}WQTg^cqUW!nw\cT�b9^cpRP-NQb ^cpRp-\���N!nw\cT"WQK+M/qO\]b Y PRV�^_WQPR\]V1\]n �L^#�CMOnwt+V+qUWQPR\]V+N�^cNQNQ\BqOP ^_WQMOX��P-W�KzBt�^cV W�t+b W�K+MO\cT Z ��P-WQK �CMOqUW�\cTsN�lm^cqOMUN�� ikMUx�V+MOX \]V W�K+P-N N�lm^cqUM`^_T�M�W�K+M�N�W�^_W�M��CMOq:W�\cT�N� � � � � MUW ��^cV+X�PFW�NjX+t�^cp � ��� � Y Tg^ � � nw\cTjWQK+MsX+t�^cp ,aPRp Y MUT�WjN}lm^cqOM ��� � � � TQMUl+T�MONQMUV W�N^�z{t�^cVCW�t+b N}Wg^_W�M PRV WQK+MsN Z N�W�MOb �sIap-NQ\�X+M:x�V+MOX5PRNyW�K+MsN�q#^cp ^_Tyl+T�\{X+t+q:W � � ! � � # � �^cV+X5PFW�N qO\]bsl�pRM���qO\]V �}t+vC^_W�M � � # � � ! � � � ���al MUTg^_W�\cTQN ^_T�M9^cp-NQ\`X+MUx�V+MOXDW�\`qgK�^cV+v]M^�z{t�^cVCW�t+b N�W�^_W�M9W�\ ^ V+M��&\]V+MfI II�� � � � �� � ��,aM:T�bfP-WQP ^cV \cl MUTg^_W�\cT�N � I II dIII� �t+NQMUX W�\ \cl MUTg^_W�M \]V9^yz{t�^cVCW�t+b N�Wg^_W�M �HP-pRp Z PRMOp-XsT�M#^cp�V t+b Y MUT�N'�HK+P-qgKfqO\cTQT�MUN�l@\]V+XfW�\yW�K+MM��{l@MOq:Wg^_W�PR\]V��c^cp-t+Mj\]n�W�K+Mj\cl MUTg^_W�P-\]V�\]V�W�K�^_WHN}Wg^_W�M � ��� I II � � � � �

� � � � �� � � � ��� � � � ��� � � � � ��� � % � � ��� � �

��K+MOV9zBt�^cV W�P-hOPRV+vjW�K+MHqOpR^cNQNQP-q#^cpMUpRMOqUW�T�\]b9^cv]V+MUW�P-q x�MUpRX>�{W ��\ ^_l+l+TQ\C^cq6K+MUN�^_T�M�l \]N 0NQP Y pRM#���aV+M9^_l+l+T�\C^cqgKDPRN W�\�z{t�^cVCW�PRhOMsW�K+MfMOV+MUTQv Z MOzBt�^_W�PR\]V>�!WQK+Mf\cW�K+MUT ^_l+l+TQ\C^cq6KDP-NjW�\zBt�^cV W�P-hOM W�K+M MOpRMOq:WQT�PRqjx�MOpRX8P-WQNQMOpRn � � \cW�K�^_l+l+T�\C^cqgK+MON+��PRp-p Y M1t+NQMOX�W�\fP-V W�T�\{X+t+qOM P-b l@\cT 0Wg^cVCW l@\]PRVCW�N��

���YT � � ���O�����F%$����9 ����� ; �F�'N����Y* � �:���9OQ

&�(

Page 19: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� M z{t�^cVCW�P-hOMjW�K+Mjx�MOpRX#/ N2MOV+MUT�v Z�Y Z P-V WQTQ\{X+t+qOP-V+v ^sz{t�^cVCW�t+b l@\]N�W�t+pR^_W�M P-V WQ\ W�K+MMOV+M:T�v Z qO\]V+X+P-W�P-\]V

� �� � � # � # � � # � � , ,, �

� � � # � �� # � S SS # �%��K+MUT�M , ,, PRNeW�K+M ,k^cbfPRpFW�\]V+P ^cV \cl MUTg^_W�\cTE^cV+X � �� ^cV+X S SS ^_T�ML\cl@MUTg^_WQ\cT�NE^cNQNQ\{qUP ^_W�MOX ��P-W�K W�K+M

x�MOp-X.�eJLK+M6,k^cbfP-p-W�\]V+PR^cVaK�^cN!MOV+MUTQv Z MUPRv]MOVC�c^cp-t+MON � ! ^cN�NQ\{qOPR^_W�MOX��HPFW�K MOV+M:T�v Z MOPRv]MOV+N}Wg^_W�MON� � ! � \]n�W�K+Myx�MOpRX`N}l@MOqOPFx�MOX Y Z

�� � � # � �� # � S SS # � � � ! � � ! � � ! � �

�aNQM`WQK+M qU\]bfb tuWg^_W�PR\]V l@\]N�W�t+pR^_W�M�SSS � �� � � �� S SS � � � W�\DNQ\]p-�CM`WQK+PRN9MOzBt�^_W�PR\]V nw\cT W�K+MMOV+M:T�v Z MOP-v]MOV �_^cpRt+MUNs^cV+XDMOP-v]MOV+N�Wg^_WQMON�� � P-TQN�W X+MUx�V+M \cl@MUT�^_W�\cT�N1^ ^^ ^cV+X5^ ^^ �eW�K+M9qUT�MO^_W�PR\]V^cV+X�^cV+V+P-K+PRpR^_W�PR\]V�\cl@MUT�^_W�\cT�NO��n T�\]b W�K+MjqO\]b l�pRM���^cb l�pRPFW�t+X+MON��

^ ^^ � � � � � � � �� � � S SS � ^ ^^ �

� � � � � � �� � � S SS � %W�K+MyqO\]bfb tuWg^_WQPR\]V l@\]N�W�t+pR^_W�MyPRNLT�M�� T�P-WQWQMOV

^ ^^ ^ ^^ � ^ ^^ ^ ^^ �

^cV+X�WQK+M ,k^cbfP-p-W�\]V+PR^cV Y MOqO\]b MON

, ,, � � � ^ ^^ ^ ^^ � �� � �

JLK+M MOP-v]MOVC�c^cp-t+M MOzBt�^_W�PR\]V Y MOqU\]bfMON

^ ^^ ^ ^^ � � ! � � � !� � � �� � � � ! � �

� M��{W�W�K+M � t+b Y MUTL\cl MUTg^_W�\cTLP-N X+M:x�V+MOX � �� *^^^ ^ ^^ ^cV+X�WQK+MyMUPRv]MOVC�c^cp-t+M � � !� � � �� � � \cT

NQP-b l�pRP-qOP-W Z PRV9nwtuT�W�K+MUT X+MUT�PF�c^_W�P-\]V+N�pRM:W/W�K+MahOM:T�\ \]n�MOV+MUT�v ZsY M2T�MOX+M:x�V+MOX Y Z WQK+M2�c^cp-t+M � ��NQ\ W�K�^_W � � !� � � �� *^^^ ^ ^^ $� � �JLK+M V+M�� MUPRv]MOVC�c^cp-t+M MOzBt�^_W�PR\]V>�

� �� � � � � � � � %T�MUp ^_W�MONaW�K+M V t+b Y MUTy\cl@M:Tg^_W�\cTkW�\9W�K+M MOV+MUT�v Z MUPRv]MOVC�c^cp-t+MON � ! � � � � JLK+MsN}Wg^_W�M � � �P-Njq#^cp-pRMOX�^�V t+b Y MUTjN�Wg^_W�M ^cV+X T�MUl+TQMONQMOVCW�N MOP-v]MOV+N�Wg^_W�MUN \]n4WQK+M MOp-MOqUWQT�P-q x�MUpRX.�7*�MOp ^_WQPR\]V+NY MUW ��MOMOV W�K+MONQM�MOPRv]MOV+N}Wg^_W�MONE^cV+XsWQK+M q:T�M#^_W�P-\]Vf^cV+Xs^cV+V+PRK+PRpR^_W�PR\]V \cl@M:Tg^_W�\cT�q#^cV Y M ��\cT � MOX\]tuW�(

^ ^^ � � � � � � � � � ^ ^^ � � � � � � � � � �

& #

Page 20: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

IaN1W�K+MUP-T V�^cbfMON P-b l�p Z ��W�K+M�^cV+V+PRK+PRpR^_W�PR\]V5\cl MUTg^_W�\cT TQMOX+t+qOMON W�K+M VBt+b Y MUT \]nLWQK+M�N}Wg^_W�MPFW1^cqUWQN1\]V5^cV+X W�K+MsqUT�M#^_W�P-\]V5\cl@MUT�^_W�\cT P-V+qUT�M#^cN�MON1W�K+M V t+b Y MUT1\]n�W�K+M N�W�^_W�M PFW ^cqUW�Nj\]V.�� MOq#^ct+N�M � PRN T�MOp ^_WQMOX W�\ � ! �EW�K+MONQM�\cl@MUT�^_W�\cT�N T�MON�l MOqUW�PF�CMOp Z T�MOX+t+qUM`^cV+X P-V+qUT�M#^cNQM�W�K+MMOV+M:T�v Z \]n!W�K+Mkx�MOpRX.�

I vcT�\]t+V+X N�Wg^_WQM � � � M��+P-N�W�N+��K+PRqgK P-N2W�K+M pR\���MON�Wal \]NQNQP Y pRM VBt+b Y MUTyN�Wg^_W�M#�jJLK+PRNP-NH^cp-NQ\sT�MUnwMUTQT�MOX`WQ\f^cNLW�K+My�_^cqOt+t+b N�Wg^_W�M�(

^ ^^ � � � �� ^ ^^ � � � � � � � �

I T�MOp ^_WQPR\]V+NQK+PFl Y M:W ��MOMOV8^cV Z V t+b Y MUTHN�Wg^_W�Mj^cV+X�W�K+Mk�_^cqOt+t+b N}Wg^_W�Myq#^cV Y M�� T�P-WQWQMOV`^cN

� � � ^ ^^ ! ��� � � �

��K+PRqgK`q#^cV�NQK+\�� K+\�� ^cpRp>N�W�^_W�MON2^_TQMyT�MUp ^_W�MOX�W�\sWQK+M vcT�\]t+V+X`N}Wg^_W�M#�

� T�\]b W�K+M MOV+MUTQv Z MUz{t�^_W�P-\]V ��M q#^cV P-V W�T�\{X+t+qOM W�K+M z{t�^cVCW�t+b qU\]V+qOMUl+W�\]n W�K+Ml�K+\cW�\]V Y Z PRVCW�MUTQl+TQMUW�PRV+v � � ^cN2W�K+M Y ^cNQP-q z{t�^cVCW�t+b \]nEMOV+MUT�v Z \]n�W�K+M x�MOp-X.�yI V t+b Y MUTN�W�^_W�M � � � �HP-pRp�T�MUl+T�MUNQMOVCW ^cV9MOPRv]MOV+N}Wg^_W�M2\]n WQK+MHx�MOpRX ��P-W�K � PRV+X+MUl MOV+X+MOVCWLl�K+\cW�\]V+N6��P-W�K^cV�MOV+MUT�v Z � � � �4J K+Mkx�MOp-X`P-W�N�MOpRn

� � � � �� � � � � � � � � ��� � � � � ��� �

P-N�qO\]bsl+T�PRNQMUX�\]n!l�K+\cW�\]V+N��'� V�W�M:T�bfN \]n�x�MOp-X`\cl@MUT�^_W�\cT�NO�

� �� W��#Z � � � �� ^ ^^ � � � ���qUTQM#^_W�MON l�K+\cW�\]V+NHP-V�W�K+Myx�MOpRX>�m^cV+X

� �� W � Z � � � � �� ^ ^^ � � ���T�MUbf\ �CMUN l�K+\cW�\]V+N��/IapRN�\sV+\cW�MyW�K�^_W

, ,, � � ^ ^^ ^ ^^ � � �� W��#Z � �� W � Z^cV+X � , ,, � � � � � � ^ ^^ ^ ^^ � � � � � � �

� T�\]b W�K+M ��\cT � X+\]V+MHN�\ n ^_T�PFWEK�^cN Y MUMOVfNQK+\��HVsW�K�^_W4WQK+M�x�MOp-XfPRN4^cNQNQ\BqOP ^_W�MUX1��P-W�KMOP-v]MOV+N�Wg^_WQMONaK�^��{PRV+v MOP-v]MOV �_^cpRt+MUNO� �HK+P-qgK ^_TQM VBt+b Y M:T�Nk\]n�l�K+\cWQ\]V+NO� l+T�\cl \cTQW�PR\]V�^cp�W�\9W�K+Mx�MOp-X#/ N MOV+MUT�v Z � � Z W�K+PRNLbfM:W�K+\{X�P-W �L^cNLW�K+Mkx�MOpRX#/ N�MOV+M:T�v Z W�K�^_W���^cN�zBt�^cV W�P-hOMOX�^cV+X�V+\cW

& "

Page 21: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

W�K+Myx�MOpRX�PFW�NQMOp-n � � tuWHW�K+P-N��L^cN�NQK+\���V�PRV�\cTQX+MUTHW�\ MOb l�K�^cNQP-hOMjW�K+M t+V+qOMUTQWg^cP-V W Z PRV+K+MUT�MUV WP-V�zBt�^cV WQt+b&N�Wg^_W�MUN��EJ K+Max�MOp-X�P-NL^cqUW�t�^cp-p Z V+\cWLP-V�^cV Z \]V+MyMUPRv]MOV+N�W�^_W�MaNQ\ V+\ MOPRv]MOVC�_^cpRt+MONq#^cV Y M nw\]t+V+X nw\cTkP-W��kJ K+M�,aMOP-NQMOV Y MUTQv�t+V+qOM:TQWg^cPRVCW Z l+T�PRV+qUP-l�pRM1TQMOp ^_W�MUNaMOV+MUT�v Z ^cV+X�W�P-bfMY Z � � � � � � �� V`W�K+P-N2bfMUW�K+\BX�W�K+M x�MUpRX#/ NaMUV+MUT�v Z � ! K�^cN Y MOMOV8z{t�^cVCW�PRhUMOX.�HJLK+M MOV+MUTQv Z MOP-v]MOV+N�Wg^_W�M PRN^ N�Wg^_W�MaT�M:l+T�MONQMOVCW�P-V+v9^ x �uMOX�V t+b Y MUT�\]n�l�K+\cWQ\]V+NO���HK+P-q6K�WQTg^cV+NQpR^_W�MON�^cN ^ x �+MUX`^cbf\]t+VCW\]n�MOV+MUT�v Z � � TQ\]b \]tuTHz{t�^cVCW�t+b T�MOpR^_W�PR\]V � � � � ��Mjv]MUW� � � � � � �Iap-NQ\+�+NQPRV+qUM � � � � � � ��Mjt+NQMjW�K+Mkl�K�^cNQM1\cl MUTg^_W�\cT � �� T�MOpR^_W�MOX�W�\ � �L^cV+X

� � � � � �� � �

� n � � PRNLhOMUT�\ W�K�^cV W�K+Mkt+V+qOMUTQWg^cP-V W Z T�MOpR^_W�PR\]V Y M:W ��MOMOV�MUV+MUT�v Z ^cV+X�WQPRbfM ��PRp-p@b9^ � MaW�K+Ml�K�^cNQMjt+V+qOMUTQW�^cPRVCW Z PRVux�V+PFW�M#�

IaV Z W�PRbfMH^cV9\ Y NQMUTQ�_^_W�P-\]V9PRN�b9^cX+M�\]VfW�K+MHx�MOp-X9W�K+MUT�M2P-N�^cV9t+V+qOMUT�Wg^cPRVCW Z �E�aV+qUMUT 0Wg^cP-V W Z PRV \ Y NQMUTQ�CMUX MOV+MUT�v Z PRNkT�MOpR^_W�MOX�WQ\�W�K+M t+V+qOMUTQW�^cPRVCW Z PRV�\ Y NQMUTQ�_^_W�PR\]V W�PRb M#�s~{PRV+qOM\]tuT�MUPRv]MOVC�c^cp-t+Ma\]n@l�K+\cW�\]V+N�PRN/^ x �+MOX V t+b Y MUT#� � � �� MOV+MUT�v Z PRN/W�\cW�^cpRp Z qOM:TQWg^cPRV>� W�K+M2l�K�^cNQMb t+N�W Y MkW�\cWg^cp-p Z t+V+qOMUT�Wg^cPRV�^cV+X�W�K t+N2t+V+bfM#^cNQtuT�^ Y pRM#�

���FS � � ���O�����F%$����9 ����� ; �F�'N��

JLK+M1x+T�N�WybfM:W�K+\{X>�@\]n�zBt�^cV W�P-hOPRV+v9W�K+M x�MOp-X MUV+MUT�v Z ^cV+X V+\cWaW�K+M1x�MOp-X PFW�NQMOp-n �>pRMOXW�\yW�K+MHMUV+MUT�v Z MOPRv]MOVC�_^cpRt+MON/^cV+X9VBt+b Y M:T�N�Wg^_WQMON���JLK+PRN/N�MOqO\]V+X9z{t�^cVCW�P-h#^_W�PR\]VsbfMUW�K+\BX1��PRp-pp-M#^cX�WQ\ N�W�^_W�MON nw\cT1��K+PRqgK WQK+M�x�MOp-X PFW�NQMOp-n�P-N ^cV�MOPRv]MUV �_^cpRt+M�\]n2^�x�MOpRX \cl@MUT�^_W�\cT��DJLK+PRN��PRp-p>^cpRp-\�� WQK+Myx�MOp-X�W�\s^_l+l+T�\C^cqgK�PFW�NLqOp ^cN�NQPRq#^cp>qU\]t+V W�M:TQlm^_TQW2P-V�WQK+Mjp-PRbfPFW��eJLK+PRN �HP-pRp Y M ^zBt�^cV W�t+b N}Wg^_W�M q#^cpRp-MOX8W�K+M qO\]K+MUT�MOVCWjN�Wg^_W�M#� � � �� WkPRNaW�K+P-Nkx�MUpRX8W�K�^_WyPRN2l+T�\BX+t+qOMOX Y Z^cV�PRX+M#^cp�p ^cN�MUT��

~BW�^_TQW�PRV+v ��P-W�K�W�K+M qOpR^cNQNQP-q#^cp>x�MOpRX

� � � � �� � � � � � � � � ��� � � � � ��� � %��M ^cvC^cPRV�X+MUx�V+M1zBt�^cV W�t+bdx�MOp-X`\cl@MUT�^_W�\cT�N

� �� W��#Z � � � �� ^ ^^ � � � ���& �

Page 22: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� �� W � Z � � � � �� ^ ^^ � � ���t+NQP-V+v W�K+MyqUT�M#^_WQPR\]V`^cV+X`^cV+V+PRK+PRpR^_W�PR\]V�\cl@MUT�^_W�\cT�N��

I z{t�^cVCW�PRhOMUX x�MUpRX&��PRpRpmpRMO^cXfW�\1MOP-v]MOV+N�Wg^_W�MUN�\]n@W�K+MHx�MOp-X�^cV+XfW�K+MOP-T�qO\cTQT�MON}l@\]V+X+PRV+vx�MOp-X MOPRv]MOVC�_^cpRt+MON�� � V+N�W�M#^cX \]n>W�K+M2MUV+MUT�v Z MOzBt�^_W�PR\]V9V+\�� ��M/�L^cVCW�W�\ NQ\]p-�CM�W�K+M2W ��\1x�MOpRXMOzBt�^_W�PR\]V+N

� �� � � � � � � � ^cV+X � � � � �� � � � � � �� n ��M X+MUx�V+M

� W � Z� � � � �� � � ���

^cV+X � � W���Z

� � � �� � � � ��� %��Mjq#^cV�N�\]p-�CM

^ ^^ � � � � �^cV+X � � ^ ^^ � � � �JLK+Mjx�MOp-X`\cl@M:Tg^_W�\cT / N MUPRv]MOVC�c^cp-t+MONa^_T�Mynw\]t+V+X�W�\ Y M

� W � Z � � � � �� � � ���^cV+X

� W��#Z � � � �� � � � � ��� �� \�� W�K+Mkx�MOpRX�PRN z{t�^cVCW�PRhOMUX.�

� �� W � Z � � � W � Z � � ��2l@MUT�^_W�\cT � �� W � Z l+T�\BX+t+qOMON�MOPRv]MOVC�_^cpRt+MON�� W � Z X+MUx�V+MOX P-V�W�MUTQbfN9\]n 6��J K+M qO\]V �}t+vC^_W�MMOzBt�^_W�PR\]V-�HP-pRp�X+MUx�V+M MOPRv]MUV �_^cpRt+MON � W��#Z/P-V`W�MUT�b NH\]n � �H~{PRV+qOMjW�K+M x�MOp-X8�_^_T�P-MON2PRV�W�PRbfM_�PFW�N MOP-v]MOVC�c^cp-t+MON ^_T�MsWQPRbfM X+MUl@MUV+X+MOV W��`JLK+MfqO\]b l�p-M��5^cbsl�pRP-WQt+X+MON *M��ul+T�MUNQNQMOX ^cN � � � � ��� � NQK+\�� W�K+MjT�MO^cp�N�t+b \]n�x�MOpRX`MUPRv]MOVC�c^cp-t+MON

� � � � � �� � � � ��� � � � � � ��� �& �

Page 23: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

W�\sMOz{t�^cp>W�K+MyqOpR^cNQNQPRqO^cp�x�MUpRX

� � � � � � � � � � � � � � � � �JLK+M2qOpR^cNQNQPRqO^cpmx�MOp-X ^cb l�pRPFW�t+X+M PRN/T�MUp ^_W�MOXsW�\ W�K+M2MUPRv]MOVC�c^cp-t+M2\]n@W�K+M�z{t�^cVCW�t+b N�W�^_W�M � � �� \��*P-W6��PRp-p Y M2NQK+\��HV9W�K�^_W4W�K+PRN/N�Wg^_W�M�PRN�^ qU\]K+MUT�MOVCWLN�Wg^_W�M2^cV+X ^ bfPRV+P-b t+b t+V+qUMUTQWg^cP-V W ZN�W�^_W�M#�

� PFT�N�W/M��ulm^cV+X WQK+PRN�N�W�^_W�M�P-VfW�MUT�b N4\]n>^jqO\]pRp-MOqUW�P-\]Vf\]n@V t+b Y MUT�N�W�^_W�MON%��P-WQK �c^_TQPR\]t+N��MUPRv]KCW�N

� � ! � ! � � ���K+MUT�M�qO\{M � qOPRMUV W�N � ! ^_T�M�T�MUp ^_W�MOXsW�\jW�K+M l+T�\ Y ^ Y PRp-P-W Z \]n x�V+X+PRV+vjW�K+MHMOP-v]MOVC�c^cp-t+M � P-V W�K+MbfMO^cNQtuT�MObfMUV W��4JLK+MjqO\BM � qUPRMOVCW�N2q#^cV Y MjqO\]b l�tuW�MOX YBZ (

� � � � ! � ! � � � � � � ���K+MUT�M � � � � � � PRn � � � � PRn � � � � N�W�^_W�MON � ^cV+X � ^_T�My\cTQW�K+\]v]\]V�^cp�N�Wg^_WQMON ���

� � ! � � � � � � � �

�aNQMkW�K+MyT�MOp ^_WQPR\]V � � � � � � W�\sv]M:W �HPFW�K � � � (� � � � � � �� � � �

JLK+M1l+T�\cl MUTQW�P-MONa\]n"W�K+M qUT�MO^_W�PR\]V ^cV+X8^cV+V+PRK+P-p ^_W�P-\]V�\cl@MUT�^_W�\cT�NaqgK�^cV+v]M1W�K+M ^ Y \��CMl+T�\BX+t+qUW2\]n�N�Wg^_W�MUN�W�\ M��ul+TQMONQNHW�K+MyqO\BM � qOP-MOVCW

� ! � � � � ��� � � � � � � � �

JLK+M2pRMUn W�NQPRX+MH\]n@W�K+MHl+T�\BX+t+qUW � � � � � q#^cV Y M2NQPRbsl�pRP-x�MUX YBZ t+NQPRV+v1WQK+M2X+MUx�V+P-WQPR\]V \]n@W�K+M^cX �}\]P-V WH\]n�W�K+MjVBt+b Y M:THN�W�^_W�M���P-WQK`^sN�K+PRn W2\]n/� �

� ! � � � � ! ��� � � ! ��� �

�yV+\���PRV+vsW�K+MjqU\{M � qOPRMOVCW�Na^cp-pR\��HNLt+N W�\ M��{lm^cV+X � � (

� � ! � � ! ��� � � �& �

Page 24: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLKuT�\]t+v]K`V+\cTQb9^cpRP-h#^_W�PR\]V.( � � ! � # ����K+PRqgK`v]PF�CMON�t+N � � �^cV+X

� � ��� � � � � #� ! ! ��� � � � �

JLK+M1l+T�\ Y ^ Y P-pRP-W Z \]n�x�V+X+P-V+v�WQK+M ^��CMUT�^cv]M VBt+b Y M:Tk\]n�l�K+\cWQ\]V+NaPRV�W�K+M N�Wg^_WQM � � �P-N

� � ! � # � � � � � � # � � # !��� � � � � � �

JLK+PRN PRN W�K+M�Se\]PRNQNQ\]V X+PRN�W�T�P Y tuW�P-\]V.�DJ K+M�Se\]PRNQN�\]V X+PRN}WQT�P Y tuWQPR\]V�nw\cTsW�K+P-NszBt�^cV WQt+b b M�0qgK�^cV+PRqO^cpLx�MUpRX P-N ^cNQNQ\{qUP ^_W�MOX ��P-W�K�P-W�N qOpR^cNQNQP-q#^cp�qO\]t+VCW�MUTQlm^_TQWO�/W�K+M NQPRV+M �L^#�CM � ^cV P-X+M#^cpNQ\]tuTQqOM ��(

� � ! � # � ���! � !��� �� W�q#^cV�^cpRN�\ Y MjNQK+\��HV`W�K�^_W W�K+M ^��CMUT�^cv]Myl�K+\cW�\]V�VBt+b Y M:T2PRN�MOz{t�^cp>W�\ W�K+M N�z{t�^_T�Mj\]n!W�K+M^cb l�p-P-W�t+X+M��

� � # � � �� � �� V W�K+M�pRP-bfP-W \]na^ p ^_T�v]M�VBt+b Y M:Tf\]nHl�K+\cW�\]V+NsW�K+M�qO\]K+M:T�MOVCW9N�Wg^_W�M�qO\cTQT�MUN�l@\]V+X+N WQ\�W�K+MqOpR^cNQNQP-q#^cp>NQPRV+M��L^#�CM#� � MOqO^ct+NQMjPFW K�^cN�qO\]V+N}Wg^cV W�l�K�^cNQMyP-W PRN�^cpRNQ\ q#^cp-pRMOX�^ qO\]K+M:T�MOVCW2N�Wg^_WQM#�

~{\5n ^_T PFW9K�^cN Y MUMOV�N�K+\���V*WQK�^_WfW�K+M�qOpR^cNQNQPRqO^cpHMOp-MOqUWQT�P-q`x�MOpRX P-NfT�MOp ^_WQMOX W�\5W�K+MMOP-v]MOVC�c^cp-t+M 6��JLK+M�MOP-v]MOV+N�Wg^_W�M � � �L^cN NQK+\���V W�\ Y M�^ qO\]K+M:T�MOVCWfN�Wg^_WQM3��K+PRqgK P-N ^NQtul MUTQl \]NQP-W�P-\]V \]n2V t+b Y MUTsN�Wg^_WQMON � � � � JLK+M�l+T�\ Y ^ Y P-pRPFW Z \]n x�V+X+PRV+v5^cV ^cV Z V t+b Y MUT\]nkl�K+\cW�\]V+N PRV*^cV Z VBt+b Y M:T�N}Wg^_W�Mc��^cV+X�qU\]V+NQMOz{t+MUV W�p Z W�K+M8qO\]K+MUT�MUV W�N�Wg^_WQMc�Hnw\]p-pR\��HN ^Se\]P-NQNQ\]V X+P-N�WQT�P Y tuW�PR\]V.�so�^_T�p-PRMUTjP-W��L^cNjNQK+\���V W�K�^_WyW�K+M qUp ^cNQNQP-q#^cp�NQ\]tuT�qOM � �� � � ^cV P-X+M#^cppR^cNQMUT �+��\]t+pRX l+T�\BX+t+qOM9Se\]PRN�NQ\]V l�K+\cW�\]V5qO\]t+VCW�PRV+v�N}Wg^_W�PRN}W�PRqON�� J K+MfqU\]K+MUT�MOVCW N�Wg^_W�MUN ^_T�MW�K+MyqOp-\]NQMON�W2^cV�^cpR\]v \]n�W�K+M qUp ^cNQNQP-q#^cp�K�^_T�bf\]V+P-qy\]N�qOPRp-p ^_W�\cT N�Wg^_WQMON��

��� � � � ���O*��E�����O� � � ������'*����#��)���F� �

JLK+MHqUp ^cNQNQP-q#^cpmNQPRV+M �L^��CM�K�^cN/V+\1t+V+qUMUTQWg^cP-V W Z PRV l�K�^cNQMH\cT�^cb l�p-P-W�t+X+M#�"J K+M2zBt�^cV90W�t+b qO\]K+MUT�MUV WkN�W�^_W�M1K�^cN2t+V+qOM:TQWg^cPRVCW Z � ^cV+X � � ��K+PRqgK�T�MOpR^_W�M W�KuTQ\]t+v]K`W�K+M5,aMOP-NQMOV90Y MUT�v T�MUp ^_W�P-\]V.�'� n!W�K+M ^��CM:Tg^cv]MjV t+b Y MUTH\]n!l�K+\cW�\]V+N�PRV+qUT�MO^cNQMOX`W�\ W�K+M qOpR^cNQNQP-q#^cp�pRPRb P-WLW�K+Mt+V+qOM:TQWg^cPRVCW Z � � � � ��\]t+p-X X+MOqUT�M#^cN�M#�*J K+MON�M`PRX+M#^cN q#^cV Y M�T�MOp ^_WQMOX M#^cNQP-p Z ��P-W�Kl�K�^cNQM N�lm^cqUM l�p-\cW�N2W�\ NQK+\���W�K�^_WaW�K+M qO\]K+MUTQMOV WjN�Wg^_WQM PRNy^9bfPRV+P-b t+b t+V+qOMUTQW�^cPRVCW Z N}Wg^_W�M^cV+X�WQ\sP-V WQTQ\{X+t+qOMyW�K+Mjl�tuT�MUp Z z{t�^cVCW�t+bdl�K+MOV+\]bfMOV+\]V`\]n�W�K+MjN�z{t+MOMOhUMOX�N�Wg^_W�M��

& �

Page 25: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� \cT2W�K+M qUp ^cNQNQP-q#^cp"MOp-MOqUWQTQ\]b9^cv]V+MUW�P-q x�MOpRX � � � � � � � � � � � � � W�K+M qO\]b l�p-M��8^cb"0l�p-P-W�t+X+MON ��MUT�MjX+MUx�V+MOX

� � � � � � � � � � � � ��� �

� � � � � � � � � � �� V W�K+PRN4q#^cNQMLW�K+MHqO\]bsl�pRM�� nwt+V+qUWQPR\]V �5��\]t+p-X Y MLT�MUl+T�MUNQMOVCW�MOX�^cN/^k�CMOqUW�\cT � � � � � ��� �

T�\cW�^_W�PRV+vsPRV`W�K+M1qU\]b l�pRM���l�p ^cV+M �HPFW�K`n T�MOzBt+MOV+q Z � ^cNHPRV�x�v]tuT�M 09� JLK+M T�M#^cp�^cV+X�PRbf^cv�0P-V�^_T Z ^ �+MUNa\]nEW�K+M l�K�^cNQ\cTyX+PR^cvcTg^cb ^_T�M nwt+V+qUWQPR\]V+Ny\]n�WQK+M N�PRV+M ^cV+X qU\]NQPRV+M z{t�^cXuT�^_W�tuT�MONW�K�^_W W�K+MjqOp ^cNQN�PRq#^cp �L^#�CM �L^cN�\cT�PRv]P-V�^cpRp Z Y T�\ � MOV�PRVCW�\��/J K+MON�M1nwt+V+qUW�P-\]V+Na^_T�MkT�MUl+T�MON�MOV WQMOXY Z z{t�^cXuTg^_W�tuTQM nwt+V+qUW�P-\]V+N

� ! � � � � � � # �

� � � �JLK+M Z ^_T�M Y \cW�K�nwt+V+qUW�PR\]V+N�\]n!W�K+Mkl�K�^cNQ\cTa^cbsl�pRP-WQt+X+Mc��� � ! � � � # �

����������� ��� � � ��� � � � � � � ����� � � � � � � � � ��� � ��

& �

Page 26: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��K+MOV8W�K+M x�MOpRX8P-Naz{t�^cVCW�PRhOMUX W�K+M qO\]V �}t+vC^_WQMs^cbsl�pRP-WQt+X+M1nwt+V+qUW�P-\]V+N Y MOqO\]bfM q:T�M�0^_W�P-\]V�^cV+X`^cV+V+PRK+PRpR^_W�PR\]V�\cl@MUT�^_W�\cT�N��

^ ^^ � � � � � � � � � � � ^ ^^ �

� � � � � � � � � � �JLK+Mjx�MOp-X`PRN M��{l+T�MONQNQMUX8^cN

� � � � �� � � � � � � � � ��� � � � � ��� � �

� V�W�K+M zBt�^cV W�P-hOMOX`qO^cNQMc�m^cb l�pRPFW�t+X+MyqO\]b l@\]V+MUV W�\cl@MUT�^_W�\cT�N�^_T�MjX+M:x�V+MOX

8 88 ! ^cV+X 8 88 # %N�t+q6K�W�K�^_W

^ ^^ 8 88 ! � � 8 88 # ^cV+X ^ ^^ 8 88 ! � � 8 88 # �JLK+M/qUp ^cNQNQP-q#^cp ^cb l�pRPFW�t+X+M�qO\]b l \]V+MOV W�nwt+V+qUW�P-\]V+N � ! % � # ��MUTQM4l+T�\cl \cTQW�PR\]V�^cp]W�\ W�K+M

qO\]N�PRV+Mj^cV+X�NQP-V+MyWQMUT�bfN�\]n�W�K+Max�MOpRX�T�MON�l MOqUW�PF�CMOp Z �EJLK+MjzBt�^cV W�t+b ^cb l�p-P-W�t+X+MaqU\]b l@\]V+MOVCW\cl MUTg^_W�\cT�N/^_T�MHN�PRbfP-p ^_T�p Z NQMUlm^_Tg^_WQMOX YBZ V+PRV+M:W Z X+MOvcT�MUMON�NQ\ WQK+M Z ^_TQM � V+\���V9^cN4W�K+M�l�K�^cNQM�0zBt�^cXuTg^_W�tuT�M�\cl@MUT�^_W�\cT�N�� J K+MUNQM�T�M#^cpL^cV+X PRb9^cv]P-V�^_T Z qO\]b l \]V+MOVCW�N \]n W�K+M`^cV+V+P-K+PRp ^_WQPR\]V\cl MUTg^_W�\cTf^_T�M ,aMUTQbfP-W�PR^cV \cl MUTg^_W�\cTQN��*rL\cT�T�MON�l \]V+X+PRV+v W�\�WQK+M�qO\]bfb tuWg^_WQPR\]VDl@\]N�W�t+pR^_W�M^ ^^ ^ ^^ � ^ ^^ ^ ^^ �]��WQK+Myl�K�^cNQM�0 z{t�^cXuT�^_W�tuT�M1\cl MUTg^_W�\cT�N nw\]pRp-\�� ^ T�MOpR^_W�PR\]V

8 88 ! 8 88 # � 8 88 # 8 88 ! �� �

JLK+M T�\{\cW 0 bfM#^cV90 NQz{t�^_T�M1�_^cpRt+MUN � N}Wg^cV+X�^_T�X X+MU�uPR^_W�PR\]V �H\]n�W�K+M l�K�^cNQM�0 z{t�^cXuTg^_W�tuTQM \cl@M:Tg^ 0W�\cTQNH^_T�M� � ! ! � 8 88 # ! � � � 8 88 ! � # � � # ! � 8 88 ## � � � 8 88 # � # �JLK+M,aMOP-NQMOV Y MUTQvft+V+qOMUTQW�^cPRVCW Z l+T�P-V+qOP-l�p-M nw\]pRp-\���N n T�\]b W�K+M qO\]b b tuW�^_W�PR\]V9T�MOpR^_W�PR\]V�^cN

� � ! � � # ��-�

� \cT W�K+MjqU\]K+MUT�MOVCWaN�Wg^_WQMyW�K+Mkl�K�^cNQM1N}lm^cqOMjl�p-\cWHP-N�NQK+\���V`PRV�x�v]tuT�M 2 �

� \cTH^sqO\]K+MUTQMOV WHN�Wg^_W�MkW�K+MjbfM#^cV l�K+\cW�\]V`V t+b Y MUT2P-N� � �� � � � #( �

Page 27: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��������� � ��� � � ��� � � � � � � ����� � �� ��� � � � � ����

^cV+X�WQK+MjN�W�^cV+X�^_T�X`X+MU�{P ^_W�P-\]V�PRN� � � � "! � 8 88 ! � # � � 8 88 # � #��K+MUT�MyW�K+M zBt�^cXuTg^_W�tuT�My\cl@MUT�^_W�\cT�N�^_T�MjT�MUp ^_W�MOX YBZ� 8 88 ! � ���� �� � 8 88 # � ��� � �JLK+M NQP-v]V�^cp 0'W�\�0 V+\]P-NQMyT�^_W�PR\ \]n!W�K+MyqO\]K+MUT�MUV WaN}Wg^_W�MyPRN� � �� �� � � #

� � � � �

JLK+MHqU\]K+MUT�MOVCW�N�W�^_W�M � � K�^cN4^jbfMO^cVf^cb l�p-P-W�t+X+M qO\]b l�p-M�� VBt+b Y MUT � MUPRv]MOVC�c^cp-t+M � ��K+PRqgK PRN4T�MUl+T�MON�MOV WQMOX`^cN/WQK+MHl�K�^cNQ\cT � � � � � � � T�\cW�^_W�PRV+v��P-WQKfn T�MOzBt+MOV+q Z � � � � T�MOpR^_W�MONW�\�W�K+M qOp ^cNQN�PRq#^cpex�MOp-X5^cb l�pRPFW�t+X+M PRV WQK+M pRP-bfP-W�� J K+MsqO\]K+MUT�MOVCW1N}Wg^_W�M l�K�^cNQM�0 zBt�^cXuTg^_W�tuT�M\cl MUTg^_W�\cT�N K�^#�CMjT�bfN��_^cpRt+MON W�K�^_W�\ Y M Z W�K+Myt+V+qOMUTQW�^cPRVCW Z T�MOpR^_W�PR\]V.�

� � ! � � # �-�

(�&

Page 28: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+M qO\]K+M:T�MOVCW2N�Wg^_WQMjP-N W�K t+N2q#^cp-pRMOX�^sbfP-V+PRb t+b t+V+qOMUT�Wg^cPRVCW Z N}Wg^_W�M#�

JLK+MjTQMOp ^_W�P-\]V+NQK+P-l Y MUW ��MUMOV�W�K+MjqO\]K+MUT�MOVCWaN�W�^_W�M ^cV+X�W�K+M \cl MUTg^_W�\cTQN�nw\cT�qUMON � 8 88 ! � � � � 8 88 # � �

� V W�K+MyqO\]K+MUT�MOVCW2N}Wg^_W�M � � � ��WQK+MyT�b N��c^cp-t+MON�\]n�W�K+Mal�K�^cNQM�0 z{t�^cXuTg^_W�tuTQMON2\cl@M:Tg^ 0W�\cTQNH^_T�MyMOzBt+P-�_^cpRMOVCW��

� � ! � � # �� �

� V8W�K+M l�K�^cNQM N�lm^cqOM l�pR\cWaW�K+P-NyP-Ny^ V+\]P-NQM qOP-TQqOpRM \]n�Tg^cX+PRt+N �� �1JLK+MUT�M M��uPRN�WkMOzBt�^cp

t+V+qOM:TQWg^cPRVCW�P-MONLPRV M#^cqgK�zBt�^cXuTg^_W�tuT�M#��I bfM#^cN�tuT�MObfMOVCW�l@M:T�nw\cT�bfMOX�\]V9W�K+PRN�qU\]K+MUT�MOVCWHN}Wg^_W�M��\]t+p-X Y M NQt Y �}MOqUW`WQ\ W�K+M bfPRV+P-b t+b M:TQT�\cT�^cN�NQMUW YBZ z{t�^cVCW�t+b bfMOqgK�^cV+PRqON�^cV+X W�K+Mt+V+qOM:TQWg^cPRVCW Z l+TQPRV+qOPFl�pRM#�

IaV+\cWQK+MUT ��^ Z W�\ �uP-M�� W�K+M�bfP-V+PRb t+b t+V+qOMUT�Wg^cPRVCW Z \]n W�K+M�qO\]K+MUT�MOVCW N}Wg^_W�M�PRNW�KuTQ\]t+v]K�W�K+M9V t+b Y MUT \cl MUTg^_W�\cT��8JLK+M VBt+b Y MUT \cl@MUTg^_WQ\cT nw\cT ^8qU\]K+MUT�MOVCW N}Wg^_W�M9nw\]pRp-\���NW�K+MLSe\]P-NQNQ\]V X+PRN�W�T�P Y tuW�P-\]V.��J K+P-N�X+PRN�WQTQP Y tuW�P-\]V K�^cNeW�K+MLbfP-V+PRb t+b t+V+qUMUTQWg^cP-V W Z nw\cT4^av]P-�CMOVbfMO^cV��_^cpRt+M#�

� \cWQMHW�K�^_W�nw\cT�W�K+M2�_^cqOt+t+b N�W�^_W�Mc�9��K+PRqgK PRN�W�K+MazBt�^cV WQt+b&MOz{t+PF�c^cp-MOVCWL\]n�V+\ x�MOp-X>�W�K+M:T�MHP-N�^cpRN�\ bfP-V+PRb t+b t+V+qOMUTQW�^cPRVCW Z �EJLK+PRN'��\]t+pRX Y MHNQK+\���V9^cN�^cVfM:TQT�\cT�qUP-T�qOp-M�\]nTg^cX+PRt+N�� qUMOV WQMUT�MOX8\]V�W�K+M \cT�PRv]P-V�\]n"W�K+Myl�K�^cNQM N�lm^cqOM l�p-\cW���oE�CMOV`W�K+Mj�_^cqOt+t+b x�MUpRX`P-N2NQt Y �}MOqUWW�\ ��t+qUW�t�^_W�P-\]V+NO��P � M#�4PFW PRN2^ V+\]PRN Z �_^cqOt+t+b2�

��� � � ��!#�����$%7���(�#��)��'*

JLK+MfzBt�^cV W�t+b bfMOqgK�^cV+PRqO^cp4t+V+qOM:TQWg^cPRVCW Z l+T�P-V+qOP-l�p-M T�M ��MOq:W�MOX YBZ � � ! � � # ��-

T�MUz{t+P-TQMON/^cVsMUTQT�\cT/qOP-TQqOpRM \]n@^_T�MO^yW�K�^_WEK�^cN�^_WEp-M#^cN�W �-

t+V+P-WQN4\]n@M:TQT�\cT�� � \cTEbfPRV+P-b t+b M:TQT�\cT\]V+M���\]t+p-X�NQt+v]v]MON}W � � ! � � # �

� t+V+P-WQN ^cNal+T�MOX+P-qUW�MOX W�KuT�\]t+v]K W�K+M WQT�M#^_W�b MOV Wy\]VW�K+M qO\]K+MUTQMOV W/N�Wg^_W�M���J K+M�t+V+qOMUTQWg^cP-V W Z ��\]t+p-X Y M�bfPRV+P-b t+b Y tuW���t+q:W�t�^_W�PR\]V+N4\]n �

� ��\]t+pRX^cp �L^ Z N�K�^#�CMkW�\ Y M X+M#^cpFW���P-W�K.�

I�V+M���bfMUW�K+\BXsW�\ Y M#^_W4W�K+MHp-PRbfPFWg^_W�PR\]V+N�\]n WQK+MHt+V+qOMUT�Wg^cPRVCW Z l+T�P-V+qOP-l�p-M�/ N/NQ\1q#^cp-pRMOXzBt�^cV W�t+b pRP-bfP-W P-N�V+\�� NQK+\���V.� JLK+M � M Z N�WQT�^_W�MOv Z Y MOK+P-V+X W�K+PRN�bfMUWQK+\{X P-N�W�\�Wg^ � M(%(

Page 29: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

^cXu�_^cV W�^cv]M�\]nuW�K+M�z{t�^cVCW�t+b�nw\cT�b t+pR^_W�PR\]V \]nuW�K+M�x�MUpRX.��JLK+MUT�M ^_T�M/W ��\kNQMUWQNe\]nm\ Y N�MUTQ�_^ Y pRMON� \cl MUTg^_W�P-\]V+N �EW�K�^_WLqO^cV Y MabfM#^cNQtuT�MUX�\]V�^cV Z NQPRV t+NQ\]PRX�^cp-p Z �_^_T Z PRV+v1x�MOp-X.(EW�K+M2l�K�^cN�Mj^cV+X^cb l�p-P-W�t+X+M�\cTeWQK+M N�PRV+M ^cV+X qO\]N�PRV+MLz{t�^cXuTg^_WQtuT�MLqO\]b l@\]V+MUV W�N���J K+MLt+V+qOMUT�Wg^cPRVCW Z l+T�PRV+qOPFl�pRMnw\cT�qUMOX ^5bfP-V+PRb t+b t+V+qOM:TQWg^cPRVCW Z \]V*W�K+MUP-T9l+T�\BX+t+qUW#� Y tuW � �kJ \]V*WQK+MONQM�lm^_Tg^cbfMUWQMUT�NP-V+X+P-�uP-X+t�^cpRp Z � �}V`WQMUT�bfN�\]n"l�K�^cNQM1N�lm^cqOM_� W�K+M1bfP-V+PRb t+bdMUTQT�\cT2PRN2qO\]Vux�V+MUX8WQ\9^cV8^_T�M#^f\]n�-��I�NQz{t+MUMOhOMOX N�Wg^_W�M �HP-pRp � NQz{t+MUMOhOM�/mW�K+M MUTQT�\cTa^_T�M#^fPRVCW�\ ^cV8MOp-pRP-l�N�M W�K�^_W ��PRp-p�b9^cP-V W�^cPRV

W�K+M�TQMOz{t+PFT�MOX bfPRV+P-b t+b t+V+qOM:TQWg^cPRVCW Z MUTQTQ\cTE^_T�M#^ Y tuW$��PRpRpBV+\cW � MOMUlsP-W"X+PRN�WQTQP Y tuW�MOX MOzBt�^cpRp ZP-V Y \cW�K5\]n4W�K+Mfz{t�^cXuT�^_W�tuT�MON���J!\�Wg^ � Mf^cXu�_^cV W�^cv]Mf\]n/W�K+P-N1z{t�^cVCW�t+b N�Wg^_W�Mc�!\cl@MUTg^_WQPR\]V+N��PRp-p Y Mjl MUT�nw\cT�b MOX�\]V+p Z \]V�W�K+M zBt�^cXuTg^_W�tuT�M���P-W�K�T�MOX+t+qOMOX�t+V+qUMUTQWg^cP-V W Z MUTQT�\cT��

JLK+MHN�z{t+MOMOhUPRV+v1qO\]V+qUMUl+W�qO\]t+p-Xf\]V+p Z K�^#�CM Y MOMOVfX+MU�CMUpR\cl@MUX7�HPFW�Kf^jz{t�^cVCW�t+b �uPRM��\]naW�K+M`MUpRMOqUW�T�\]b9^cv]V+MUW�P-q�x�MOp-X.� ~{z{t+MOMUhOPRV+vDPRNf^5WQ\cWg^cpRp Z zBt�^cV WQt+b l�K+MOV+\]bfMOV+\]V.� J K+Ml�K�^cNQMjN�lm^cqOMyl�pR\cW�nw\cTa^sv]MUV+MUTg^cp�NQz{t+MUMOhOMOX�N�W�^_W�MjP-N�N�K+\���V`PRV�x�v]tuT�M�39�

����������� ��� � � ��� � � � � � � ��� ����� ��� � � � ����

� V WQK+PRNsx�v]tuTQM � � ! � � # �-

Z MUW�� � � ! � �� �HK+P-pRM � � # � �

� � ��K+PRp-M�\]V+MzBt�^cXuTg^_W�tuT�M1P-N�T�MUX+t+qOMOX PRV`MUT�T�\cT2W�K+M1\cWQK+MUTaz{t�^cXuT�^_W�tuT�M1P-N�l+T�\cl \cTQW�PR\]V�^cp-p Z MOV+K�^cV+qOMUX Y Z( #

Page 30: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

MUT�T�\cT��H�kV+M b t+N�WH\]V+p Z t+NQM PRV+nw\cT�bf^_W�PR\]V�T�MOqO\cT�X+MUX P-V WQ\9\]V+M1z{t�^cXuTg^_WQtuT�Mc� \ Y �uP-\]t+NQp Z W�K+MzBt�^cXuTg^_W�tuT�M��HPFW�K�TQMOX+t+qOMOX�zBt�^cV W�t+b MUTQTQ\cT��

� t�^cVCW�P-Wg^_WQP-�CMOp Z N�l M#^ � P-V+v+�HNQzBt+MOMOhOMOX�N�Wg^_W�MUN ^_T�M�T�MUl+T�MON�MOV WQMOX PRV zBt�^cV W�t+b b M�0qgK�^cV+PRqUN YBZ W�K+M�NQz{t+MUMOhOMOX \cl@M:Tg^_W�\cT4PRVCWQT�\{X+t+qUMOX Y Z ~BW�\]p-MUT � � ����� � � �� ��� � ��J K+P-N/NQzBt+MOMOhOM\cl MUTg^_W�\cT�PRN M��ul+TQMONQNQMOX8^cN�^snwt+V+q:W�PR\]V`\]n�W�K+Mjq:T�M#^_W�P-\]V�^cV+X`^cV+V+P-K+PRp ^_WQPR\]V�\cl MUTg^_W�\cTQN��

~ ~~ � & � ��� � �� � & �g^ ^^ # � &_^ ^^ # � %��K+MUT�M & � � ��� PRN�^sqU\]b l�pRM���V t+b Y MUT��

JLK+M N�z{t+MOMOhUM \cl@M:Tg^_W�\cT�q#^cV�WQTg^cV+N�nw\cT�b W�K+M qO\]K+M:T�MOVCW2N�Wg^_WQM

� � � � ! � � � # � � � ���%P-V W�\ W�K+MyNQz{t+MOMUhOMOX�N�Wg^_WQM

%& � � ! � ��W ��� � � Z � � � # � �:W ��� � � Z �

JLK+MjN�z{t+MOMOhUM1\cl@MUT�^_W�\cT�^_WQW�MOV t�^_W�MON�\]V+MjqO\]bsl@\]V+MOVCWH\]n�W�K+MyTQ\cWg^_W�MOX�qO\]b l�pRM���^cb l�pRPFW�t+X+M^cNLP-W�^cb l�p-P-x�MON�W�K+Mk\cW�K+M:THqO\]bsl@\]V+MOVCW���I N�z{t+MOMOhUPRV+v n ^cq:W�\cT � � & � N�l@MUqOP-x�MON W�K+MyX+MOvcT�MOM\]n/WQK+MONQMf^cq:W�PR\]V+N�� J K+MsNQz{t+MUMOhOM \cl MUTg^_W�\cTyl@M:T�nw\cT�bfNj\]V W�K+MsqUT�M#^_W�P-\]V5^cV+X5^cV+V+P-K+PRp ^_WQPR\]V\cl MUTg^_W�\cT�N�^cN NQK+\���V Y MUpR\���

� Z t+NQMj\]n!W�K+My\cl@MUT�^_W�\cTHP-X+MOVCW�P-W Z �

� ��� � � � ��� � � � ��� % �� � � #��� ��� % ��� % � � � � � � �

~ ~~ � & � ^ ^^ ~ ~~ � & � *^^^ �$��� � ^ ^^ � &� � � � ^ ^^ � & & ���� � � ^ ^^ � & # & �+ �� � ^ ^^ � & # & # �

- �� � � � �

*^^^ � � � & & ���� � � & & � � #

- �� � � � � � ^ ^^ � & � & � & & � �

+ �� & � & & � � #

0 �� � � � �

*^^^ � � � � & � #��� � � & �

- �� � � � � � ^ ^^ � & � & � & � #

+ �� & � & � 0 �

� � � � �*^^^ � � � � & � #

��� � � & � - �� � � � � � ^ ^^ &

� & � � � & � � � & � X+ �� � & ��0 �� � � � �

*^^^ � �� � � � � � � � � � � � � � � ^ ^^ &� & � � �� � � � � � � � � � � � � �

~ ~~ � & � ^ ^^ ~ ~~ � & � ^ ^^ � � � � � � � � ^ ^^ � ��� � � � � � � �� V�WQK+M N�^cbfMyb9^cV+V+MUTO�

~ ~~ � & � ^ ^^ ~ ~~ � & � *^^^ � � � � � � � � ^ ^^ � � ��� � � � � � � � �( "

Page 31: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+M NQzBt+MOMOhOMj\cl@MUT�^_W�\cTHqO^cV Y MyM��ul+TQMONQNQMOX�P-V�W�M:T�bfN \]n!P-WQN�qO\]V+v��}t+vC^_W�M#(

~ ~~ � & � �~~~ � ! � & � �~~~ � � & � �JLK+PRNLl+T�\cl@M:TQW Z X+MOb \]V+N�WQTg^_W�MUN W�K�^_W W�K+MyNQz{t+MUMOhOM1\cl MUTg^_W�\cT�PRN�^st+V+PFWg^_T Z \cl@MUT�^_W�\cT��

JLK+M N�z{t+MOMOhUMOX`N�Wg^_WQM ��PRpRp>N}W�PRp-p Y M1^ bfPRV+P-b t+b&t+V+qOMUTQW�^cPRVCW Z N�Wg^_WQM

� � ! � � # �- %Y tuW M#^cqgK z{t�^cXuTg^_WQtuT�M1��PRp-p Y M MOPFW�K+MUT qO\]b l+T�MON�NQMOX \cT M��ulm^cV+X+MOX.�fJ K+M l�K�^cN�\cT1N�W�P-pRpeK�^cN

W�K+MyN�^cbfMyqO\]b l�p-M���^cb l�p-P-W�t+X+M

� 8 88 ! � � � � 8 88 # � %Y tuW�W�K+M * | ~��c^cp-t+MONH\]n�W�K+M zBt�^cXuTg^_W�tuT�MjMUTQT�\cT�\cl@M:Tg^_W�\cT�N �HP-pRp>NQqO^cpRM1^cN

� � ! �� � � � � � # �

� � �W�\sqgK�^cV+v]MjW�K+Mjb9^cv]V+P-W�t+X+Mk\]n!WQK+Myl�K�^cNQ\cT��%� V�W�M:T�bfN \]n�l�K+\cW�\]V`V t+b Y MUTO�

� � �� � � � # � � � � � # � � ��

� ���� ��� � � � � � � � � ��� � � � � � � � ���� # � � � � � � # � � � � � � � # � � ���

W�K+M�* | ~�M:TQT�\cTkPRV`l�K+\cWQ\]V V t+b Y MUTa�_^cpRt+M PRN2�_^_T�PRMOX.� � Waq#^cV Y M M#^cN�PRp Z �CMUT�PFx�MOX8W�K�^_Wanw\cThOM:T�\�NQzBt+MOMOhOP-V+v � � � �:�4WQK+M�bfMO^cV ^cV+X N}Wg^cV+X�^_T�X X+M:�uP ^_WQPR\]V \]n W�K+M l�K+\cW�\]V V t+b Y MUT\cl MUTg^_W�\cT T�MOX+t+qOMyW�\sWQK+M N�^cbfMa�_^cpRt+MONH^cN�v]PF�CMOV`nw\cTH^sqO\]K+M:T�MOVCWaN�Wg^_W�M��

� V8W�K+M l�K�^cNQMsN}lm^cqOMsl�p-\cW#�@W�K+M MOpRp-P-l�NQM �HP-pRp Y M \cT�PRMOVCW�MOX ^_Wy^�qOM:TQWg^cPRV�^cV+v]pRM���P-W�KT�MUN�l@MOq:WaW�\ W�K+M qO\]bsl�pRM��`^cb l�pRPFW�t+X+M \]n"WQK+M1l�K�^cNQ\cT��2JLK+PRN2^cV+v]pRM ^cV+X`W�K+M N�q#^cpRP-V+v9n ^cqUW�\cT��PRp-p@�c^_T Z ��P-W�K�W�K+MyNQz{t+MOMUhOPRV+v l+TQ\{qOMON�N��

JLK+MyN�l@MOqUP ^cp�q#^cNQM��HK+MOV�W�K+Mjb PRV+\cT�^ �+P-N \]n�W�K+MyMOpRp-P-l�NQMjpRPRV+MUN�tul-�HPFW�K�W�K+Mkl�K�^cNQ\cT^cb l�p-P-W�t+X+M�P-Neq#^cpRp-MOX l�K+\cW�\]V90 V t+b Y MUT4NQz{t+MUMOhOPRV+v���I l�K+\cW�\]V90 VBt+b Y M:T 0 NQzBt+MOMOhOMUX9N�Wg^_W�M�K�^cNNQbf^cpRpRM:T�t+V+qOMUTQWg^cP-V W Z PRV W�K+MLTg^cX+P ^cp{X+P-T�MOq:W�PR\]V.�EJLKBt+N�W�K+MLl�K+\cW�\]VsV t+b Y MUT4K�^cN Y MOMOVsb9^cX+Mp-MONQNEt+V+qOMUTQWg^cP-V.�$�}V W�K+PRN�N�W�^_W�M � � � � �� � NQ\+�CqO\]b lm^_TQMOX1��P-W�K W�K+M qO\]K+MUT�MUV W/N�Wg^_W�Mc� ^��NQt Y�� Se\]P-NQNQ\]V � l�K+\cWQ\]V V t+b Y MUT4X+PRN�WQTQP Y tuW�P-\]V1��PRpRp+M��+PRN}W�� � VsW�K+M�pRPRb P-W#�_WQK+M�MOp-pRPFl�NQM W�Tg^cV+N 0nw\cT�b N�PRVCW�\ ^ TQPRV+v MOV+qOPFT�qOpRP-V+v WQK+MyqU\]b l�pRM�� l�p ^cV+M#�Eikt+MaW�\ W�K+Mkt+V+qOMUTQWg^cP-V W Z T�MUp ^_W�P-\]V+NQK+P-lY MUW ��MOMOV8l�K+\cW�\]V8VBt+b Y MUTy^cV+X�l�K�^cNQM W�K+M1l�K�^cNQM Y MOqU\]bfMONabf\cT�Myl+T�\cl@\cT�W�PR\]V�^cp-p Z t+V+qOMUT 0Wg^cP-V.�eIap-W�K+\]t+v]K"��M2X+\jV+\cW�PRVCW�MOV+XfWQ\jl�tuT�NQt+MHVBt+b Y M:T�NQzBt+MOMOhOMOX N�W�^_W�MONO�CW�K+MONQMHN�Wg^_W�MON/^_T�MV+\cW+��P-W�K+\]tuWkP-V WQMUT�MON�W�� �aV+M PRNQN�t+M W�K�^_W2V+MOMOX+NynwtuTQW�K+MUTkT�MON�M#^_T�qgK�P-N2W�K+M pR\���MUTkpRP-bfP-W�W�K�^_W( �

Page 32: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

q#^cV Y Ms^_W�Wg^cPRV+MOX Y Z V t+b Y MUTyNQz{t+MUMOhOPRV+v��+� V \cW�K+MUT+��\cT�X+NU�@W�K+M5�HP-XuW�K \]n�WQK+M1T�PRV+v b t+N�WY MjP-V �CMON}W�PRvC^_W�MUX.�

ILWj^cpRp�\cW�K+MUT ^cV+v]pRMUNyW�K+M NQzBt+MOMOhOMOX5N}Wg^_W�M �HP-pRpeM��uK+P Y P-Wk�_^_T�PR\]t+NypRM:�CMOpRNy\]n/V t+b Y MUT^cV+X l�K�^cNQM NQz{t+MOMUhOPRV+v���JLK+MONQM N�Wg^_W�MUNEbf^ Z l@\]NQNQMUNQN4MUP-W�K+MUTENQt Y�� Se\]P-NQNQ\]V \cTENQtul@MUT � Se\]PRNQNQ\]V� � � � � �� � �El�K+\cW�\]V9V t+b Y MUT�N�W�^_W�PRN�WQPRqON���JLK+MONQMaN}Wg^_W�MON�^_TQM � V+\��HV ^cN4z{t�^cXuTg^_WQtuT�M�0l�K�^cNQM�0 NQzBt+MOMOhOMOX N�Wg^_W�MON��5~{PRV+qUM�^cV Z x�MOp-X q#^cV Y M NQM:lm^_Tg^_W�MOX�PRVCW�\8P-W�N W ��\8z{t�^cXuT�^_W�tuT�MONY Z b t+p-W�PFl�pRPRqO^_W�PR\]V ��P-W�K*^DNQPRV+M8\cT qO\]N�PRV+M � pR\Bq#^cpH\]NQqUPRpRpR^_W�\cT�^_W9W�K+M�T�P-v]K W l�K�^cNQM �6�HW�K+MzBt�^cXuTg^_W�tuT�M ��P-W�KfTQMOX+t+qOMOX�t+V+qOMUTQW�^cPRVCW Z bf^ Z Y MaqgK+\]NQMOV.� � W�b t+N�W Y MaV+\cWQMOX9W�K�^_W�l@M:T�nwMOqUWzBt�^cXuTg^_W�tuT�M�0'l�K�^cNQM�0 NQz{t+MOMUhOPRV+v q#^cV+V+\cW Y M \ Y Wg^cPRV+MUX.� �}Vs\cT�X+MUT4W�\yTQMOX+t+qOM�WQK+M�V+\]P-NQMHP-Vs\]V+M\]n WQK+M2z{t�^cXuTg^_WQtuT�MON/W�\jhOMUT�\1WQK+M�l�K+\cW�\]V9V t+b Y MUT ��\]t+pRXfK�^#�CMHW�\1v]\yW�\1P-Vux�V+P-W Z ^cV+XfWQKBt+NW�K+MyMOV+MUTQv Z T�MUz{t+P-TQMOX ��\]t+p-X Y MjPRVux�V+PFW�M#(

� � �� � � � # � � � � � # � � � �JLK+PRN4NQt+v]v]MON�W�NEW�K�^_W4K+PRv]KfP-V W�MUV+NQP-W Z p ^cNQMUTQN'��PRp-p Y M�T�MUz{t+P-TQMOXfPRVs\cT�X+MUT4W�\jl+T�\BX+t+qOM2M � qOPRMUV WzBt�^cXuTg^_W�tuT�MyNQz{t+MUMOhOPRV+v��

JLK+M`�_^_T�PR\]t+N9bfP-V+PRb t+b t+V+qOMUTQWg^cP-V W Z N}Wg^_W�MON ^_T�M�N�K+\���V PRV x�v]tuT�MON3�]^5^cV+X4� Y �S4PRqUW�tuTQMOX`^_T�MaW�K+Mal�K�^cNQMjN�lm^cqOMkl�pR\cW�N ^cV+X�W�K+MkqO\cTQT�MON}l@\]V+X+PRV+v MOpRMOq:WQT�PRqax�MOp-X�t+V+qOM:TQWg^cPRVCW Z �

(��

Page 33: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��������� � ��� � � � � � � � � � � � � � � ��� ��� ����� � � � ��� � �� � � ���� � �� �� � � �

( �

Page 34: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��������� � ��� � � � � � � � � � � � � � � ��� ��� ����� � � � ��� � �� � � ���� � �� �� � � �

( �

Page 35: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+MfT�MON}Ws\]n�W�K+P-N1W�K+MONQP-N PRN qO\]V+qOM:T�V+MOX ��P-WQK�zBt�^cXuTg^_W�tuT�M�0 l�K�^cNQM�0 NQz{t+MUMOhOMOX N�W�^_W�MONTg^_WQK+MUT1W�K�^cV W�K+M9V t+b Y MUT 0 NQzBt+MOMOhOMOX�N�Wg^_WQM#��JLK+MUT�M ^_TQMfNQMU�CMUT�^cp4T�M#^cN�\]V+N nw\cT ^`qgK+\]PRqOM9\]n\]V+MfW Z l Mf\��CMUT W�K+Mf\cW�K+M:T�� � \cT v]MOV+MUTg^cp4l�tuTQl@\]NQMUNO�E^`NQz{t+MOMUhOMOX�N�Wg^_W�M9P-N ^`z{t�^cXuTg^_WQtuT�M�0l�K�^cNQM�0 NQzBt+MOMOhOMOX5N}Wg^_W�M#� � o4�CMUV V t+b Y MUTyNQzBt+MOMOhOMOX N�Wg^_W�MUNyN�z{t+MOMOhUM W�K+M zBt�^cXuTg^_W�tuT�MON�� � IzBt�^cXuTg^_W�tuT�M�0'l�K�^cNQM�0 NQz{t+MOMUhOMOX*N�Wg^_W�M�q#^cV Y M�t+NQMUnwt+p�nw\cT l�K�^cNQM`NQMUV+NQP-W�PF�CM�b M#^cNQtuT�MOb MOV WQN��JLK+M l+T�P-b9^_T Z PRVCW�MUTQMON�Wanw\cT2WQK+PRN�TQMONQM#^_T�qgK�W�K+MON�PRN/�L^cN�PRV`W�K+MjX+MU�CMOp-\cl�bfMOVCWa\]ne^ NQzBt+MOMOhOMUXx Y MUT�\cl+W�PRq/v Z T�\]NQqU\cl@M#��JLK+M�v Z T�\]N�qO\cl@M�P-Ne^2l�K�^cNQM�NQMOV+N�P-W�PF�CM�X+MU�uP-qOM Y ^cNQMOX \]V W�K+ML~u^cv]V�^cqM� MOqUW��EJLK+Mav]MOV+MUTg^_WQPR\]Vf\]n>NQzBt+MOMOhOP-V+v q#^cV Y Ma^_l+l�p-PRMOXfWQ\ NQMU�CMUTg^cpml�K�^cNQM2NQMUV+NQP-W�PF�CMa\cl+W�PRqO^cpl+T�\BqOMONQN�MON��

( �

Page 36: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

# �

Page 37: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� � <�= �!�>�>?!�'�!; �'� 0H� 34����

4 �8����� ��������)���8�:9 �"!#���$��%&�'�(��������*

� V5zBt�^cV W�t+b bfMOqgK�^cV+PRqON ^`qU\]K+MUT�MOVCW N�Wg^_W�MfP-N v]MOV+MUTg^_WQMOX5W�KuT�\]t+v]K�^cV5\cl@MUT�^_W�PR\]V\]V�W�K+M N�l MOqOPR^cp�V t+b Y MUTHN�Wg^_W�M_�uW�K+Mj�_^cqOt+t+b N�Wg^_W�M#�EJLK+Mj�_^cqOt+t+b N�Wg^_W�MyPRN t+NQMOX�WQ\sT�MOpR^_W�MW�K+Myv]MOV+MUT�^cp�V t+b Y MUT�N�Wg^_W�MkW�\ W�K+M qO\]K+M:T�MOVCW2N�Wg^_WQMyW�KuTQ\]t+v]K�W�K+MyX+PRN�l�pR^cqOMObfMOVCW2\cl MUTg^_W�\cTO�i ii � ���4J K+MjqO\]K+MUT�MUV WHN�Wg^_W�MyPRN�v]MOV+MUTg^_W�MUX YBZ W�K+Myl+T�\{qUMONQN

� � �iii � � � � � �

JLK+M nwt+p-p�M��ul+T�MON�NQPR\]V`nw\cT�W�K+MyX+PRN�l�pR^cqOMObfMOVCW2\cl MUTg^_W�\cT�PRN

i ii � � � � � � �� � � # � � ^ ^^ � � ��� ^ ^^ �

JLK+PRN \cl@MUTg^_WQ\cT#�!p-P � MsWQK+M&,k^cbfPRpFW�\]V+P ^cV nw\cT ^�qU\]K+MUT�MOVCW N�Wg^_W�M_�"PRN TQMUl+T�MONQMUV W�MUX Y ZP-V`W�MUT�bfNH\]n"W�K+M qUT�M#^_WQPR\]V8^cV+X8^cV+V+PRK+P-p ^_W�P-\]V�\cl@MUT�^_W�\cT�N ^ ^^ ^cV+X�^ ^^ � � n"W�K+M M��ul \]V+MOVCW�P ^cp�PRNM��{lm^cV+X+MOX`P-V�^ J"^ Z p-\cT NQMUT�P-MON�W�K+MUNQM \cl MUTg^_W�\cTH^_l+l@M#^_TH^cN�WQMUT�bfNL\]n"MU�CM:T Z \cT�X+MUT��

� V�W�K+M NQzBt+MOMOhOMj\cl@MUT�^_W�\cT#�

~ ~~ � & � ��� � � �� & � ^ ^^ # � �

� & ^ ^^ � � %& � � ���

W�K+M qUT�M#^_WQPR\]V ^cV+X ^cV+V+P-K+PRpR^_W�PR\]V�\cl@MUTg^_WQ\cT�N`^_T�M T�MUl+T�MUNQMOVCW�MOX YBZ z{t�^cXuT�^_W�PRq8W�MUT�b N�� IJ"^ Z p-\cT N�MUT�PRMUN1M��ulm^cV+N�PR\]V5\]n/W�K+MUNQMfNQzBt�^_T�MOX5M��{l@\]V+MOVCW�P ^cp-N p-M#^cX+N W�\`\]V+p Z W�MUT�bfNj\]n�MU�CMOV\cT�X+M:T��HJLK+PRNan ^cq:WapRM#^cX+N�W�\ W�K+M1W�M:T�bfPRV+\]p-\]v Z �}W ��\fl�K+\cW�\]V�N�Wg^_WQM ���HJ ��\fl�K+\cW�\]V+NaP-b l�p ZP-V W�M:Tg^cqUW�P-\]V ^cbf\]V+v W ��\�\cTfb \cT�M9x�MOpRX+N�� I v]MOV+MUT�^cp�,k^cbfP-p-W�\]V+PR^cVDq#^cV Y M3��TQP-WQW�MUV W�\X+MON�qUT�P Y MjW�K+MjMOV+MUT�v Z \]n!WQK+M PRVCW�MUT�^cqUW�PRV+v x�MOpRX+N

, ,,�� ��� � ^ ^^ ! Y YY � ^ ^^ ! Y YY � %��K+MUT�M Y YY PRNy^cV \cl@MUTg^_WQ\cT \cTkl+T�\BX+t+qUW1\]n4\cl@MUTg^_WQ\cT�N � PRnENQMU�CMUTg^cpex�MOp-X+N1^_T�M PRVC�C\]p-�CMUX �k^cV+X� PRN ^�qO\]tul�p-PRV+v�qO\]V+N}Wg^cV Wjl+T�\cl@\cT�W�PR\]V�^cp�W�\�P-V WQMOv]MUT � ^cV+X W�\�W�K+M V+\]V+pRPRV+MO^_T�P-W Z \]n�W�K+MN Z N�W�MOb ��K+PRqgK&�HP-pRpmNQMUTQ�CM�W�\ qO\]tul�p-MHW�K+MHx�MUpRX+N����D^cpRp-N�� � � � � � ��� � �K�^cN�X+MONQqUTQP Y MUX WQK+PRN,k^cbfP-p-W�\]V+PR^cV PRV�WQMUT�bfN \]n�W�K+MjV+\]V+pRP-V+M#^_THN�t+NQqOMUl+W�P Y PRp-P-W Z \]n�W�K+M b P �+P-V+v b9^_W�MUT�PR^cp

, ,, � � � W ! Z � ^ ^^ # ��� W ! Z ^ ^^ # � %# &

Page 38: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��K+MUT�M � P-N2MOP-WQK+MUT � \cT + ��J K+MUNQM1l+T�\{qUMONQNQMONaqO^cV Y M ^cqOqO\]bsl�pRPRN�K+MOX YBZ V+\]V+pRPRV+MO^_T�P-W�P-MON2\]nNQMUqO\]V+X`\cT W�K+P-T�X�\cT�X+MUT�� � \cT

� � % � W # Z � ��U W # Z� + % � W X[Z � � # U W X[Z

��K+MUT�M�� PRNkW�K+Msl�t+bsl x�MOpRX.� JLK+M N�z{t+MOMOhUPRV+v`lm^_Tg^cbfM:W�MUT��HP-pRp Y Msl+T�\cl@\cTQWQPR\]V�^cp"W�\�WQK+PRNV+\]V+p-PRV+M#^_T�PFW Z ^cV+X�W�K+M p-MOV+vcW�K�\]n"PRVCW�MUTg^cqUP-W�\]V.�

� � � W ! Z �JLK+M�P-V WQMUTg^cqUW�P-\]V ,k^cbfP-p-W�\]V+PR^cV X+MON�qUT�P Y MOX ^ Y \��CM�P-N NQP-bfPRpR^_T W�\ W�K�^_W X+MONQqUTQP Y PRV+v

W�K+MsV+\]V+pRP-V+M#^_T l+T�\BqOMONQN�MON � V+\��HV ^cNjlm^_Tg^cbfM:WQT�PRqs^cb l�p-P-x�q#^_W�P-\]V ^cV+X nw\]tuT 0 �L^#�CMfbfP �+PRV+v��� T�\]b W�K+M M#^_T�pRP-MON�W�W�K+MO\cT�M:W�PRq#^cpkM��{l�pR\cTg^_WQPR\]V \]nyW�K+M�N�z{t+MOMOhUMOX \cT �}W ��\�0'l�K+\cW�\]V � N}Wg^_W�MW�K+MUNQMkV+\]V+pRPRV+MO^_T�l+T�\{qOMUNQNQMON ��MUT�M2�{PRM���MOX�^cN�WQK+MaV�^_W�tuTg^cp@bfMO^cV+N/W�\ qUT�M#^_WQM2W�K+MkbfPRV+P-b t+bt+V+qOM:TQWg^cPRVCW Z N}Wg^_W�MON��

� V8W�K+M�,k^cbfP-p-W�\]V+PR^cV>�W�K+M NQzBt�^_T�MOX \cl@MUTg^_WQ\cT�Ny^_T�M1l+T�\{X+t+q:W�Nj\]neW�K+M \cl MUTg^_W�\cT�Nk\]nW ��\�PRV+X+PF�uPRX+t�^cp!bf\{X+MON�� � T�\]b V+\]V+p-PRV+M#^_Ty\cl+W�P-qONkP-WkPRN � V+\���V WQK�^_WaW�K+MsN Z N�W�MUb \]n'�L^#�CMMOzBt�^_W�PR\]V+N MON}Wg^ Y pRP-NQK+MOX Y Z ^ V+\]V+p-PRV+M#^_T PRVCW�MUT�^cqUW�PR\]V PRN ^ qU\]tul�pRMOX N Z N�WQMOb2�D�aV+M�bf\BX+MP-N1qO\]tul�pRMUX�W�\`WQK+M9\cW�K+MUT�N Y Z W�K+M9V+\]V+p-PRV+M#^_T�PFW Z �`JLKBt+N W�K+P-N1V+\]V+pRP-V+M#^_T�P-W Z MON�Wg^ Y p-PRNQK+MON ^qO\cT�T�MOp ^_WQPR\]V Y M:W ��MOMOVsWQK+M�l�K+\cW�\]V+NePRV W�K+M�W ��\abf\BX+MON���~{zBt+MOMOhOP-V+vjP-Nev]MOV+MUTg^_W�MUX Y Z Wg^ � PRV+v^cXu�_^cV W�^cv]Mj\]n!WQK+PRN qO\cTQT�MOpR^_W�MOX�lm^cPFTH\]n�l�K+\cW�\]V+N��

~{P-V+qOMfW�K+M9zBt�^cXuTg^_W�tuT�M9V�^_W�tuTQM9\]n�NQz{t+MOMUhOPRV+v PRN l�K�^cN�M�X+M:l@MOV+X+MOVCW � z{t�^cXuTg^_WQtuT�MONP-b l�p Z W�MUT�b N�� � X+MOvcT�MOMUN�\]tuWL\]n@l�K�^cNQM��EW�K+MaPRX+MO^cp V+\]V+pRP-V+M#^_T�l+T�\BqOMONQN ��PRp-p@^cpRN�\ Y M2l�K�^cNQMNQMUV+NQP-W�PF�CM#�4J K+P-N N�t+v]v]MON�W�NLW�K�^_WLW�K+Mklm^_Tg^cbfMUWQTQPRqk^cb l�p-P-x�MUT Y ^cNQMUX`\]V�MUP-W�K+MUTLW�KuTQMOMj\cT nw\]tuT�L^#�CM�\cl+W�P-q#^cpBb P �+P-V+v/��\]t+p-X Y M�^av]\{\BX1q#^cV+X+PRX�^_WQM#��J K+M�lm^_T�^cbfMUWQT�P-q�^cb l�p-P-x�MUT!PRN�^Hl�K�^cNQMNQMUV+NQP-W�PF�CMjX+M:�uPRqUM1^cV+X`PFW�P-NHV+\cWH^cV�P-V+K+MUT�MOVCW�p Z V+\]PRN Z X+M:�uPRqUM#�

� V \cl+W�PRq#^cpelm^_Tg^cb MUWQT�P-q l+TQ\{qOMON�NQMON ^�bfMOX+PRt+b l \]NQNQMONQN�PRV+v�^�K+PRv]K�V+\]V+p-PRV+M#^_TQP-W Z PRNl�t+b l MOX � M��+qOPFW�MOX � Y Z \]V+M�\cT W ��\�N�W�T�\]V+v l�t+bsl x�MOp-X+N��5�5M#^ � NQP-v]V�^cp�x�MOpRX+N ^_T�M�^cpRNQ\X+PFT�MOqUW�MUX`W�KuT�\]t+v]K`W�K+M1b MOX+PRt+b2��J K+M1V+\]V+p-PRV+M#^_TQP-W Z qUT�M#^_W�MUN2qO\]tul�pRMUX���^��CM1MUz{t�^_W�P-\]V+NHNQ\W�K�^_WeWQK+M ��M#^ � NQP-v]V�^cpRN�^_T�MLqO\]tul�p-MOX W�\kM#^cqgKs\cW�K+M:TE^cV+X W�K+M�l�t+b l � N ���eJLK+MLV+\]V+pRPRV+MO^_T�P-W�P-MON^_T�MyW�K+M1NQMUqO\]V+X ^cV+X�W�K+P-TQX�\cT�X+MUTaV+\]V+p-PRV+M#^_THNQt+NQqOMUl+WQP Y PRp-P-W�P-MONO��U W # Z�^cV+X�U?WYX[Z �LJLK+M1NQP-v]V�^cp�L^#�CMONH^_T�MjX+MUV+\cW�MOX ��NQP-v]V�^cp � ^cV+X ��PRX+p-MUT ���

JLK+M N�MOqO\]V+XD\cT�X+MUT V+\]V+p-PRV+M#^_T NQt+NQqOM:l+W�P Y P-pRP-W Z PRNjt+NQMOXDPRV�WQK+M \cl+W�P-q#^cpElm^_T�^cbfMUWQT�P-q^cb l�p-P-x�MUT��/� WaqO\]tul�pRMUNj^9NQP-V+v]pRM l�t+bsl WQ\ WQK+M NQPRv]V�^cp!^cV+X P-X+pRMUT�� � I N�l@MUqOP ^cp"qO^cNQM � V+\��HV^cNLX+MOv]MOV+M:Tg^cq Z \{qUqOtuT�N �HK+MOV W�K+Myn T�MOzBt+MOV+qOPRMUN�N�^_WQPRNQn Z W�K+MkqO\]V+X+PFW�PR\]V � � � � � � � ��� � \cT

#�(

Page 39: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

^_l+l+T�\cl+TQP ^_W�Mfl�K�^cNQM b9^_WQq6K+P-V+v�qO\]V+X+P-WQPR\]V+N \]V5W�K+MfW�KuT�MUM&�L^��CMf�CMUqUW�\cT�NO�eW�K+M9N�PRv]V�^cp�^cV+XP-X+pRMUTH^_T�Mj^cb l�pRPFx�MOX Y Z W�K+Mjl�t+b l`^cN�W�K+M Z l+TQ\clm^cvC^_W�M#�

� W P-N ^�l�K�^cN�M�N�MOV+NQP-WQP-�CM9X+MU�{PRqOM Y MUq#^ct+NQM P-W ^cb l�p-P-x�MON \]V+M�zBt�^cXuTg^_W�tuT�Mfl�K�^cN�M�\]nW�K+M NQP-v]V�^cpEb \{X+M��HK+P-pRM P-W ^_WQW�MUVBt�^_W�MUNyW�K+M \cW�K+MUT�� IaV�^cV�^cpR\]v Z \]n/^�l�p ^ Z vcTQ\]t+V+X�N ��PRV+vq#^cV�X+MONQq:T�P Y MjW�K+Mal�K�^cNQMyNQMOV+NQPFW�P-�CMj^cqUW�P-\]V.�EJ K+MkN ��PRV+vs\]NQqOPRp-p ^_W�MUNL^_WH^ qOMUT�Wg^cPRV�n T�MOzBt+MOV+q Z� ��JLK+M2N ��PRV+v1P-N/l�t+NQK+MOX � l�t+b l MOX ��l MUT�P-\{X+PRqO^cpRp Z �"J!\1b9^cP-V Wg^cP-VsW�K+MHN �HP-V+v1\]NQqOP-pRpR^_W�PR\]VsP-WV+MOMUX+NHW�\ Y Mjl�t+NQK+MUX ^_WH^sn TQMOz{t+MOV+q Z \]n � � �%� n!WQK+MjN ��PRV+v1�L^cN�l�t+NQK+MUX ^_W W�K+MyW�\cl`\]n"PFW�N\]NQqUPRpRpR^_W�PR\]V � P � M#�j^_Wy^ qOMUTQWg^cP-V l�K�^cN�M �kPFW+��\]t+pRX ^cb l�p-PRn Z PFW�Nabf\cW�P-\]V.��� nEP-W+��MUTQM l�t+NQK+MUX^_WLW�K+M Y \cWQWQ\]b \]n�P-W�NL\]NQqUPRpRpR^_W�PR\]V � ^_W2� � X+MOvcT�MUMONH\]tuW�\]n�l�K�^cNQM � P-W ��\]t+p-X�X+M#^cbsl�pRPRn Z PFW�Nbf\cWQPR\]V.��~{PRV+qOMfW�K+M9zBt�^cXuTg^_W�tuT�MUN ^_T�MfV+PRV+M:W Z X+MOvcT�MOMON \]tuW \]n�l�K�^cNQM_��WQK+M9\]V+MfPRV5l�K�^cNQM��P-W�K9W�K+Mal�t+b l�P-NL^cb l�pRPFx�MOX �HK+P-pRMaW�K+Ma\]V+Mk\]tuWL\]n�l�K�^cN�MyP-NLX+M#^cb l�pRPFx�MOX.�EJ K+P-N ^cb l�pRPFx 0q#^_WQPR\]V � ^_WQW�MUVBt�^_W�P-\]V`^cp-NQ\9^_l+l�pRP-MONHW�\sW�K+M zBt�^cV W�t+b bfMOqgK�^cV+PRqO^cp ��t+qUWQt�^_W�PR\]V+Na^cN�NQ\{qOPR^_W�MOX��P-W�KsM#^cqgK9z{t�^cXuTg^_WQtuT�M#�eIaVfP-X+M#^cp�X+MOv]MOV+MUTg^_WQMHlm^_Tg^cbfMUW�T�PRq ^cb l�p-P-x�MUT4v]MOV+MUTg^_WQMON/NQzBt+MOMOhOMUXp-PRv]KCW��

I lm^_Tg^cb MUWQT�P-qL^cb l�pRPFx�MUT$��\cT � N Y MOp-\�� WQKuT�MONQK+\]p-Xf^cV+X l+T�\{X+t+qOMUN4p-MONQN�N�l@\]VCWg^cV+MO\]t+NMOb PRNQNQP-\]V WQK�^cV ^ p ^cNQMUT�� J K+M \]V+p Z V+\]P-NQMsN�\]tuT�qOM P-NaW�K�^_Wy\]n4W�K+M l�t+b l � � \cT ^�qO\]K+MUT�MUV WN�W�^_W�M l�t+bsl&�HPFW�Kf^cV ^cb l�pRPFW�t+X+M p ^_T�v]M qO\]b lm^_T�MUX7�HPFW�KsWQK+MHz{t�^cVCW�t+b t+V+qOMUT�Wg^cPRVCW Z P-WEq#^cVY MyWQTQM#^_W�MOX`P-V�PFW�N�qUp ^cNQNQP-q#^cp�pRP-bfP-W��

JLK+M9\]tuWQl�tuW NQP-v]V�^cp/N�W�^_W�MfPRN nw\]t+V+X Y Z \cl@M:Tg^_W�PRV+v�\]V WQK+M9PRVul�tuW N�Wg^_WQM7�HPFW�K5W�K+MNQzBt+MOMOhOMs\cl@MUT�^_W�\cT�� JLK+M l�K�^cN�M \]n/N�z{t+MOMOhUPRV+v+���u��n TQ\]b & � � ��� ��P-NjX+M:W�MUT�bfP-V+MOX Y Z W�K+Ml�t+b l�/ Nyl�K�^cN�M#� J K+MsNQz{t+MUMOhOMfn ^cqUWQ\cT � PRNkl+T�\cl@\cT�W�PR\]V�^cpeW�\�W�K+M bfMUX+PRt+bM/ NyV+\]V+p-PRV+M#^_TQP-W Z^cV+X WQK+M�P-V W�M:Tg^cqUW�P-\]V pRMOV+vcWQK.� IaV P-V+qUT�M#^cN�M�PRV NQz{t+MOMUhOPRV+v N�K+\]t+pRX \BqOqOtuT Y Z PRV+qUTQM#^cNQPRV+vW�K+M PRVCW�MUTg^cqUWQPR\]V p-MOV+vcW�K.��J K+M \cl+W�PRq#^cp�lm^_Tg^cbfM:WQT�PRqs^cb l�p-P-x�MUT q#^cV Y M l�tuW PRVCW�\8^�q#^#�uPFW ZT�MUNQ\]V�^cV WH^_W�W�K+Mal�t+b l�^cV+X�N�PRv]V�^cp>n T�MOzBt+MOV+qOP-MON WQ\sqUTQM#^_W�MkNQMU�CMUT�^cp@lm^cNQNQMON \]n�P-V WQMUTg^cqUW�P-\]V.�JLK+PRN PRN�q#^cpRp-MOX`^cV�\cl+W�PRq#^cp>lm^_Tg^cb MUWQT�P-qy\]N�qOPRp-p ^_W�\cT��

� \]tuT 0 �L^��CM bfP �uPRV+vDMOb l�p-\ Z N�WQK+M W�K+PFT�X \cT�X+M:T`V+\]V+pRP-V+M#^_T�NQt+NQqOMUl+WQP Y PRp-P-W Z \]n W�K+MbfMUX+PRt+b2�eI W�K+P-T�X�\cT�X+MUT l+T�\BqOMONQN�MOb l�pR\ Z N�nw\]tuT��L^#�CMON � \cT�zBt�^cV WQt+b b MOqgK�^cV+PRq#^cp-p Z nw\]tuTl�K+\cW�\]V+N � P-V W�K+M�PRVCW�MUTg^cq:W�PR\]V.� � V W�K+P-N l+TQ\{qOMON�NsW ��\ l�t+bsl �L^#�CMONf^_TQM�t+NQMUX W�\ qO\]tul�pRMW�K+M8NQP-v]V�^cpa^cV+X PRX+p-MUT �L^��CMUN�� �kMOV+MUTg^cp-p Z � � � � ! � � � # � � � � � V*W�K+M8X+MOv]MUV+MUTg^_W�Mq#^cN�M � � ! � � # � � � � � J K+P-N K�^cN ^cV ^cXu�c^cVCWg^cv]Mf\��CMUT WQK+MfNQMOqO\]V+X5\cTQX+MUT1l+T�\BqOMONQNP-V W�K�^_WjP-WyK�^cNkW ��\�N�WQTQ\]V+v�x�MOp-X+N nw\cTjM#^cNQPRM:T1X+MUW�MUqUW�PR\]V.� �/^_T�PR\]t+Na�CMUT�N�PR\]V+Ny\]n�nw\]tuT 0 ��^��CMbfP �+P-V+v9NQqgK+MObfMONyM��+P-N�WyX+MUl@MUV+X+PRV+v`\]V8W�K+M X+P-T�MUqUW�PR\]V \]nEl+TQ\clm^cvC^_W�PR\]V \]nEWQK+M ��^��CMONyPRVCW�\W�K+MLV+\]V+p-PRV+M#^_T4bfMOX+P-t+b2�!I*N�l@MUqOP ^cp+q#^cN�M�\]nmnw\]tuT 0 ��^��CM�bfP �uPRV+vaPRN � V+\���V ^cN�\cl+W�P-q#^cpul�K�^cNQMqO\]V �}t+vC^_WQPR\]V�^cN \]V+Mj\]n�W�K+M NQP-v]V�^cpRN PRN b9^cX+Mj^sqO\]V �}t+vC^_W�Mj\]n�W�K+Mj\cW�K+MUT��

##

Page 40: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

rL^#�CMON � � ���� � ��� � �+l+T�MON�MOV WQN�^cV M��uqOMOp-pRMOVCW/l�P-qUW�tuT�M \]n nw\]tuT 0 �L^#�CMHbfP �+PRV+v)/ N"l+T�\�0

X+t+qUWQPR\]V�\]n�NQz{t+MUMOhOMOX`N}Wg^_W�MON��4JLK+Mjnw\]p-pR\��HP-V+vsP-N Y ^cN�MOX`\]V�K+P-NH^_T�W�PRqOp-M#�$� V�K+PRN NQP-b t+pR^_W�PR\]V>�W ��\ N�W�T�\]V+v qO\]t+VCW�MUT 0'l+T�\clm^cvC^_W�PRV+v5��^��CMON�l�t+bsl�^jW�K+P-TQX9\cT�X+MUT�V+\]V+p-PRV+M#^_TLbfMUX+PRt+b �HK+P-q6K��PRp-p�qU\]tul�pRMjWQK+MjW ��\ l�t+b l�bf\{X+MUN���P-W�K�W�K+MjW ��\fN�PRv]V�^cp�bf\{X+MUN���JLK+M NQP-v]V�^cp�b \{X+MON�^_T�M^cp-NQ\ qU\]t+V W�M:T 0 l+T�\clm^cvC^_WQPRV+v����aV+M-�L^#�CM�P-N ^ qO\]K+M:T�MOVCWfN�Wg^_WQM WQK+M�\cW�K+M:T P-N WQK+M��_^cqOt+t+bN�W�^_W�M#�

� V W�K+M9nw\]tuT 0 �L^#�CM9bfP �uPRV+v�l+T�\{qOMUNQNO�"W�K+M9NQP-v]V�^cp'��^��CM9P-N ^cb l�pRPFx�MOX Y Z V+\]V+pRP-V+M#^_TqO\]tul�p-PRV+v��P-WQK W�K+M�l�t+bsl �L^��CMUN��EJ ��\ �L^��CMUN�^_T�MHl+TQ\{X+t+qOMOX.�u^jWQTg^cV+NQb P-WQW�MUX1�L^#�CMa^cV+X9^l�K�^cNQM�0 qO\]V �}t+vC^_W�MUX T�M ��MOq:W�MOX1��^��CM#��� K+MOV W�K+MONQM �L^#�CMONE^_T�MLqO\]b Y PRV+MUXs^_WE^V0 � � 0 � Y M#^cbN�l�p-P-WQWQMUT#�BW ��\ NQz{t+MOMUhOMOX �L^#�CMON�^_T�MHl+TQ\{X+t+qOMOX.� � V � PRv]tuT�M2� � n T�\]b r ^#�CMON ��W�K+M2v]MOV+MUT�^_W�PR\]V\]n�NQz{t+MOMUhOMOX�N�Wg^_WQMONHP-N�NQK+\���V.�

Iap-p%�L^#�CMON ^_T�M9T�MUl+TQMONQMOVCW�MOX P-V5W�K+M9x�v]tuT�M YBZ W�K+MUP-T qO\]b l�p-M��D^cb l�p-P-W�t+X+MUN�� J K+MP-V+qOPRX+MOVCW�N�PRv]V�^cp��L^#�CMHPRN4^cNQNQt+b MOX W�\ Y MHP-Vf^ qU\]K+MUT�MOVCW�N�W�^_W�M���P-W�KsbfM#^cVsqO\]b l�pRM��s^cb l�pRP 0W�t+X+M � � ��� ^cV+X MUTQTQ\cTkqOP-T�qUpRM � � �kJ K+M �_^cqOt+t+b N�W�^_W�M PRN2T�M:l+T�MONQMOVCW�MOX YBZ PFW�NaMUTQTQ\cTkqOP-T�qUpRM^_W W�K+M \cTQPRv]PRV�\]n!W�K+Myl�K�^cNQM N}lm^cqOM l�pR\cW��/JLK+M qO\]bsl�pRM���^cb l�p-P-W�t+X+MUN�\]n!WQK+MyT�M ��MOqUW�MOX8^cV+XWQT�^cV+NQbfP-W�W�MOX �L^#�CMONk^_T�M NQK+\���V�W�\ Y M qU\]b l+T�PRN�MOX�\]neW�K+M1NQP-v]V�^cp"^cV+X�W�K+M �_^cqOt+t+b �L^#�CMON^cV+X�^cb l�p-P-x�MOX5X+t+M9W�\`W�K+Mfl�t+bsl Y Z ^�n ^cqUW�\cT � � � Z � T�MONQV+MUp / N pR^���N1W�K+MfWQT�^cV+NQbfP-W�W�MOX�L^#�CM7��PRp-p � MOM:l�WQK+M9N�^cbfMsl�K�^cN�M�^cNjW�K+M9PRV+qOP-X+MOVCW��L^��CM1�HK+P-pRM W�K+MfTQM ��MOqUW�MUX ��^��CM&��PRp-pqgK�^cV+v]M l�K�^cNQM Y Z ��� �fX+MOvcT�MOMUN�� � pRt+qUWQt�^_W�PR\]V+NaP-V8WQK+M WQTg^cV+NQb P-WQW�MUX8^cV+X8TQM ��MOqUW�MUX�L^#�CMON^_T�Mk^cX+X+MUX � PRV+qO\]K+MUTQMOV WQp Z �/X+t+M2WQ\ qO\]tul�pRP-V+v P-V9W�K+MabfP �uPRV+vjMOz{t�^_W�P-\]V+N��EJ K+P-N�b9^ � MON�MO^cq6K\]tuWQl�tuW��L^#�CM K�^#�CM vcTQM#^_W�MUTyt+V+qOMUT�Wg^cPRVCW Z W�K�^cV WQK+M PRV+qOP-X+MOV WjqO\]K+MUTQMOV WjN�Wg^_WQM#� � \cW�M1W�K�^_W\]V+M`zBt�^cXuTg^_W�tuT�M���t+qUW�t�^_W�P-\]V n T�\]b WQK+M�PRVul�tuW7�L^��CM-�HP-pRp�l+T�\{X+t+qUM ��t+qUW�t�^_W�P-\]V+Nf\]n2W�K+MN�^cb MjNQP-v]V`PRV�W�K+MjW ��\f\]tuW�l�tuW/�L^#�CMON2^cV+X`WQK�^_W�W�K+Mj\cW�K+MUTHPRVul�tuW/��^��CM1zBt�^cXuTg^_W�tuT�M ��t+q�0W�t�^_WQPR\]V-��PRp-p�l+TQ\{X+t+qOM ��t+q:W�t�^_W�PR\]V+NH\cl+l@\]NQPFW�M P-V`NQPRv]V�PRV�W�K+MjW ��\f\]tuWQl�tuW/��^��CMON�� �}V`WQK+PRN�L^ Z � ��t+qUW�t�^_W�P-\]V+NHP-V�W�K+MjW�Tg^cV+NQbfPFWQW�MOX3�L^��CMyT�MOb9^cP-V�l�K�^cN�M�0 l+T�MUNQMUTQ�CMOX ^cV+X���t+qUWQt�^_W�PR\]V+NP-VDWQK+M TQM ��MOqUW�MUX �L^#�CM Y MOqO\]b Mfl�K�^cNQM�0 qU\]V �}t+vC^_W�MOX.� � \cT W�K+M9�c^cqOt+t+b P-Vul�tuW �L^��CM � P-V90qOP-X+MOVCW n T�\]b WQK+M�\cl+l \]NQP-WQM�N�PRX+M�\]n W�K+M�V+\]V+pRP-V+M#^_T bfMOX+P-t+b �yW�K+M T�MU�CMUTQNQM�P-N WQT�t+M#��J K+MWQT�^cV+NQbfP-W�W�MOX ^cV+X T�M ��MUqUW�MOX �L^#�CMON9V+\�� K�^#�CM�qO\cTQT�MOpR^_W�MOX V+\]PRN�M`N�Wg^_W�P-N�W�P-qON�����K+MOV W�K+MNQP-v]V�^cpRNa^_TQM1qO\]b Y PRV+MOX8^_W2^50 � � 0 � Y M#^cbfN�l�p-P-WQW�M:THW�K+M W ��\9\]tuW�l�tuWaNQPRv]V�^cp-N/��PRpRp Y MjT�MUl 0T�MUNQMOVCW�MOX8^cNHP-V � PRv]tuTQM � � � ^cpRNQ\fn TQ\]b rL^��CMUN ����JLK+M1bfP-VBt+N NQP-v]V`PRV`\]V+Mj\]tuWQl�tuWaNQP-v]V�^cp�PRNT�MUz{t+P-TQMOX Y Z qU\]V+NQMUTQ�_^_W�PR\]V�\]n!MOV+MUTQv Z �

JLK+M N�PRv]V�^cpRNH^_W�WQK+M \]tuWQl�tuW�l@\cTQW�N�\]n!W�K+M Y M#^cbfN}l�pRP-W�W�MUTH^_T�M Y \cW�K`NQzBt+MOMOhOMUX.�LJ K+M��t+qUWQt�^_W�PR\]V+NjPRV MOPFW�K+MUT \]tuWQl�tuW�L^#�CMf^_TQM \ Y Wg^cP-V+MOX PRV W ��\`N�W�MUl�N�� rL\]K+M:T�MOVCW�p Z ^cX+X W�K+M��t+qUWQt�^_W�PR\]V�qO\]VCWQT�P Y tuWQPR\]V+N n T�\]b W�K+M9P-V+qOPRX+MOVCW"�L^��CM ^cV+XD�_^cqOt+t+b �L^#�CM#��JLK+M9W ��\ P-V90l�K�^cNQM/z{t�^cXuTg^_W�tuTQMON ��PRp-pB^cX+X ^cV+XjW�K+M/W ��\H\]tuW 0 \]n 0 l�K�^cN�M�z{t�^cXuTg^_W�tuTQMON ��PRpRp]N�t Y WQTg^cqUW���J ��\MOp-pRPFl�NQMONy\]n4MUT�T�\cT1^_TQMsnw\cT�b MOX.� � PRV�^cp-p Z ^cX+X W�K+M W ��\�V+\]P-NQMsMUpRpRPFl�NQMONyPRV+qO\]K+M:T�MOVCW�p Z W�\�v]MUW

# "

Page 41: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��������� �� � � ��� � � � � � ������ � ��� � �� ��� � ��� ��� � � � �� ���

# �

Page 42: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

������������� ��� � ��� ��� � ���� � � � � � ��� � � � � � � ��� � � �� ���

# �

Page 43: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

W�K+M W�\cWg^cp ��t+qUWQt�^_W�PR\]V+N1P-V�\]V+Ms\]tuWQl�tuW l \cTQW N�PRv]V�^cp � J K+M x�V�^cp4MUpRpRPFl�NQM1��PRp-peK�^��CMsb9^ �}\cT^cV+X`b PRV+\cT�^ �+MON ��K+PRqgK�^_T�MyX+MUW�MUTQbfPRV+MOX YBZ W�K+MjNQz{t+MOMUhOM n ^cqUWQ\cT � �

�� � � ^cV+X �

� � � � �� ^cNQMUX1\]V1M#^_T�p Z W�K+MO\cT�MUWQPRq#^cp ��\cT � �_NQzBt+MOMOhOP-V+v2K�^cN Y MUMOV ^cqOqO\]b l�p-PRNQK+MUX1t+NQPRV+v�W�K+MONQM

V+\]V+p-PRV+M#^_T bfMUW�K+\BX+N��sI NQK+\cTQWyT�MU�{PRM�� PRNyv]P-�CMUV W�\�M��ulm^cV+X \]V W�K+M V+\]V+p-PRV+M#^_Tyl+T�\{qUMONQNQMONW�K�^_W�K�^#�CM Y MOMOV�NQt+qOqUMONQNQnwt+p-p Z t+N�MOX�W�\sv]MOV+MUTg^_W�MjNQz{t+MUMOhOMOX�N�W�^_W�MON \]n!pRP-v]K W��

� V ��� �&0{�eNQzBt+MOMOhOP-V+v�L^cN NQt+qUqOMONQNQnwt+p-p Z v]MOV+MUT�^_W�MOX�nw\cT WQK+Mfx+T�N�W W�PRb M YBZ ^�WQM#^cbn T�\]b I4J��yJ � MUpRp [ ^ Y N � � � ��� �� � � � � � � ��� � � �eJ K+M Z T�MUX+t+qOMOX W�K+M/zBt�^cV WQt+b V+\]P-NQM Y Z ^cVP-V+P-W�PR^cp�3�0Q� ��� � ^cV+X1p ^_W�M:T"tul W�\1��3�� ���e~{zBt+MOMOhOP-V+v �L^cN!l+T�\BX+t+qOMOX Y Z Y ^cq � ��^_T�X nw\]tuT 0 ��^��CMbfP �+P-V+v�P-V NQ\{X+P-t+b ^_W�\]b N�MOV+qUpR\]NQMOX Y Z ^�q#^��{P-W Z � � ^cq � ��^_T�X1bfM#^cV+N�W�K�^_W!WQK+M/l�t+b l5�L^#�CMON��M:T�M�qU\]t+V W�M:T 0 l+T�\clm^cvC^_WQPRV+v��EJ K+M NQ\BX+PRt+b ^_W�\]bfN ��MUT�M ��M#^ � p Z l�t+b l MOX1��P-W�Ks^kX Z M�pR^cNQMUTqOp-\]NQM4WQ\ W�K+MUP-T!TQMONQ\]V�^cV+qOM�MUV+MUT�v Z �!ILW�W�K+PRN�M��+qOPFWg^_W�P-\]Vjp-MU�CMOp'� W�K+M/V+\]V+p-PRV+M#^_TQP-W Z PRN�PRV+qUT�MO^cNQMOX.�o4V+qOpR\]NQP-V+v�W�K+M9bfMOX+P-t+b PRV�^`q#^#�uPFW Z ��P-W�KD\]V+p Z \]V+M9MOVCWQTg^cV+qOM�0 M��+PFW l@\cTQW ^cqUqO\]b l�pRP-NQK+MOXW ��\ T�MONQt+pFW�N�� � P-T�N}W�PFW�^cpRpR\���MOX�nw\cT b t+p-W�PFl�pRM2lm^cNQNQMUN�W�KuT�\]t+v]K�W�K+MkV+\]V+pRP-V+M#^_THb MOX+PRt+b ^cV+XW�K+M:T�MOnw\cT�M2P-V+qUT�M#^cN�MOX9PRVCW�MUTg^cq:W�PR\]V Y MUW ��MOMOV9W�K+MH^_W�\]bfN4^cV+X W�K+M�q#^��{P-W Z bf\{X+M��E~{MOqO\]V+X9W�K+MNQP-V+v]pRM l@\cT�WkX+PRX V+\cW ^cp-pR\�� ^cV M��uWQMUT�V�^cp"V+\]P-NQMsN�PRv]V�^cp!W�\ MOVCW�MUT�� J K+M \]tuWQl�tuWyNQP-v]V�^cp �L^cNqO\]bsl@\]NQMOX \]n�l�K�^cNQM qO\]V �}t+vC^_W�M�l�K+\cW�\]V lm^cP-T�N$��P-W�K n T�MOzBt+MOV+qOP-MON/N Z bfbfMUW�T�PRq#^cp-p Z X+PRN}l�p ^cqOMOX^ Y \]tuW�W�K+Myl�t+b l`n TQMOz{t+MOV+q Z ^cV+X`qU\cTQT�MON�l \]V+X+PRV+v WQ\sW�K+Mjq#^��{P-W Z T�MON�\]V�^cV WHn T�MOz{t+MUV+qOPRMON��

ILW | �}J � ��� � � �� � � � ����� �!^cV+\cWQK+MUTHW�MO^cb&l+T�\{X+t+qOMUX�NQz{t+MOMUhOPRV+v Y Z nw\cT �L^_T�Xnw\]tuT 0 �L^#�CM bfP �uPRV+v�PRV ^�NQ\{X+P-t+b �_^_l@\cT�MOV+qOp-\]NQMOX Y Z ^ K+MO^_W�l�P-l M#� JLK+MOP-T�NQz{t+MUMOhOPRV+vT�M:l+T�MONQMOVCW�MOX ^ -��&TQMOX+t+qUW�P-\]V`PRV�z{t�^cVCW�t+b V+\]P-NQM Y MOp-\�� W�K+MjN�Wg^cV+X�^_T�X�z{t�^cVCW�t+b p-PRbfPFW��

JLK+M1bf\]N}W2NQt+qOqUMONQNQnwt+peNQzBt+MOMOhOP-V+v9W�\fX�^_W�M1K�^cN Y MOMOV ^cqOqO\]bsl�pRPRN�K+MOX2�HPFW�K�^cV�\cl+W�P 0q#^cp"lm^_T�^cbfMUWQT�P-q \]NQqOPRp-p ^_W�\cT�� � � ���� � � � ��� � �E^_WkW�K+Ms�aV+PF�CMUT�NQPFW Z \]n�J!M��+^cNy^_WjIat+N}W�PRVNQt+qUqOMOMOX+MOXDP-V�NQzBt+MOMOhOP-V+v�W�K+M zBt�^cV WQt+b V+\]P-NQMC2 +�� Y MOpR\�� W�K+Ms�_^cqOt+t+b pRMU�CMUp � �aV+pRP � M ^V+\cT�bf^cp\cl+W�P-q#^cplm^_T�^cbfMUWQT�P-qH\]NQqUPRpRpR^_W�\cT/WQK+MkJ!M���^cN/vcT�\]tul�t+NQMa\]V+p Z \]V+M2l�t+b l�^cV+X V+\ P-V90l�tuW4NQPRv]V�^cp � � V+N�W�M#^cXsW�K+M�V+\]P-N Z �_^cqOt+t+b �L^cN4N�z{t+MOMOhUMOX.�4I l+T�\BqOMONQN � V+\��HV ^cNElm^_T�^cbfMUWQT�P-qX+\��HV�qO\]V �CM:T�NQPR\]V�W�\{\ � l�pR^cqOM P-V+NQPRX+M ^ qUT Z N�Wg^cp>\]n"p-P-W�K+P-t+b V+P-\ Y ^_W�M � N�WQT�\]V+v U W # Z ��l�p ^cqOMOXP-V+NQPRX+Mj^ qO^��{P-W Z T�MON�\]V�^cV WH^_WLW�K+Mal�t+b l`^cV+X�P-W�NLK�^_T�b \]V+PRqan T�MOzBt+MOV+q Z �/J K+P-NLl+TQ\{qOMON�N�q#^cVY M WQK+\]t+v]K Wy\]n4^cN2W�K+M ^ Y NQ\cTQl+W�P-\]V \]n4^9NQPRV+v]p-M l�K+\cWQ\]V \]nEn T�MOzBt+MOV+q Z � ^cV+X W�K+M P-V+N�Wg^cV90Wg^cV+MU\]t+NaMObfPRN�NQPR\]V�\]n"W ��\9qO\cT�T�MOp ^_WQMOX�l�K+\cW�\]V+NO�@M#^cqgK ^_WaK�^cp-n�WQK+M1PRVul�tuWkn T�MUz{t+MOV+q Z �2J K+Mq#^#�uPFW Z ^cvC^cPRV�M��uW�MUV+X+MOX�W�K+MjPRVCW�MUTg^cqUWQPR\]V�WQPRbfM#��JLK+Mjlm^_T�^cbfMUWQT�P-qk\]NQqOPRp-p ^_W�\cTLX+P @MUTQMOV WQP ^cpRp ZNQqO^cpRMOX W�K+M W ��\`z{t�^cXuT�^_W�tuT�MON YBZ P-W�Nyl�K�^cNQMfNQMUV+NQP-W�PF�CM \cl MUTg^_W�P-\]V.� �kV+M z{t�^cXuTg^_W�tuTQM7�L^cN^cb l�p-P-x�MOX�^cN WQK+Mj\cW�K+M:T/�L^cN X+M#^cb l�p-P-x�MOX.�

�2W�K+MUT NQt+qOqUMONQNQnwt+pfN�z{t+MOMOhUPRV+v b M#^cNQtuT�MOb MOV WQN K�^#�CM�l+TQ\{X+t+qOMOX l�K+\cW�\]V V t+b Y MUTNQzBt+MOMOhOP-V+v��1~{t Y�� Se\]P-NQNQ\]V X+PRN�WQTQP Y tuW�P-\]V+Ny\]nel�K+\cW�\]V qO\]t+VCW�NyK�^cN Y MOMOV ^cqgK+PRMU�CMOX8W�KuT�\]t+v]K

# �

Page 44: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

NQM:�CMUTg^cp"bfM:W�K+\{X+N��j�aV+Msb MUW�K+\{X>� � V+\��HV ^cNk^9z{t�^cVCW�t+b V+\]V+X+MObf\]p-P-W�P-\]V b M#^cNQtuT�MOb MOV WO�t+NQMUN�^ nwMOMOX Y ^cq � qO\]V W�T�\]pN Z N�W�MUb W�\ pR\���MUT/WQK+MHV+\]PRN�MH\]V9^ p-PRv]KCW Y M#^cb2�E�aV+p Z \]V+M�l�K+\cW�\]V\]nE^9qO\cTQT�MUp ^_W�MOX8lm^cP-Tal+TQ\{X+t+qOMOX YBZ ^9lm^_T�^cbfMUWQT�P-q ^cb l�p-P-x�MUTkP-Na\ Y NQMUTQ�CMOX.�jJLK+M TQMONQt+p-Wy\]nW�K+MkbfMO^cNQtuT�MObfMUV W PRNLnwMOX Y ^cq � W�\ WQK+Mj^cbsl�pRP-x�M:TL\cT�N�\]tuT�qOM#���kV+p Z W�K+MkbfM#^cNQtuT�MUX�l�K+\cW�\]VY M#^cb P-N2bf\{X+PFx�MOX.��J K+P-N2nwMOMOX Y ^cq � qO\]VCWQT�\]p�q6K�^cV+v]MUN2W�K+M1l�K+\cW�\]V�\{qUqOtuTQT�MOV+qUM WQPRbfMON�� ILW� J �jJk� � � � � � � � ��� � �� � � � ����� ��T�MOX+t+qUMOX W�K+M9V+\]P-NQM9PRV�^�NQMOb PRqO\]V+X+t+qUWQ\cTspR^cNQMUT Y Z^ Y \]tuW � ��� �4JLK+PRN'�L^cN�^cqgK+P-MU�CMOX Y Z N�tul+l+T�MONQNQP-V+v ^cb l�pRPFW�t+X+M ��t+q:W�t�^_W�PR\]V+N/PRVsWQK+M2qOtuTQT�MUV WNQtul+l�p Z � JLK+PRN qU\]V+N�Wg^cVCW9qOtuTQT�MUV W9N�tul+l�p Z ��^cNsl+T�\BX+t+qOMOX Y Z NQP-b l�p Z ^_WQW�^cq6K+P-V+v5^ pR^_T�v]MT�MUNQPRN�WQ\cTHP-V�NQMUTQPRMON/��P-WQK�^ �C\]p-Wg^cv]MyNQtul+l�p Z �

IaV8P-b l@\cTQW�^cV WaP-NQNQt+M q#^cV Y M qO\]V+N�PRX+MUT�MUX ^_WaW�K+P-Nkl \]PRVCW��kIapRp�W�K+M NQqgK+MObfMONy^ Y \��CMW�K�^_WsMOb l�p-\ Z MUX \cl+W�P-q#^cp�l�t+b l�PRV+v+�/TQMOz{t+PFT�MOX ^ N�WQT�\]V+v+��qU\]K+MUT�MOVCWfl�t+b l Y M#^cb2� � nHW�K+MzBt�^cV W�t+b V+\]P-NQM8pRP-bfP-W nw\cT�^5pR^cNQMUT �HPFW�K � � l�K+\cW�\]V+N P-N � � � W�K+MUV nw\cT W�K+MN�W�T�\]V+v l�t+b l2��P-WQK ��� � l�K+\cW�\]V+N � � � � �:�+W�K+M zBt�^cV W�t+b V+\]PRNQMjpRP-bfP-W NQK+\]t+p-X Y Ml+T�\cl \cTQW�P-\]V�^cp W�\ ��� � �/JLK+MUT�MUnw\cT�MyWQK+MyP-NQNQt+Mk\]n�z{t�^cVCW�t+b V+\]PRNQMkP-V WQK+Mkl�t+bsl Y M#^cbb t+N�W Y M ^cX+XuT�MONQNQMUX YBZ W�K+M NQz{t+MOMUhOMUT��9JLK+M V t+b Y MUT NQz{t+MUMOhOPRV+v�W�MOqgK+PRzBt+M PRNj\]n/P-V W�M:T�MON�WY MOq#^ct+NQMLW�K+MUT�MLP-NEV+\yNQt+qgKsTQMOz{t+PFT�MObfMOVCWE\]V WQK+MLl�t+bsl � � WeTQMOb9^cPRV+N"WQ\ Y MLNQMOMOVsPRn�l+Tg^cqUW�P-q#^cp~ � * PRbsl+T�\ �CMUbfMOVCWHP-N l \]NQNQP Y p-M���P-WQK�NQzBt+MOMOhOMOX�p-PRv]KCW��

IaV+\cWQK+MUT�PRbsl@\cTQWg^cVCW�PRNQNQt+M WQK�^_W`b t+N�W Y M5^cX+XuT�MONQN�MOX P-N�W�K+M t+N�M5\]n1T�M#^cpypRPRv]KCWNQ\]tuTQqOMON�� I qO\]K+M:T�MOVCW N�Wg^_W�M�X+\{MONfV+\cW M��+P-N�W�� | ^cV Z vC^cNsp ^cNQMUTQN l+T�\{X+t+qUM`V+M#^_T�p Z P-X+M#^cpqO\]K+M:T�MOVCW pRP-v]K W Y tuW bf\]N�Wj\cW�K+MUTjW Z l@MON \]n�p ^cNQM:T Y MO^cbfN qO\]VCWg^cP-V V+\]PRNQM1�HK+P-q6K TQMONQt+p-WQN1PRVl�K+\cW�\]V5N}Wg^_W�PRN}W�PRqONyNQ\]bfM��HK+MUTQM Y MUW ��MUMOVDSe\]PRNQNQ\]V ^cV+X � \]N�M�0 o4PRV+N�W�MUPRV.��J K+P-N P-Njlm^_TQW�P-qOt90pR^_T�p Z W�T�t+M�nw\cT4X+PR\BX+M�pR^cNQMUT�N ��K+PRqgK N�^cq:T�P-x�qOM�qO\]K+MUT�MUV+qOMHnw\cT4NQPRhUM#�EJ K+M z{t�^cVCW�t+b \cl@MUT�^_W�\cT�NK�^#�CM�X+MO^cp-W �HPFW�K P-X+M#^cp+NQ\]tuT�qUMON��4J K+M PRNQN�t+M�\]nqO\]V+qOMUT�V V+\�� P-N4P-nmW�K+M qOpR^cNQNQPRqO^cpmV+\]P-NQM qOP-T�qUpRMq#^cV Y MyNQz{t+MOMUhOMOX.�

IaV PRb l \cTQWg^cVCW/W�MOqgK+V+P-q#^cp P-NQNQt+M2T�MOpR^_W�MOX WQ\ v]MOV+MUTg^_W�P-V+v1NQzBt+MOMOhOMOX�N�Wg^_WQMHPRN4l+T�MONQMUT�� 0P-V+v N�z{t+MOMOhUMOX`N�Wg^_WQMON��EJ K+MyNQzBt+MOMOhOMOX�N�Wg^_W�MkP-NL^ n Tg^cv]P-pRMa\]V+M#�/�aV+qOMyWQK+MyN�z{t+MOMOhUMOX�N�W�^_W�MkPRNv]MOV+M:Tg^_W�MOX PFWyb t+N}W Y M l+TQMONQMUTQ�CMUX.� IaV Z V+\]PRNQM NQ\]tuT�qOMUN1PRV8W�K+M M��ul MUT�PRb MOV W���PRpRpeX+MUN�WQT�\ ZW�K+M9l�tuT�PFW Z ^cV+X q#^cV+qUMOpL\]tuW ^cV Z NQzBt+MOMOhOP-V+v�^cqgK+PRM:�CMOX.� IapRp/PRV+N�WQTQt+bfMOVCWsV+\]P-NQMc�ENQt+qgK ^cNpR^cNQMUTkn T�MOzBt+MOV+q Z �}PFWQW�MUT#� b t+N}W Y M NQtul+l+TQMONQNQMOX.� J K+M1l�t+bsl�PRV+v \]nE^_W�\]bfNHb t+N�WkV+\cW Y M ^_WW�KuTQMONQK+\]pRX�NQPRV+qOMjN�l@\]VCWg^cV+MO\]t+NHMObfPRN�NQPR\]V�qO\]t+pRX`\BqOqOtuT2^cV+X�^cX+X`V+\]PRN�M#�/I Y NQ\cT�l+W�PR\]V>� ��t+\�0T�MUNQqOMOV+qOM_�"^cV+X bf\{X+M PRVCW�MUTQnwMUT�MOV+qOM ^cpRNQ\�X+MOvcTg^cX+M NQzBt+MOMOhOP-V+v�� � � WyPRNkV+\cW�MOX8W�K�^_WkW�K+MUT�bf^cpV+\]P-NQMjX+\BMONHV+\cW l�p ^ Z ^sn ^cqUWQ\cT2NQP-V+qOM � ��� � ��� ^_WH\cl+W�P-q#^cp�n T�MOzBt+MOV+qOPRMUN�� �

# �

Page 45: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

4 �F4 � � �$���� ���F����� �"!#�����$%7�8��9

�aV+qOM1N�z{t+MOMOhUPRV+v9PRN�v]MOV+MUTg^_WQMOX�P-WHb t+N}W Y MjX+MUW�MOq:W�MOX.�LikMUl@MOV+X+P-V+v \]V�W�K+M W Z l M \]nNQzBt+MOMOhOP-V+v l+T�\BX+t+qOMOX9X+P MUT�MOVCW�X+M:W�MOqUW�P-\]VsW�MUq6K+V+P-z{t+MON/q#^cV Y M MOb l�p-\ Z MUX.� � W4PRN�W�K+M l�K+\cW�\�0X+P-\{X+MaW�K�^_W�^cqUW�t�^cp-p Z qO\]t+VCW�NLW�K+Myl�K+\cWQ\]V+N�NQ\ W�K+MON�MjX+MU�{PRqOMUN�b t+N�W K�^#�CM ^ K+PRv]K�z{t�^cVCW�t+bM � qOPRMUV+q Z �/v]\B\{XDl�K�^cNQM�NQMUV+NQP-W�PF�uPFW Z �E^cV+X Y M�n TQMOM�n TQ\]b ^cbsl�pRP-x�M:Ts\cTs\cW�K+MUTsPRV+N}WQT�t+bfMOVCWV+\]P-NQM#�

JLK+M W�KuT�MOM W Z l MONk\]n4X+M:W�MOqUW�P-\]V N�q6K+MUbfMONkW�K�^_Wkq#^cV M��uWQT�^cqUWyPRV+nw\cT�b9^_WQPR\]V`W�\ NQK+\��NQzBt+MOMOhOP-V+v K�^cN�\BqOqOtuTQTQMOX ^_T�M X+P-T�MOq:W`X+MUW�MUqUW�PR\]V>�aK+\]b \{X Z V+M X+MUW�MUqUW�PR\]V>�k^cV+X Y ^cp ^cV+qOMOXK+\]bf\BX Z V+MkX+MUW�MUqUW�PR\]V.�

ikPFT�MOqUW X+MUWQMOqUW�P-\]V�P-N V+\cW NQt+P-W�^ Y pRM9nw\cT v]MOV+MUTg^cp/NQz{t+MOMUhOMOX�z{t�^cXuTg^_W�tuTQM�X+M:W�MOqUW�P-\]V.�JLK+M X+MUWQMOqUW�\cT#��W�K+Msl�K+\cWQ\{X+PR\BX+Mc��PRNyNQMOV+NQPFW�P-�CM W�\�l�K+\cW�\]V�VBt+b Y M:T�� S4K+\cW�\]V V t+b Y MUT1P-V90�C\]pF�CMON W�K+M�b9^cv]V+PFW�t+X+M`\]naW�K+M�qO\]bsl�pRM�� ^cb l�pRPFW�t+X+M`NQ\5PFW&��PRpRp�qO\]b Y PRV+M`MUz{t�^cp2qO\]VCWQT�P 0Y tuW�P-\]V+N n T�\]b Y \cW�KDz{t�^cXuTg^_WQtuT�MON���JLK+M9V+\]PRN Z z{t�^cXuT�^_W�tuT�M7��PRp-p/qO\��CMUT tul ^cV Z T�MOX+t+qOMUX��t+qUWQt�^_W�PR\]V+N�P-V W�K+M�\cW�K+MUT�zBt�^cXuTg^_W�tuT�M��EikPFT�MOqUW/X+MUW�MOqUWQPR\]Vfq#^cV Y MHt+NQMUXfW�K+\]t+v]KfW�\ X+M:W�MOqUWW�K+MyNQt Y�� Se\]P-NQNQ\]V�qO\]t+VCW�PRV+v N�Wg^_W�P-N�W�PRqUN \]n�l�K+\cW�\]V�V t+b Y MUTHNQz{t+MOMUhOPRV+v��

,a\]b \{X Z V+M X+M:W�MOqUW�P-\]V ^cV+X Y ^cpR^cV+qOMOX K+\]bf\{X Z V+M X+M:W�MOqUW�P-\]V5^_T�M l�K�^cNQM NQMOV+NQPFW�P-�CMW�MUq6K+V+P-z{t+MON�� I l�K+\cW�\{X+P-\{X+M`b P �+MUNsW�K+M`P-V+qO\]bfP-V+v pRP-v]K W9N�PRv]V�^cp���P-WQK ^�N�WQT�\]V+v]M:T pR\{qO^cp\]NQqUPRpRpR^_W�\cT���JLK+M2l�K�^cNQMaPRV+nw\cTQb9^_W�PR\]V PRN/l+T�MUNQMUTQ�CMOX.�/J K+Map-\{q#^cpm\]NQqOP-pRpR^_W�\cT�n T�MOzBt+MOV+q Z P-N�W�K+MN�^cb M2^cN4WQK+M2NQPRv]V�^cpmn T�MOzBt+MOV+q Z NQ\1W�K�^_W/WQK+M2X+P MUT�MOV+qOM � PRVCW�MUT�bfMUX+P ^_W�M �en T�MOzBt+MOV+q Z PRN�hOM:T�\��

����� � � � � �� � � � � � � � � � � � �

JLK+MHl�K+\cW�\BqOtuTQT�MOVCW�l+T�\cl \cTQW�PR\]V�^cp�W�\ WQK+M2pR\Bq#^cp\]N�qOPRp-p ^_W�\cT4V+\]PRNQMHPRN�V+M#^_T�X+qapRMU�CMOp-N�^cV+X9q#^cVY M x�pFW�MUT�MUX \]tuW�� J K+M9l�K�^cNQM�\]nLW�K+M�p-\{q#^cp4\]NQqOP-pRp ^_WQ\cT q#^cV�TQM#^cX \]tuW W�K+M NQP-V+M�\cT qU\]NQPRV+MzBt�^cXuTg^_W�tuT�MyqO\]b l \]V+MOV WH\]n�W�K+MjNQPRv]V�^cp@x�MUpRX.�

� VjK+\]bf\{X Z V+M4X+MUWQMOqUW�P-\]V ^�NQzBt+MOMOhOMUX NQPRv]V�^cp Y MO^cb P-N�b P �+MUX ��P-W�K ^�pR\Bq#^cp]\]NQqOP-pRpR^_W�\cTT�MUnwMUT�MOV+qOM Y M#^cb � Wg^ � MOV�\# �WQK+M PRV+PFW�P ^cp Y M#^cb Y MOnw\cT�M P-W��L^cN NQzBt+MOMOhOMUX � ^_W�0 � 0 0 � Y M#^cbN�l�p-P-WQWQMUT���J K+M�NQtul@M:TQl@\]NQPFW�PR\]V \]n�W�K+MON�M�W ��\ ��^��CMONsPRN X+MUW�MOq:W�MOX ��P-W�K ^ l�K+\cW�\BX+PR\{X+M�^cNNQK+\���V`PRV � PRv]tuT�Ms�]� �

� n�W�K+M9p-\{q#^cpE\]NQqOP-pRp ^_WQ\cT1l�K�^cNQM9PRN ^cX �}t+N}W�MOX�qO\cTQT�MOq:W�p Z �!WQK+M9NQtul@MUT�l@\]NQPFW�PR\]V�\]tuWQl�tuWY M#^cb P-N1l�K+\cW�\]V5VBt+b Y MUT NQz{t+MUMOhOMOX.�8JLK+Mfl�K+\cW�\{qUtuTQT�MOVCW��HP-pRp4NQK+\�� ^�V+\]PRNQM pRMU�CMOpEW�K�^_WP-N Y MOp-\�� W�K+M t+NQt�^cp"NQK+\cWkV+\]P-NQM pRM:�CMOp �kJLK+M pR\Bq#^cp!\]NQqUPRpRpR^_W�\cTaP-NaPRV�l�K�^cNQM5��P-W�K�W�K+M NQP-v]V�^cpzBt�^cXuTg^_W�tuT�M&��P-W�K5T�MUX+t+qOMOX���t+q:W�t�^_W�PR\]V+N��� nLW�K+M9pR\Bq#^cp�\]NQqOP-pRpR^_W�\cT1l�K�^cNQM �L^cN1�_^_T�PRMUX Y ZV+P-V+MUW Z X+MOvcTQMOMONfPFW1��\]t+p-X Y M�PRV l�K�^cNQM3�HPFW�K W�K+M�V+\]PRN Z z{t�^cXuT�^_W�tuT�M`^cV+X W�K+M�X+MUWQMOqUW�\cT

#��

Page 46: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� �� ����� � � �� �� ��� � ��� �

l�K+\cW�\BqOtuTQT�MUV W���\]t+p-X T�PRN�Mf^ Y \��CM W�K+M NQK+\cW V+\]PRN�MfpRMU�CMUp ��J K+M pR\{qO^cpE\]N�qOPRp-p ^_W�\cT PRN1^cp �L^ Z NqO\]V+N�PRX+MUT�MUXDWQ\ Y M ^`qO\]K+MUT�MOVCW N�W�^_W�M�� � � ��� ��K+MUT�M ��P-NjW�K+Msl�K�^cNQM7��P-W�K�TQMON�l@MUqUW1W�\W�K+MHNQPRv]V�^cp �eI �CMUT Z v]\{\BX l�K�^cNQM2b9^_WQq6K PRN4TQMOz{t+PFT�MOX Y M:W ��MOMOV9W�K+M2p-\{q#^cp�\]NQqOP-pRpR^_W�\cT�^cV+X9PFW�NNQP-v]V�^cp �

� ^cpR^cV+qOMOX8K+\]bf\{X Z V+M1X+MUW�MUqUW�PR\]V)�L^cNat+N�MOX Y Z /t+MOV ^cV+X rLK�^cV8\]n | ��J � � � ������ � � � ��� � ��PRV�W�K+MyM#^_T�p Z ��� � �'/ N�^cNH^ �L^ Z W�\sbfM#^cNQtuTQMjW�K+MyNQz{t+MUMOhOMOX`�_^cqOt+t+b x�MUpRX.�%� VW�K+P-NeNQqgK+MObfMLpRP-v]K W�n TQ\]b Y \cW�K \]tuWQl�tuW�l \cTQW�Ne\]n+W�K+M=0 � 0 0 � Y M#^cb�N�l�p-P-WQW�M:TE^_T�MLt+NQMOX.� � V WQK+PRNbfM:W�K+\{XfW�K+M:T�MaPRN�V+\5�L^cN}W�MOX�MOV+MUT�v ZsY MOq#^ct+N�M Y \cW�K Y M#^cb N�^_T�Mat+NQMOX.�4JLK+M Y M#^cb&N}l�pRP-W�W�MUTq#^ct+N�MON ^�l�K�^cNQM�NQK+P-n W9W�K�^_W ^cpRp-\���NsWQK+M`NQz{t+MUMOhOMOX �c^cqUt+t+b qO\]VCWQT�P Y tuWQPR\]V+NfW�\�WQK+M�pR\{qO^cp\]NQqUPRpRpR^_W�\cT�W�\ X+P @MUT YBZ ��� �yX+MOvcT�MOMON/PRV MO^cq6K \]tuWQl�tuW�NQP-v]V�^cp ��J ��\ X+M:W�MOqUW�\cTQN%��PRpRp�bfMO^cNQtuT�MY \cW�K \]tuWQl�tuW NQPRv]V�^cp-N�� J K+MUNQM l�K+\cW�\BqOtuTQT�MOVCW�N ^_T�M W�K+MOV5X+P @MUT�MUV+qOMOX5W�KuT�\]t+v]K MUpRMOqUW�T�\]V+PRq^cb l�p-P-x�MUTQN��eJLK+PRN�X+P MUT�MOV+qOP-V+v1\cl@M:Tg^_W�PR\]V M� MOqUW�PF�CMOp Z qO^cV+qOMOpRNE\]tuW4^cpRp{WQK+MLl�K+\cWQ\]VsV t+b Y MUT��t+qUWQt�^_W�PR\]V+N�X+t+M W�\sWQK+M1pR\Bq#^cp>\]NQqOP-pRp ^_WQ\cT�x�MOp-X.��JLK+M NQzBt+MOMOhOMOX8NQP-v]V�^cp>x�MOpRX Y MOqO\]bfMON W�K+MX+\]bfP-V�^cV W�NQ\]tuT�qOMa\]n�V+\]PRN�M#��IaN/W�K+MapR\Bq#^cpm\]NQqOPRp-p ^_W�\cT�PRN/�_^_T�PRMUX9PRV9l�K�^cNQM2W�K+MaX+MUWQMOqUW�\cT ��PRp-pNQMUM���t+qUW�t�^_W�P-\]V+Nj^ Y \ �CM ^cV+X Y MOpR\�� WQK+M NQK+\cWkV+\]PRNQM p-MU�CMOp �aJ K+MUNQM MOz{t�^_W�P-\]V+Nk^_T�M1q#^_T�T�PRMOX\]tuW�PRV�W�K+M NQMUqUW�PR\]V�\]V`v Z TQ\]NQqO\cl@MUN��

JLK+M2l�K+\cW�\]V�N�Wg^_W�P-N�W�P-qON�\]n>W�K+Ma\]tuWQl�tuWLx�MOp-X+NL^_T�MaX+MUW�MUTQbfPRV+MOX Y Z W�K+MOPFT ^cb l�pRPFW�t+X+M��t+qUWQt�^_W�PR\]V+N�� JLK+MONQM ��t+qUW�t�^_W�P-\]V+N qO\]V+NQP-N�W9\]nHWQK+M�pR\Bq#^cpL\]NQqOP-pRp ^_WQ\cT ��t+q:W�t�^_W�PR\]V+N1�HK+P-q6K^_T�M�qO\cTQT�MOpR^_W�MOX � M:TQT�\cT9qOPFT�qOp-MON �f^cV+X W�K+M�NQzBt+MOMOhOMUX�NQP-v]V�^cp ��t+q:W�t�^_W�PR\]V+N&��K+PRqgK*^_T�M`V+\]VqO\cT�T�MOp ^_WQMOX � MUTQT�\cT MOp-pRPFl�NQMON ���EJLK+MkX+P @M:T�MOV+qOP-V+v \cl@M:Tg^_W�PR\]V&��PRp-p@q#^cV+qOMUp>\]tuW�W�K+MkqO\cTQT�MOpR^_W�MOX��t+qUWQt�^_W�PR\]V+N ^cV+X � MOMUl WQK+M V+\]V qO\cT�T�MOp ^_WQMOX ��t+qUW�t�^_WQPR\]V+N n TQ\]b W�K+MsPRV+X+PF�uPRX+t�^cp�zBt�^cXuTg^ 0W�tuTQMON��

" �

Page 47: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � � � � � � � ����� � � �� �� ��� � ��� �

4 � A � ��!#�����$%$����9 � �F��� �O� HJ�����8� �ON ;=��>?�� � �'����� �

�aV+MHvcTQ\]tul9^_W'� ��| IapRb9^cX+MOV1*HMON�M#^_T�qgK r�MOV WQMUT�K�^cN4qO\]V+qOMOVCWQTg^_W�MUXf\]Vsl+T�\BX+t+qOPRV+vNQzBt+MOMOhOMUX�N�Wg^_W�MON PRV�\cl+W�PRq#^cp@x Y MUT�N ���

��� ������ �� � � � ��� � � �/JLK+PRN�vcT�\]tul`K�^cN�NQt+qOqOMOMUX+MOX

P-V�l+T�\{X+t+qUPRV+v�^ pRP-bfP-WQMOX`^cbf\]t+VCW2\]neN�z{t+MOMOhUPRV+v Y Z t+NQP-V+vfW�K+M l+T�\BqOMONQN2\]neV+\]V+X+MUv]MOV+MUTg^_W�Mnw\cT ��^_T�X�nw\]tuT 0 �L^#�CMjbfP �+P-V+v P-V�WQK+Myx Y MUT��4J K+Mkx Y MUT l+T�\��uP-X+MONH^ bfMOX+P-t+b �HPFW�K�^ vcT�MO^_W�MUTP-V W�M:Tg^cqUW�P-\]V9pRMOV+vcW�KfWQK�^cV9q#^cV Y M2nw\]t+V+X PRV ^1q:T Z N�W�^cp\cT�qO^��{P-W Z ��J K+M2x Y MUT�q#^cV Y M2qO\]Vux�v�0tuT�MUXf^cN4^kT�MUNQ\]V�^_W�\cT YBZ nwt+N�PR\]VfN�l�p-PRqOP-V+vjPFW�N�MOV+X+N/nw\cT4^cVsMU�CMOV vcTQM#^_W�MUTEPRVCW�MUT�^cqUW�PR\]V pRMUV+vcW�K.�JLK+Myl+TQ\{qOMON�N/�L^cN q6K+\]N�MOV�^cN V+\]V+X+MOv]MOV+MUTg^_WQM Y MOqO^ct+NQM W�K+Mkx Y MUT��L^cNLW�\ Y MjNQP-V+v]pRMybf\{X+M��I NQP-V+v]pRM�b \{X+M6��PRp-p l+T�\BX+t+qOM�vcT�M#^_WQMUTex�MOpRX X+MUV+NQP-W�P-MONE^cV+X1W�K+MUT�MUnw\cT�MLvcT�M#^_W�MUT"V+\]V+pRPRV+MO^_TE^cq�0W�P-\]V.��~{PRV+v]p-M�N�lm^_W�PR^cpubf\{X+MUNeq#^cV+V+\cW Y MLPRX+MUV W�PFx�MOX PRV ^aNQPRV+v]p-M b \{X+M/x Y MUT�� � Z NQMUlm^_T�^_W�PRV+vW�K+M bf\BX+MONjP-V�n T�MUz{t+MOV+q Z W�K+M bf\{X+MUNyqU\]t+pRX Y MsP-X+MOV WQP-x�MOX.�sJ K+P-N���^cN1^cqOqO\]bsl�pRPRN�K+MOX Y Zbf\BX+t+p ^_W�P-V+v W�K+M NQP-v]V�^cp ��P-W�K8^cqU\]t+N�W�\ � \cl+W�P-q bf\{X+t+pR^_W�\cT�N�WQ\fl+T�\{X+t+qOM NQP-X+M Y ^cV+X bf\{X+MON��JLK+M b9^cP-V Y ^cV+X�^cV+X�P-W�N�NQPRX+M Y ^cV+X+N���MUT�MjNQMOVCWaPRVCW�\sWQK+M � � � 0 b MUW�MUT�nwt+NQMOX�NQP-pRP-q#^ x Y MUTk^cNl�t+b l bf\BX+MON��DJLK+M�l+T�MUNQMOV+qOM`\]n NQMU�CM:Tg^cp�l�t+b l�N TQMONQt+p-WQMOX PRV�V+\cW W ��\ l�K+\cW�\]V N�Wg^_W�MUNO�Y tuW K+PRv]K+MUT \cT�X+MUT�� PRV WQK+PRN q#^cNQM�nw\]tuT�� � \]tuT qO\cTQT�MUp ^_W�MOX l�K+\cW�\]V+N1��M:T�M�N Z bfbfMUW�T�PRq#^cp-p ZX+P-N�l�p ^cqOMUX�^ Y \]tuWkM#^cqgK l�t+b l n T�MUz{t+MOV+q Z �yJLK+M NQz{t+MUMOhOPRV+v�pRM:�CMOpRN ��M:T�M pRPRb P-W�MOX�W�\�^ Y \]tuW� � 0 � ��� ��I b9^ �}\cT1l+TQ\ Y pRMOb`�!q#^ct+NQMOX YBZ W�K+Mfz{t�^cN�P � r�� \cl@M:Tg^_W�PR\]V>� �L^cN1W�K+M9\{qUqOtuT 0T�MUV+qOMj\]n�v]t+PRX+MUX`^cqO\]t+N�WQPRq+�L^#�CM � T�P-pRpR\]t+P-V NQq#^_WQW�M:T�PRV+v � �yI�� � ~ ���+JLK+PRN�l+T�\BqOMONQN NQq#^_W�W�MUT�N

" &

Page 48: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

l�K+\cW�\]V+N5��P-WQK5^cqO\]t+N�W�P-q#^cp4l�K+\]V+\]V+N \]n�W�K+Msx Y MUT b9^_WQMUT�P ^cp ��rL\B\]pRP-V+v�W�K+M x Y MUT T�MOX+t+qOMUXW�K+M � T�PRp-pR\]t+P-V�NQqO^_WQW�MUT�P-V+v Y tuWH^cpRNQ\ T�MOX+t+qOMOX`WQK+MjW�KuT�MUNQK+\]pRX`nw\cT � T�PRp-pR\]t+P-V�\]NQqUPRpRpR^_W�PR\]V.�

JLK+M`l+T�\ Y p-MObfN9MOV+qO\]t+VCW�MUTQMOX P-V WQK+PRN M��ul MUT�P-bfMOVCW&�HP-pRp�V+MOMOX W�\ Y M`T�MON�\]p-�CMOX*PRVW�K+M�nwtuW�tuT�M#� *HMUqOMOVCW9lm^_l@MUT�N9K�^#�CM`X+MOb \]V+N�WQTg^_W�MUX x Y MUTfNQz{t+MOMUhOPRV+v ��P-W�K l�t+p-NQMOX pR^cNQMUT�N� � � ��� � � � � � �� ��� � � � P Y MUT�N l \]NQNQMON�NQPRV+v8p ^_TQv]M V+\]V+pRP-V+M#^_T�PFW�PRMON1^_T�Mf\]V+Mfn ^cqUWQ\cT1W�K�^_W5��PRp-pb9^_W�W�MUT�PRV1W�K+M�nwtuW�tuTQM�X+MU�CMOpR\cl�b MOV W"\]n+NQz{t+MOMUhOPRV+vkPRV1x Y MUT�N��EJLK+M/T�MObf^cPRV+X+MUTe\]nuWQK+PRN!W�K+MUNQPRN��PRp-p>\]V+p Z ^cX+XuT�MONQN W�K+PRN�PRNQN�t+M#�

� V*^cX+X+P-WQPR\]V W�\5NQzBt+MOMOhOP-V+v�WQK+M�z{t�^cVCW�t+b V+\]PRN�Mc� WQK+M2� ��| vcT�\]tul�^cpRNQ\5X+MUbf\]V90N�W�Tg^_W�MOX W�K�^_WkW�K+M qOp ^cNQN�PRq#^cpeV+\]P-NQMsP-NjN�z{t+MOMOhUMOX � �

��� ��������� � � � ��� � � �1I V+\]V+X+MOv]MOV90

MUT�^_W�Mknw\]tuT 0 �L^#�CMybfP �uPRV+v M��ul MUT�P-bfMOVCW �L^cN l MUT�nw\cT�b MOX�P-V�^ x Y M:T�T�P-V+v TQMONQ\]V�^_W�\cT��$� V�WQK+PRNM��{l@MUTQPRbfMOVCW�\]V+M z{t�^cXuT�^_W�tuT�My\]n!Tg^cV+X+\]bdV+\]PRNQM��L^cN2^_W�W�MOV t�^_W�MOX.�/IaV�T�n"V+\]P-NQM v]MOV+M:Tg^_W�\cT�L^cNLt+NQMUX�W�\ XuT�P-�CMj^ bf\{X+t+pR^_W�\cTLN Z N�W�MOb ��K+PRqgK�q:T�M#^_W�MOX�qOp ^cN�NQPRq#^cp�^cbsl�pRP-WQt+X+Mk^cV+X�l�K�^cNQMbf\BX+t+p ^_W�P-\]V+NL\]V�W�K+Mjl�t+bsl Y M#^cbdW�K�^_W��L^cNHNQMUV WaP-V WQ\sW�K+Myx Y MUT��LJLK+M V+\]P-NQM P-NHqOpR^cNQNQP-q#^cpY MOq#^ct+NQMkP-WLP-N�l�K�^cNQMkPRV+X+MUl MOV+X+MOVCW2^cV+X V+\ qO\cTQT�MUp ^_W�P-\]V9M��+P-N�W�N Y M:W ��MOMOV W�K+MkV+\]PRNQMaP-V�MO^cq6KzBt�^cXuTg^_W�tuT�M#��� V WQK+M NQ^cbfM b9^cV+V+MUTy^cNkX+MONQq:T�P Y MOX ^ Y \ �CM W�K+P-NaqOp ^cNQN�PRq#^cpeV+\]P-NQM PRVul�tuW��L^cNNQzBt+MOMOhOMUX YBZ ^ Y \]tuW 0 X � �

4 �YT � � ���O*�� � ���O* ������E���#��*

~{zBt+MOMOhOMUX N�Wg^_W�MUNy\]nEpRP-v]K WyqO\]t+p-X�P-b l+T�\��CM b9^cV Z \cl+W�PRq#^cpeN Z N�W�MUbfN�� r�\]bfb t+V+PRqO^ 0W�P-\]VDN Z N�WQMObfN1qO\]t+p-X P-V+qUT�M#^cN�M WQK+MOP-T qgK�^cV+V+MOpLq#^_lm^cqOPFW Z PRV5x Y M:Ts\cl+WQPRqON ^cV+XDpR\���MUT W�K+MUP-TMUT�T�\cT2Tg^_W�MUN��LIapRNQ\9^ x Y MUTkqO\]b b t+V+P-q#^_W�P-\]V+N�p-PRV+M1qO\]t+p-X Y M1N}l�pRPRqUMOX`W�\fb9^cV Z \cW�K+MUTaqO\]b"0b t+V+PRqO^_W�PR\]V p-PRV+MON ��P-W�K \cl+W�P-q#^cpBW�^_l�N���J K+MUNQM�Wg^_l�NeqO\]t+pRX Y M�l�t+bsl@MOX Y Z ^2NQz{t+MOMUhOMOX N}Wg^_W�MW�\ ^cNQN�tuT�Mjb PRV+PRb t+b pR\]NQNLPRV W�K+Mkb9^cP-V�p-PRV+M#� [ ^_T�v]MUT V+MUW ��\cT � N qU\]t+pRX Y MyqO\]V+V+MOqUW�MUX-��P-W�Kx Y MUT�N ��P-W�K9bfP-V+PRb t+b NQPRv]V�^cpX+MOvcT�MOX�^_WQPR\]V.� | t+q6K \]n�NQzBt+MOMOhOP-V+v l+TQ\]vcT�MONQN �L^cN/\cT�PRv]P-V�^cpRp Zbf\cWQP-�_^_W�MOX YBZ W�K+M X+MONQP-TQM W�\ bfM#^cNQtuT�M vcTg^#�uPFWg^_W�PR\]V�^cp ��^��CMON ��P-W�K ^cV�PRVCW�MUT�nwM:T�\]bfMUW�M:T���aTg^��{P-Wg^_WQPR\]V�^cp9�L^#�CMONO�{^cN4l+T�MUX+PRqUW�MUX YBZ l�K Z NQP-qON6��\]t+p-X Y ML�CMUT Z NQb9^cp-p �"J�\ bfM#^cN�tuT�M�W�K+MUP-Tbf\��CMObfMUV W�\]n ^ybfPFTQT�\cT�P-Vs\]V+M�^_T�b \]n ^cVsPRVCW�MUT�nwM:T�\]bfMUW�M:T%��\]t+p-X TQMOz{t+PFT�MH^cqUqOtuTg^cq Z Y MUpR\��W�K+M NQK+\cWjV+\]PRNQM pRP-bfP-W�� J K+MsbfPRV+P-b t+b l�K�^cNQM X+P @MUTQMOV+qOMc��� � ��bfM#^cNQtuT�^ Y pRM �HPFW�K ^ qO\]V90�CMOVCW�P-\]V�^cp�P-V WQMUT�nwMUT�\]b MUW�MUT�PRN�l+T�\cl \cTQW�PR\]V�^cp>W�\ �

�HK+MUTQM P-N WQK+M V t+b Y MUT�\]n�l�K+\cW�\]V+Nlm^cNQN�PRV+v9W�KuT�\]t+v]K�W�K+M P-V W�M:T�nwMUT�\]bfM:W�MUTkX+tuT�P-V+v WQK+M bfM#^cNQtuT�MUbfMOVCWaPRVCW�MUTQ�_^cp � | \]N}W ��t+qUW�t90^_W�P-\]V+N ^_T�PRN�M�n TQ\]b W�K+M t+VBt+N�MOX PRVul�tuW l \cTQW / N1�_^cqOt+t+b ��t+qUW�t�^_WQPR\]V+N�� � Z T�MUl�pR^cqOPRV+v8W�K+M�_^cqOt+t+b ��P-W�K�^�NQz{t+MUMOhOMOX��c^cqOt+t+b PFW K�^cN Y MOMOV�MON�WQPRb9^_W�MUX W�K�^_W W�K+M9l�K�^cNQM X+P MUT�MOV+qOMbfMO^cNQtuTg^ Y pRM Y MUW ��MOMUV W�K+MjW ��\ ^_T�bfN/��PRp-p Y M1l+T�\cl@\cTQWQPR\]V�^cp�W�\ � �a~{PRV+qUM P-NHW Z l�P-q#^cpRp Z^ p ^_T�v]MyVBt+b Y MUTHW�K+P-N ��\]t+pRX Y M1^ NQPRv]V+PFx�q#^cV WHPRb l+TQ\ �CMOb MOV W P-V`^cqOqOtuT�^cq Z �

" (

Page 49: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+Mfl+T�MOqUPRNQP-\]V�\cl+WQPRq#^cp�l�K�^cNQM bfM#^cNQtuTQMObfMOVCW5��PRpRp4^cpRp-\�� nw\cT W�K+M9NQ^cbfM P-b l+T�\��CM�0bfMUV WjPRV \cl+WQPRq#^cp�v Z TQ\]NQqO\cl@MUN���~{z{t+MOMUhOMOX5v Z TQ\]NQqO\cl@MUN ��PRpRp Y Mf^ Y pRM W�\`bfMO^cNQtuT�MsTQMOp ^_W�PF�CM\cl+W�P-q#^cp@l�K�^cNQM��P-WQK�l+T�MOqUPRNQP-\]V Y M Z \]V+X�W�K+MjN}Wg^cV+X�^_T�X`zBt�^cV W�t+b pRP-bfP-W��

4 �FS � ;=�F> �$ H �:���8� �5Q�@��* � ���?�

JLK+M \cl+W�P-q#^cpkv Z T�\]N�qO\cl@M P-N`^ TQ\cWg^_W�PR\]V�NQMOV+NQ\cT8t+N�MOX PRV P-V+MUTQW�PR^cpyv]t+P-X�^cV+qOM N Z N 0W�MUbfN2^cV+X8\cW�K+MUT2v]MO\cl�K Z NQPRqO^cpe^_l+l�pRP-q#^_W�PR\]V+N��HJLK+MONQM \cl+W�P-q#^cp�X+M:�uPRqUMONk^_T�M T�M:l�p ^cqOP-V+v�\]p-X+MUTbfMUq6K�^cV+P-q#^cp!v Z T�\]NQqO\cl MONHW�K�^_Wa^_T�M Y ^cNQMOX8\]V�N�l�P-V+V+PRV+v bf\]bfMOVCW�t+b �HK+MUMOpRN��a�al+W�P-q#^cp!v Z 0T�\]N�qO\cl@MON9\# MUT�^cXu�_^cV Wg^cv]MUN9\]naNQPRhOM_��qO\]N}W#�Lp ^cq � \]nkbf\��uP-V+v�lm^_TQW�NO� ^cV+X PRbsl+T�\ �CMUX NQMOV90NQPFW�P-�{P-W�P-MON�� J K+M�\cl+W�PRqO^cp v Z T�\]NQqO\cl M�P-N MOPFW�K+MUT9^8T�PRV+v�p ^cNQMUT v Z T�\]N�qO\cl@M�\cT9^ x Y MUTf\cl+WQPRqv Z T�\]NQqO\cl M#�-� V5W�K+MfT�P-V+v�p ^cNQMUT1v Z T�\]NQqU\cl@Mc�"W�K+M:T�M9PRN ^�vC^cP-V5bfMOX+PRt+b PRV+NQP-X+MfW�K+Mfq#^#�uPFW Z �r�\]t+V WQMUT 0 l+TQ\clm^cvC^_W�PRV+v2�L^#�CMONyl+T�\{X+t+qOM ^�n T�MOz{t+MUV+q Z NQK+P-n W5��K+MOV T�\cWg^_W�P-\]V�P-N ^_l+l�pRP-MOX�W�\W�K+M9qO^��{P-W Z �3� V5W�K+Mfx Y MUT \cl+W�PRqfv Z T�\]NQqO\cl M W�K+M9NQ\]tuTQqOM PRN1\]tuW�N�PRX+MfW�K+Mfx Y MUT T�PRV+v���J K+MqO\]t+VCW�MUT 0 l+T�\clm^cvC^_W�P-V+v��^��CMON l+T�\BX+t+qOM�^�l�K�^cN�M�NQK+P-n W��HK+MUV T�\cWg^_WQPR\]V5PRN ^_l+l�p-PRMOXDW�\�W�K+Mx Y MUT�TQPRV+v�� � \cW�K�W Z l@MONL\]n!X+M:�uPRqUMON ^_T�M Y ^cN�MOX�\]V W�K+M ~u^cv]V�^cqyM� @MOqUW W�K�^_W NQMOV+N�MONHP-V+MUTQW�PR^cpT�\cW�^_W�PR\]V \]nL^ Y \{X Z ��J K+M ^cP-b \]n�WQK+PRN1W�K+MON�PRN1P-N W�\�PRVC�CMON�WQPRvC^_W�MfN�z{t+MOMOhUPRV+v8PRV x Y MUT�N NQ\\]V+p Z W�K+M1x Y M:Tj\cl+WQPRq v Z T�\]N�qO\cl@M5��PRp-p Y M T�M:�uPRM���MOX.��� WkP-NaV+\cW�MOX8W�K+\]t+v]K8W�K�^_WkNQz{t+MUMOhOPRV+vqO\]t+p-X"�}t+N�W2^cN ��MUpRp Y M ^_l+l�pRPRMUX�W�\ T�PRV+vsp ^cNQMUT�v Z TQ\]NQqO\cl@MUN��

JLK+M9~u^cv]V�^cq M� @MOq:W v]MOV+MUTg^_WQMON1^cV5\cl+W�P-q#^cpelm^_W�K X+P @MUT�MUV+qOMfW�K�^_W1P-Njl+T�\cl \cTQW�P-\]V�^cpW�\s^ T�\cWg^_W�P-\]V T�^_W�M#��IaV�\cl+WQPRq#^cp@lm^_W�K�X+P MUT�MOV+qUM � ��PRp-p Y MyM��{l@MUT�P-MOV+qOMOX YBZ W ��\ qO\]t+V90W�M:TQl+T�\clm^cvC^_W�P-V+v9pRPRv]KCW Y M#^cbfNaPRV8^fx Y MUTkpR\B\cl8\]n�T�^cX+PRt+N � �mT�\cWg^_W�P-V+v ^_T�\]t+V+X8P-W�NHqOMOVCWQTg^cp^ �uPRN ^_W2^ Tg^_W�M � �m^cqOqU\cT�X+PRV+v WQ\ � - � �

� %��K+MUT�M � PRN�W�K+My^_T�MO^ � � #�MOV+qOp-\]NQMOX YBZ WQK+Myp-\{\cl�^cV+X � �� PRN�W�K+Ma�CMOp-\{qOPFW Z \]n�WQK+MapRPRv]KCWWQT�^��CMOp-PRV+vsPRV�^ x Y MUT��HPFW�K�T�MOn T�^cqUW�P-�CMjPRV+X+M�� � �/J K+M1\cl+WQPRq#^cp>lm^_W�K�X+P @M:T�MOV+qOM ^_T�P-NQMON�n T�\]bX+P @MUT�MUV WjX+PRN�W�^cV+qOMONjW�Tg^��CMUpRMOX YBZ W�K+M qOp-\{q � ��PRNQM ^cV+X qO\]t+V WQMUT�qOp-\{q � ��PRNQM Y M#^cb Ny\��CMUTyW�K+MN�^cb MfW�PRbfM9P-V WQMUTQ�_^cp ����I X+P @M:T�MOV+qOM�PRVD\cl+W�PRqO^cp�lm^_W�K p-MOV+vcW�K�pRM#^cX+N W�\ ^�X+P MUT�MOV+qOM�PRVl+T�\clm^cvC^_WQPR\]V�WQPRbfMON��

� � � �� � � �� � � - � � � # �

� # - � �

� # � �

� \cT2^ x Y MUT���\]t+V+X`tul�P-V`^ qO\]PRp.��P-W�K W�tuT�V+NO�

� � - � � � # � �

" #

Page 50: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+M5X+P MUT�MOV+qOMDP-V l+TQ\clm^cvC^_W�PR\]V W�P-bfM Y MUW ��MOMOV W�K+M W ��\ qO\]t+VCW�MUT�l+T�\clm^cvC^_W�PRV+v Y M#^cbfNq#^ct+N�MON2^ V+\]VuT�MOqOPFl+T�\{q#^cp�l�K�^cNQMjNQK+PRn W � � � � �

� � � � ���

PRV�W�K+Mjx Y MUT��

� � � � � � � � � � ��- � � � # � � � � �

� � � �

� W PRN V+\cW�MUX*W�K�^_W9WQK+M ^ Y \ �CM8X+MUTQP-�_^_W�PR\]V PRv]V+\cTQMON9T�MOp ^_WQP-�uPFW Z qO\]b l�p-MUW�MOp Z � J K+M8qO\cT�T�MOqUWX+MUTQP-�_^_W�PR\]V"��\]t+pRXst+NQMHv]MOV+M:Tg^cp+T�MOp ^_WQP-�uPFW Z � � \cW�K b MUW�K+\{X+N�X+\+� K+\���MU�CMUT#�BMOV+Xftul&��P-W�K W�K+MN�^cb MyN�\]pRtuW�P-\]V.�

�/^_T�P-\]t+N ^cMUT�\]N�lm^cqOM�^cV+X ^cN�WQT�\]N}lm^cqOM�l�pR^_W�nw\cT�bfNjW�K�^_W ��\]t+pRXDMOb l�p-\ Z v Z T�\]NQqU\cl�PRqN Z N�W�MOb N4T�MOzBt+P-T�MH^cqOqOtuTg^_WQM2bfM#^cNQtuTQMObfMOVCW�\]n@�CMUT Z NQbf^cpRp+T�\cWg^_W�P-\]VsTg^_WQMON���IaN�^cVfM��+^cb l�pRM_�W�K+MkT�\cWg^_WQPR\]V Tg^_W�My\]n!W�K+MyM#^_TQW�K � �

���PRN�^_l+l+T�\��uPRb9^_WQMOp Z ��0 X+MOvcT�MOMUN�l@M:T2K+\]tuT#��\cTH^ Y \]tuW

3!� � ��� Tg^cX+PR^cV+N�l MUT�N�MOqO\]V+X.�&JLK+M W Z l�PRq#^cp2T�MUz{t+P-TQMObfMOVCW�nw\cT`^cP-T�q:Tg^cn W�V�^#�uP-vC^_W�PR\]V�^cpMOzBt+P-l�bfMUV WEPRNeW�\yNQMOV+N�M T�\cW�^_W�PR\]V+N�\]n � � � ��X �

�\cT 3 � � � ��� Tg^cX+PR^cV+NEl MUTENQMOqO\]V+X.�4JLK+PRN

T�MUz{t+P-TQMOX�^cqOqOtuT�^cq Z P-V�T�\cWg^_WQPR\]V�q#^cV Y MyWQTg^cV+NQpR^_W�MOX`P-V WQ\f^sT�MUz{t+P-TQMObfMOVCWH\]V�W�K+M bfMO^cNQtuT�M\]n�V+\]VuT�MOqUP-l+T�\Bq#^cp"l�K�^cNQM NQK+PRn W�� r�K+\{\]N�PRV+v�^9qO\]V+NQMUTQ�_^_W�PF�CM N�MUWk\]nElm^_T�^cbfMUW�MUTQNO�>^fx Y MUTy\]nP-V+X+M�� ���,0{�/� � � ��W�tuTQV+NO�e^`v Z TQ\]NQqO\cl@M ^_T�M#^`\]nL^_l+l+T�\��+P-b9^_W�MOp Z � � ��NQzBt�^_T�MfqOMOVCW�P-bfMUW�MUTQNO�^cV+X�^�� �� NQ\]tuTQqOMc�

� � � � � ���10�� � � �u� � # � � � � � � �� � � � � ��� � � � + ��� � � � � � ! � 3 �.+ � � � ��� � � � � � ��� � ��� � � � � � � � �

~{K+\���V P-VDx�v]tuTQM��+8P-N ^�x Y MUT \cl+W�P-q9v Z T�\]N�qO\cl@M9NQM:W tul ^cN ^`x Y MUT \cl+W�PRqfP-V WQMUT 0nwMUTQ\]bfMUW�MUT��� V ^�x Y MUT \cl+W�PRq P-V W�M:T�nwMUT�\]bfM:W�MUT pRP-v]K W n TQ\]b ^ NQ\]tuTQqOM � t+NQt�^cpRp Z ^8p ^cNQMUT � PRNX+PF�uPRX+MUX PRVCW�\yW ��\ Y MO^cbfN YBZ ^ 0 � 0 0 � Y M#^cb N�l�pRPFWQW�MUT/^cV+XsWQK+MOVfqO\]tul�p-MOXfPRVCW�\ Y \cW�K MOV+X+N�\]nW�K+Myx Y MUTHqO\]PRp�NQMUV+NQ\cT���JLK+M p-PRv]KCW�W�K�^_W�qO\]bfMUN�\]tuW�M#^cqgK�NQPRX+Mjb t+N�WHv]\ Y ^cq � W�KuTQ\]t+v]K�W�K+MY M#^cb&N�l�p-P-WQW�M:TL^cV+X�P-V WQ\ ^ l�K+\cWQ\{X+MUW�MUqUW�\cT��EJLK+PRN�X+MUW�MUqUW�\cT ��PRpRpX+MUW�MOq:W�W�K+MaNQtul@M:TQl@\]NQPFW�PR\]V\]n�W�K+MaW ��\1�L^#�CMON��4J K+MyPRVCW�MUTQnwMUT�MOV+qOM \]n�W�K+M Y M#^cb N b t+N�W Y MjbfMO^cNQtuT�MOX�PRV�W�K+Myl+TQMONQMOV+qOM\]n�T�\cWg^_W�P-\]V`^cN�^sn T�P-V+v]M NQK+P-n WH\cT�PRV�^cV+\cWQK+MUTHN�MOV+NQM ^cN�^ l�K�^cNQM NQK+PRn W��

JLK+M�p-PRbfPFW�PRV+vDn ^cqUWQ\cT�nw\cT`^�l�K�^cNQM b M#^cNQtuT�MOb MOV W3��PRpRp Y M W�K+M l�K+\cW�\{X+M:W�MOqUW�\cT�/ N^ Y P-pRP-W Z W�\�X+PRN�WQPRV+v]t+PRN�K Y MUW ��MOMOVDW�K+M NQK+PRn W P-V5W�K+M PRVCW�MUT�nwMUTQMOV+qOM lm^_WQW�MUT�VD\]n�W�K+M qO\]t+VCW�MUTl+T�\clm^cvC^_WQPRV+v��L^��CMUNsX+t+M W�\8T�\cWg^_W�P-\]V ^cV+X V+\cW p ^cNQMUTsV+\]PRN�M#�5JLK+M�nw\]p-pR\��HP-V+v X+MUTQP-�_^_W�PR\]VP-N Y ^cNQMOX*\]V � � ���� � � � ��� � � � � V x�v]tuT�MD� - W�K+M�PRVCW�MOV+NQPFW Z \]naW�K+M8^#�CMUTg^cv]M`X+MUWQMOqUW�\cTl�K+\cW�\BqOtuTQT�MUV W �

�PRNkl�pR\cWQWQMOX5^cvC^cPRV+N}W V+\]VuT�MUqOP-l+T�\Bq#^cp�l�K�^cNQMfNQK+P-n W � � �9r�\]V+N�WQT�t+qUWQP-�CM P-V90

W�M:T�nwMUT�MOV+qUM Y Z W�K+M�W ��\���^��CMON�T�MON�t+p-W�N�PRV l@MO^ � l�K+\cW�\{qOtuT�T�MOVCW��e� K+MOV W�K+MUT�MLP-NEV+\kT�\cWg^_WQPR\]VY \cW�K`lm^_W�K8pRMOV+vcWQK+Nk^_T�M1W�K+M N�^cbfM1^cV+X qU\]V+N�WQT�t+qUWQP-�CM PRVCW�MUTQnwMUT�MOV+qOM ��PRpRp�\{qUqOtuT��aJLK+M hOMUT�\l�K�^cNQM�NQK+PRn WfWQK+MUT�MOnw\cT�M�qO\cTQT�MON}l@\]V+X+NfW�\�WQK+M�l@M#^ � l�K+\cW�\BqOtuTQT�MOVCW�� IaNsTQ\cWg^_W�PR\]V \{qOqUtuT�NO�� � N�K+PRn W�N n T�\]b W�K+M \cT�P-v]PRV�^cV+X ^8qO\cTQT�MUN�l@\]V+X+P-V+v�qgK�^cV+v]M�P-V�l�K+\cWQ\{qOtuTQTQMOV WsPRN N�MOV+NQMOX.�| ^ �+P-b t+b � � NQMUV+NQP-W�PF�uPFW Z W�\1T�\cWg^_W�P-\]V q#^cV Y Mk^cqOz{t+PFT�MOX YBZ bf^cPRVCWg^cPRV+P-V+v1W�K+Ma\cl@MUT�^_W�PRV+v

" "

Page 51: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � ��� � �� � � � � � � ��� � ���� ��� ���

l \]PRVCW2^_W2^ �� Y PR^cN���JLK+PRN l�K�^cNQM P-N���K+MUT�MjWQK+M b9^ �uPRb t+b NQpR\cl Mj\]n�W�K+M NQP-VBt+N�\]PRX�^cp�n T�PRV+v]M

lm^_WQWQMUT�V \BqOqOtuT�N��EIaV Z ^_l+l�pRP-MOXsT�\cW�^_W�PR\]V+N$��PRpRpu�_^_T Z W�K+M PRVCW�MUTQnwMUT�MOV+qOMHP-TQTg^cX+PR^cV+qOM�^cV+X1��P-W�KPFW�W�K+Mkl�K+\cW�\BqOtuTQT�MOVCW��

S4K�^cNQM8t+V+qOMUTQW�^cPRVCW Z ��PRp-pHT�MON�t+p-W�n T�\]b t+V+qOMUT�Wg^cPRVCW�PRMUN�^_T�P-NQPRV+v�PRV W�K+M NQ\]tuT�qUM#� I��t+qUWQt�^_W�PR\]V`P-V�W�K+MjpRPRv]KCW�PRVCW�MOV+NQPFW Z ��\]t+p-X Y MjbfPRNQP-V WQMUTQl+T�MUWQMOX�^cN2^ T�\cWg^_W�P-\]V.�/JLK+M l�K�^cNQMt+V+qOM:TQWg^cPRVCW Z�� � � � � � W�K+Myt+V+qOMUTQWg^cP-V W Z PRV�V+\]VuT�MOqUP-l+T�\Bq#^cp 0'l�K�^cNQM�0 N�K+PRn WabfMO^cNQtuT�MObfMUV W �6��PRp-pY Mjl+T�\cl \cTQW�PR\]V�^cp>W�\sNQK+\cW2V+\]P-NQM X+PF�uP-X+MOX Y Z W�K+MjPRVCW�MUT�nwM:T�MOV+qOM1lm^_WQWQMUT�V`n T�P-V+v]M1NQp-\cl@M#�/J K+MbfP-V+PRb t+b MUTQTQ\cT �HP-pRp�\{qUqOtuT ��K+MOV`W�K+M1n T�P-V+v]M NQp-\cl@M1P-NHb9^ �uPRb t+b2� � TQ\]b � P-v]tuT�M � - WQK+PRNb9^ �uPRb t+b&NQp-\cl@MyPRN MOz{t+PF�c^cp-MOVCWHW�\ W�K+Mj�_^cpRt+M � �

��4J K t+N

� � � � � � � � �� �

" �

Page 52: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � ����� � � � � �� � � � � � � � � � �� �� � � � ��� ��� ����� ��� � �

� V�WQMUT�bfN \]n�W�K+M ^��CM:Tg^cv]MjV t+b Y MUTH\]n!l�K+\cW�\]V+NO� �� �+W�K+Myl�K�^cNQM MUT�T�\cT2P-N

� � � � � ! �� � � �

�� � �

�! �� %

��K+MUT�M�

P-N/W�K+M2P-V �CM:T�NQM Y ^cV+X ��PRXuW�K9\]n@W�K+MHN Z N�WQMOb&^cV+XfW�K+Mab M#^cNQtuT�MOb MOV W/PRVCW�MUTQ�_^cp�W�PRbfM��JLK+MjT�MUNQt+p-W�P-V+vsl�K�^cNQMjt+V+qOMUTQW�^cPRVCW Z PRNLW�K+MjN�^cbfMyNQ\]pRtuW�P-\]V�bfMUV W�P-\]V+MOX�l+TQMU�uP-\]t+NQp Z �

JLK+M ^cqOqOtuT�^cq Z PRV5X+M:W�MUT�bfP-V+PRV+v`W�K+Mfl�K�^cN�M�N�K+PRn W PRN pRPRb P-W�MOX YBZ WQK+Mfl�K+\cW�\{X+MUWQMOq�0W�\cT zBt�^cV W�t+b M � qOPRMOV+q Z ^cV+X t+p-W�P-b9^_W�MOp Z�Y Z WQK+M�nwt+V+X�^cbfMOVCWg^cpLz{t�^cVCW�t+b V+\]PRN�M�PRV�W�K+MbfMO^cNQtuT�MObfMUV W4\]n l�K�^cNQM#� � Z t+NQPRV+v NQz{t+MOMUhOMOX9N�Wg^_WQMON4\]n pRPRv]KCW4PRV W�K+M v Z TQ\]NQqO\cl@M W�K+MHzBt�^cV90W�t+b V+\]PRNQMkqO\]t+p-X Y MkTQMOX+t+qOMOX Y MOpR\�� WQK+MyN}Wg^cV+X�^_T�X�z{t�^cVCW�t+b pRP-bfP-W��"J K+MaT�MOX+t+qUMOX�l�K�^cNQM��t+qUWQt�^_W�PR\]V+N�\]n�W�K+MjNQz{t+MOMUhOMOX�z{t�^cXuT�^_W�tuT�MON ��\]t+pRX�PRV+qUT�MO^cNQMjW�K+Mjv Z T�\]N�qO\cl@MyNQMOV+NQPFW�P-�{P-W Z �

I NQzBt+MOMOhOMUXsx Y M:T/P-V W�M:T�nwMUT�\]bfM:W�MUTEqO\]t+pRX X+MUW�MUqUW4^kl�K�^cNQMLX+P @MUT�MUV+qOM Y Z ^ Y ^cp ^cV+qOMOXK+\]bf\BX Z V+M1X+M:W�MOqUW�P-\]V�W�MOqgK+V+PRzBt+M ^cNaNQK+\���V8PRV�x�v]tuT�M9��09� � MUpR\�� W�K+M qU\]b l�tuWg^_W�P-\]V+Na^_T�Mq#^_T�T�PRMOX \]tuW4W�\jNQK+\���W�K�^_W4NQzBt+MOMOhOMOX9N�PRv]V�^cpRN ��PRpRpm^cp-pR\�� nw\cT�^ b \cT�M�l+T�MOqOP-NQM2bfM#^cN�tuT�MObfMOVCW\]n l�K�^cNQM#� ~{MUbfPRqOpR^cNQNQP-q#^cp�W�K+MO\cT Z P-N ^_l+l�p-PRMOX K+MUT�M#��I qOpR^cNQNQP-q#^cp ^cV�^cp Z N�PRN PRN NQPRbsl�pRMUT W�\nw\]p-pR\�� ^cV+X8^_T�T�P-�CMON2^_WHW�K+M1NQ^cbfMjT�MUNQt+p-Wk^cN�W�K+M1z{t�^cVCW�t+b ^cV�^cp Z N�PRN��LJLK+M1MOV+X�T�MON�t+p-W ��PRp-pNQK+\�� W�K�^_W�NQz{t+MOMUhOPRV+v WQK+MjNQP-v]V�^cp.�HP-pRp>pRMO^cX�W�\s^cV`PRb l+TQ\ �CMOX�bfM#^cNQtuTQMObfMOVCW��

I N�WQT�\]V+v p-\{q#^cp \]NQqOP-pRpR^_W�\cTsx�MUpRX PRN qO\]b Y PRV+MOX ��P-W�K ^ ��M#^ � NQPRv]V�^cpLx�MOp-X ^_WfW�K+M0 � 0 0 � Y M#^cbdN�l�pRPFWQW�MUT�� � V�W�K+Myq#^cp-qOt+p ^_W�P-\]V+N WQK+MyT�MUnwMUT�MOV+qOM Y M#^cb���PRpRp Y Mjb \{X+t+p ^_WQMOX�^_W�^X+P @MUT�MUV W n T�MOz{t+MUV+q Z � JLK+PRNyq#^cV bf\{X+MOp"WQK+Msn T�MUz{t+MOV+q Z NQK+P-n W�MOX�x�MOp-X bf\BX+MONkt+NQMOX5PRV W�K+M

" �

Page 53: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � � � � � � � ����� � � �� �� ��� � ��� �� � ��� ������ � � ��

x Y MUT bfP �+PRV+v�M��ul MUT�P-bfMOVCW1X+\]V+M Y Z W�K+M1� ��| T�MON�M#^_T�qgK5W�M#^cb ��� � � � ��� ��� �� � � � ����� � �JLK+M NQPRv]V�^cp Y M#^cb ��K+PRqgK�b \{X+MOp-NHW�K+M NQPRv]V�^cp!n T�\]b W�K+M v Z TQ\]NQqO\cl@M���PRp-p!K�^#�CMs^9X+P @MUT�MUV Wl�K�^cNQM�� JLK+MONQM W ��\ Y M#^cbfN���PRpRp Y M T�MOqO\]b Y PRV+MUX PRV ^ nwt+N�PR\]V N}l�pRPRqUM�\]n W�K+M�W ��\8x Y M:T�N��JLK+MH\]tuWQl�tuWEl@\cT�W�N%��PRp-p+qO\]V W�^cPRVsWQK+MHNQt+b ^cV+X X+P @MUT�MUV+qOM2\]n W�K+M NQP-v]V�^cp^cV+XsW�K+M�T�MUnwMUT�MOV+qOMx�MOp-X+N��aIaNk^ T�MON�t+p-Wk\]n�qO\]V+NQMUT��c^_W�P-\]V8\]nEMUV+MUT�v Z ^fbfP-VBt+NaN�PRv]V�b t+N�WkM��uPRN�WaP-V�W�K+M NQMOqO\]V+Xx�MOp-X>�m^cNQNQt+bfP-V+vf^ l�p-t+NHNQP-v]V�P-V�W�K+Mkx+T�N�WHx�MUpRX.�

��K+MOV5W�K+M x�MUpRXD\]n�MOP-WQK+MUT \]tuWQl�tuW1l \cTQW P-N X+MUW�MUqUW�MOX Y Z ^`NQzBt�^_T�Mfp ^�� X+MUW�MOqUWQ\cT#�W�K+M1W ��\fx�MUpRX8qO\]VCWQT�P Y tuWQPR\]V+Nk^_T�M bfP �+MOX>�^cV+X�W�K+M \]tuWQl�tuWkqOtuT�T�MOVCWkqO\]V W�^cPRV+Nk^fijr W�M:T�b^cV+XD^cV IHr�W�MUT�b T�MONQt+pFW�PRV+v�nw\cTQb P-V W�M:T�nwMUT�MOV+qUM#�`JLK+MfqOpR^cNQNQPRqO^cp/^cV�^cp Z NQP-N \]n�W�K+Mfb P �+P-V+vMOzBt�^_W�PR\]V�q#^cV Y M NQK+\���V Y MOp-\�� �

��K+MOV9q#^cp-qOt+p ^_WQPRV+vjWQK+MHX+MUW�MUqUW�\cT�qUtuTQT�MOVCW#�ub t+p-WQP-l�p Z WQK+MHqO\]b l�p-M�� x�MOp-X ^cb l�pRPFW�t+X+MY Z � ��� � �C^cX+XsPFW�NeqO\]b l�p-M�� qO\]V �}t+vC^_WQM�^cV+X NQzBt�^_T�M�W�K+M�NQt+b2� � \cTe\]V+MLX+MUW�MUqUW�\cT#� ��M�\ Y Wg^cP-V.(

� � ����� # � � ! ���� # �

���� ��� � � � � ! � � � � � # � � ��� � � � � � ��� �

� � � �! � � � � � � �# � � ����� � � ����

#" �

Page 54: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� ! � �! � � # � �# � � #!� � � # W � � � � Z � � ##� � � # W � � ��� Z � � � � �!� � � � # W � � � � Z � � � �#� � � � # W � � ��� Z �%

� � ! � # � � � W # � � ��� Z � � ��� � � ! � �# � � � W ��� � � � Z � � �! � # � � W ��� � � � Z � � �! � �# � � � � W # � � ��� Z � � ���^cV+X�nw\cTHW�K+Mj\cW�K+MUT�X+MUW�MOq:W�\cT#�

��� ����� # � � ! ���� # �

���� ��� � � � � ! � � � � � # � ����� � � � � � ��� �

� � � �! � � � � � � �# � � � ��� � � ����

#

� ! � �! � � # � �# � � #!� � � # W � � � � Z � � ##� � � # W � � ��� Z � � � � �!� � � � # W � � � � Z � � � �#� � � � # W � � ��� Z �

� � ! � # � � � W # � � ��� Z � � ��� � � ! � �# � � � W ��� � � � Z � � �! � # � � W ��� � � � Z � � �! � �# � � � � W # � � ��� Z � � ��� �J!^ � PRV+v W�K+MyqOtuTQT�MUV WaX+P @MUTQMOV+qOMc�

� ��� � � � � ��� %^cp-p@W�K+MjWQMUT�bfNLq#^cV+qOMUp�\]tuW�M��+qUMUl+W2nw\cT W�K+M pR^cN�W�nw\]tuT�� � �

� ��� � � � ! � # � � � W # � � ��� Z � � ���� � � ! � �# � � � W ��� � � � Z� � � �! � # � � W ��� � � � Z� � � �! � �# � � � � W # � � ��� Z � � ��� �� V�WQK+M z{t�^cVCW�t+b bfMOqgK�^cV+PRqO^cp!^cV�^cp Z NQP-N�\]n!WQK+M bfP �+PRV+v MOzBt�^_W�PR\]V>�+W�K+MyW�MUT�bfN ��P-W�K

NQP-X+M Y ^cV+X�qU\]b l@\]V+MOVCW�N�\]n � � �HP-pRp V+\cW ^_l+l M#^_T Y MOqO^ct+NQM+�HK+MOV�qO\]V+NQP-X+MUT�PRV+v W�K+MaNQzBt+MOMOhOMUXNQP-v]V�^cp.��MjP-v]V+\cT�MjWQK+MONQMjW ��\ W�MUT�b N�^cV+X`^_T�Mjp-MOn W/��P-WQK

� ��� � � � ! � �# � � � W ��� � � � Z � � � �! � # � � W ��� � � � Z �" �

Page 55: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � � � � ��� � ��� � ��� � � �� � ��� � � � �������

4 � � � � ���O* ������E�'��� � ����������

JLK+MaV+\]VuT�MOqUP-l+T�\Bq#^cp l�K�^cNQMkX+P MUT�MOV+qUMyb M#^cNQtuT�MOb MOV W�\]V � � q#^cV Y M2l+T�MUX+PRqUW�MUX Y ZPFW�N�MUN�W�PRbf^_W�\cT#� �� �m^cN�NQK+\���V`P-V�x�v]tuT�Ms�2 �

o/^cqgK Y M#^cb n T�\]b W�K+M pR^cNQMUT2qO^cV Y M TQMUl+T�MONQMUV W�MUX Y Z P-W�N�MOpRMOq:WQT�PRqyx�MOpRX.�LJLK+PRN x�MOpRXb t+N�W�PRVyW�tuT�V Y M4NQK+\���V ^cN�W�K+MENQt+b \]n+^�N�PRv]V�^cp]W�MUT�b�� � � � l�pRt+N�WQK+M4zBt�^cV W�t+b bfMOqgK�^cV+P-q#^cpV+\]P-NQM WQMUT�bfNO�$����^cV+X � � � � JLK+M W ��\�z{t�^cVCW�t+b V+\]PRN�M W�M:T�bfN ��PRpRp Y MsN�z{t+MOMOhUMOX.���}V W�K+Mx�v]tuT�M ����PRN4lm^_Tg^cpRp-MOpmWQ\�� � Y MOqO^ct+NQMaW�K+M Y MO^cb PRN4X+MUx�V+MOX�^cN Y MUPRV+v1T�M#^cp���K+MOV P-W�qU\]bfMON\]tuW�\]n�W�K+Mjp ^cNQM:T��

� \�� pRM:W#�� ! � ! � � � ! � � � � ! � � �! � ! � � � ! � � � � ! �� # � # � � � # � � � � # � � �# � # � � � # � � � � # �" �

Page 56: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� ��� � � � � ! � � � ! � � � � ! � � � � # � � � # � � � � # � � � � � W ��� � � � Z�j� � � ! � � � ! � � � � ! � � � � # � � � # � � � � # � � � � W ��� � � � Z � � ! � � # � � � ! � � # � � � � ! � � # � � � ! � � # � � � ! � � # �� � � ! � � # � � � � ! � � # � � � � ! � � # � � � ! � � # � � � � � � W ��� � � � Z� � � ! � � # � � � ! � � # � � � � ! � � # � � � ! � � # � � � ! � � # �� � � ! � � # � � � � ! � � # � � � � ! � � # � � � ! � � # � � � � � W ��� � � � Z � � � ! � � � ! � � � � # � � � # � � � � ! � � # � �� � � � ! � � � # � � � # � � � � # � � � ! � � � ! � ��� � � � � W ��� � � � Z� � � � ! � � � ! � � � � # � � � # � � � � ! � � # � �� � � � ! � � � # � � � # � � � � # � � � ! � � � ! � � � � � � W ��� � � � Z �

ikMUx�V+M� � � ! � � � ! � � � � # � � � # � � � � ! � � # �

^cV+X� � ! � � � # � � � # � � � � # � � � ! � � � ! � � �

JLK+MONQM�W ��\�W�MUTQbfN K�^��CM�NQPRv]V+PFx�q#^cV W bfM#^cV+P-V+v�nw\cT WQK+M Z T�MUl+T�MON�MOV W W�K+M�T�MO^cp�^cV+XP-b9^cv]PRV�^_T Z V+\]PRNQM W�MUT�b NkTQMON�l@MUqUW�P-�CMUp Z PRV W�K+M PRV90 l�K�^cN�Mf^cV+X zBt�^cXuTg^_W�tuT�M qO\]b l \]V+MOV WQNj\]nW�K+MyMOp-MOqUWQT�P-qjx�MOp-X`\]n�WQK+MjW ��\ Y M#^cbfN��

� \�� M��{l+T�MONQN � ��� � ^cN� ��� � � � � � � � � � � � W ��� � � � Z � � � � � � � � � � W ��� � � � Z

� � � � � W ��� � � � Z � � � � W ��� � � � Z � � � � � � � � W�� ���� � � Z � � � � W � ���

� � � Z � � � � � ��� � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� P-V�^cpRp Z �� ��� � - � � � � � � � � � � � � - � � � � � � � � � � � � �

� �

Page 57: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

4 � � � � ���O����)������ ���'NF�'�����F� �

��K+MOV*W�K+M�p ^cNQM:T Y M#^cb PRN9N�z{t+MOMOhUMOX PFW�NfW ��\ zBt�^cXuTg^_W�tuT�M�qU\]b l@\]V+MOVCW�N ��PRpRp Y MM��+^cbfPRV+MUX.� [ MUW

� � ��� � ��� � � � � � ��� � � � � � � ��aV+M \]n!WQK+MONQM ��PRp-p>K�^��CM ^sX+MOq:T�M#^cNQMOX8V+\]P-NQMyWQMUT�b ^cV+X�W�K+My\cW�K+MUT/��PRp-p>K�^��CM ^cV`PRV+q:T�M#^cNQMOXV+\]P-NQM W�MUT�b2� � V8W�K+M p ^ Y M��{l@MUT�P-bfMOVCWaW�K+M \]tuWQl�tuWkX+MUW�MUqUW�\cTyqOtuTQT�MUV W��HP-pRp Y M bfP �uMOX2��P-W�K^�N�PRV+M9\cT1qU\]NQPRV+MfW�\�NQMUlm^_Tg^_W�M \]tuW1W�K+MfzBt�^cXuTg^_W�tuT�MfX+MUNQP-T�MUX>�eV�^cbfMOp Z W�K+Mf\]V+M1�HPFW�K W�K+Mp-\���M:THV+\]P-NQMjW�M:T�b2� � W�PRN PRbsl@\cTQWg^cVCWLW�\ qU\]V+NQPRX+MUTHW�K+MjN�PRV+M1^cV+X�qO\]NQPRV+Mjt+NQMOX�P-V�W�K+MybfP �uMUTW�\ Y M�V+\]P-NQMOp-MONQN Y MOq#^ct+NQM`W�K+MUNQM`K�^#�CM�^�n T�MOzBt+MOV+q Z \]n � �HK+P-q6K P-N b t+qgK vcT�M#^_WQMUTfW�K�^cVW�K+M9N�z{t+MOMOhUMOX N�PRv]V�^cp�^_W � � � J K+Mfl�K�^cN�M9X+P @M:T�MOV+qOM MON�WQPRb9^_W�\cT �HP-pRp Y M9q#^cp-qOt+p ^_WQMOXDn T�\]bW�K+MyPRVC�CMUT�N�MjWg^cV+v]MOVCW�\]n � X+P-�{PRX+MOX YBZ ��� | MO^cNQtuT�MObfMUV W�N�\]n�W�K+Mk�_^_T�P ^_W�P-\]V+N�P-V�WQK+Mjl�K�^cNQMX+P @MUT�MUV+qOM1MON�WQPRb9^_W�\cT ��PRp-p>W�MOpRp@WQK+M M��{W�MOVCWH\]n!WQK+MjNQzBt+MOMOhOP-V+v��

� � ��� � � � � � � � � - � ��� � � � � � � � � � - � � � � � � � � � � � � � � � � � � �

- � � �� ��� � � � � � � �� ��� � � � � � � � � � � � - � � �� � � � � � � � �

� � � � � � � � � � � � � �

� � � ��� � � � � � � � � � � � � � � �[ P � M���PRN�Mc�+W�K+M � t�^cXuTg^_W�tuT�MjNQPRv]V�^cp�P-N

� � � � � � � � � � � � - � � � � � � � � � � � � - � � � � � � � � � � � � � � � � � � �

- � � �� � � � � � � � � � � � � �� � � � � � ��� � - � � �� � � � � � � � � � � � � � �

� ��� � � � ���

� � � � � � � � � � � � � � � � � � �JLK+Mjl�K�^cNQMjMON�W�P-b9^_W�\cT PRN

�� � � � � ! � �� � %��&

Page 58: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

^cV+X�WQK+MjMUT�T�\cT2P-V�P-W q#^cV Y M qU\]b l�tuW�MOX YBZ NQt+bfb PRV+v W�K+Mj�_^_T�PR\]t+N qO\]VCWQT�P Y tuW�PR\]V+N�(

� �� � � � � � � ! � �� � � � ��� � ! � � � ! � � � ��� � ! � � � ! � � � ��� � # � � � # � � � ��� � # � � � # �

�� � ! � � � � � � ! � �� � � � ����� � ��� � � � � " # � � ! � � �� � ! � � � � � � ! � � � � � � � � � � ��� � � � � "$# � � ! �

� �� � # � � � � � � ! � �� � � � � � � � ����� � � � "$# � � # � � �� � # � � � � � � ! � � � � � � � � � � ����� � ��� "$# � � # � �

oE�c^cp-t�^_W�PRV+v M#^cqgK�W�M:T�bdPRV+X+P-�{PRX+t�^cp-p Z �uW�K+Mkx+T�N�WHPRN�(

�� � ! � � � � � � ! � �� � � � ����� � ��� � � � � "$#

� � � � � �� � ! � � � � � � � � �

� � ! � �� # � � # � � ����� � ��� � � � � "$#

� � � � ! � � # � � � ! � � # � � � � � � � � � ��� � � # � � � � � � � �- � � ! � � # � � � ! � � # � � #

� � � � � ! � � # � � � ! � � # � � � � � � � ����� � � # � ��� � � � � � �- � � ! � � # � � � ! � � # � � #

��%W�K+MyNQMOqU\]V+X`W�MUT�bdPRN�(

�� � ! � � � � � � ! � � � � � � � � � � ��� � � � � "$# � � � � � �� � ! � � � � � � � � �

� � ! � �� # � � # � � � � � � ��� � � � � "$#

� � � ! � � # � ��� � � � � � � � ! � � # � � � � � � � � � � � # � � � � � � � �- � � #! � � ## � � � #! � � ## # �

� � � � ! � � # � � � � � � � � � � ! � � # � � � � � � � � � � � � � # � � � � � � � �- � � #! � � ## � � � #! � � ## � �

� ! �� #! � � � #! � ��%(

Page 59: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+MjW�K+PFT�X�WQMUT�bdPRN�(

�� � # � � � � � � ! � �� � � � � � � � ����� � � � "$#

� � � � � �� � # � � � � � � � � �

� � # � �� # � � # � � � � � � ����� � � � "$#

� � � � ! � � # � � � # � � # � � � � � � � � � ��� � � ! � � � � � � � �- � � ! � � # � � � # � � ! � � #

� � � � � ! � � # � � � # � � ! � � � � � � � ����� � � ! � ��� � � � � � �- � � ! � � # � � � # � � ! � � #

��%^cV+X�x�V�^cp-p Z �uW�K+Mynw\]tuTQW�K�W�MUT�bdPRN

�� � # � � � � � � ! � � � � � � � � � � ����� � ��� "$# � � � � � �� � # � � � � � � � � �

� � # � �� # � � # � � � � � � � ��� � ��� "$#

� � � ! � � # � ��� � � � � � � � # � � ! � � � � � � � � � � � � ! � ��� � � � ���- � � #! � � ## � � � ## � � #! � �

� � � � ! � � # � � � � � � � � � � # � � ! � � ��� � � � ����� � � ! � � � � � � � �- � � #! � � ## � � � ## � � #! � �

� � # �� ## � � � ## � �r�\]b Y PRV+PRV+v W�K+MyW ��\ V+\]V+hOMUTQ\ W�MUT�b NO�

� �� � ! �� #! � � � #! � � � ! � � � # �� ## � � � ## � � � # � %��K+PRqgK`q#^cV Y MkT�M#^_TQTg^cV+v]MUX�^cN

� ! � � � ! � � � ## � � � ## � � � � # � � � # � � � #! � � � #! � �� � #! � � � #! � � � � ## � � � ## � � � ! � � � ! � � � ## � � � ## � � � � # � � � # � � � #! � � � #! � �� #! � � ## � � � #! � � ## � � � ## � � #! � � � #! � � ## � �

� #

Page 60: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+MaW�MUT�bfN�WQK�^_WLqO\]V W�^cPRV�� #! � \cT � ## � ^_T�Ma�CMUT Z NQbf^cpRp qU\]b lm^_T�MOX W�\ W�K+Mk\cW�K+MUT�N ^cV+X�b9^ ZY MjqO\]V+N�PRX+MUT�MUX�V+MOv]pRP-v]P Y pRM��/JLK+PRN pRM#^#�CMON�� � �

� �� � ! � � � ! � � ## � � � # � � � # � � #! �� #! � � ## � � # � � � ! � � � ! � � � # �� ! � � # � �

JLK+MLW ��\jMUT�T�\cT�N4^ Y \��CMLTQMUl+T�MONQMUV W4T�\{\cW 0 bfM#^cV90 NQz{t�^_T�M��_^cpRt+MONE\]nT�^cV+X+\]b VBt+b Y M:T�N��JLK+MUT�MOnw\cTQM�W�K+M�W�\cWg^cp MUTQT�\cT"PRN"nw\]t+V+X Y Z Wg^ � P-V+vHW�K+M�N�z{t�^_T�M�T�\B\cW"\]nuW�K+M�N�t+b \]n+W�K+M�NQzBt�^_T�MON\]n�W�K+M P-V+X+P-�uP-X+t�^cp�MUTQT�\cT�N��

� �� ! � � # � � � � ! � � � # � � � ! � � � � # � � � #� ! � � # ��! � � � � � � � � # � � � � � � � � � #�� �� � � � � � � � �� �

JLK+PRN9N�W�^_W�MON9W�K�^_WfW�K+M�l�K�^cNQM8X+P @MUT�MUV+qOM b M#^cNQtuT�MOb MOV W ��PRp-pHK�^#�CM�t+V+qOMUTQW�^cPRVCW Z WQK�^_W PRN^_l+l+T�\��+P-b9^_W�MOp Z ^fnwt+V+qUW�PR\]V8\]neW�K+M1P-b9^cv]PRV�^_T Z V+\]P-NQM1W�MUTQb \��CMUT2W�K+M NQP-v]V�^cp�W�M:T�b2�L� K+MOVW�K+Myp ^cN�MUT Y M#^cbdNQP-v]V�^cp>PRNLNQz{t+MUMOhOMOX�WQK+MjP-b9^cv]PRV�^_T Z V+\]PRNQMyqO\]b l \]V+MOVCW ��PRp-p@X+MOqUTQM#^cNQM1^cV+XW�K t+N�WQK+M z{t�^cVCW�t+bdV+\]PRN�M PRV�W�K+Mjl�K�^cN�M bfM#^cN�tuT�MObfMOVCW �HP-pRp�^cpRN�\ Y MkT�MOX+t+qUMOX.�

� "

Page 61: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� �

Page 62: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� ��� G4�'�A ( �A����������. � �!���"#�$�#%

� V5W�K+M x+TQN�W W ��\8q6K�^_l+WQMUT�N NQz{t+MUMOhOPRV+v)�L^cN P-V W�T�\{X+t+qOMUX>�4^cV+XDPFW�N ^_l+l�pRP-q#^_W�P-\]V W�\�0�L^_TQX PRb l+TQ\ �{PRV+v W�K+MfNQMOV+N�P-W�PF�uP-W Z \]n�^ x Y MUT \cl+WQPRq v Z T�\]NQqO\cl M"��^cN X+MObf\]V+N}WQTg^_W�MOX.�fJ K+Mt+pFW�PRb9^_WQM v]\C^cp!\]neW�K+P-NHW�K+MON�PRNk\cT�PRv]P-V�^cpRp Z ��^cN2W�\�^cqUW�t�^cpRp Z v]MUV+MUTg^_W�M NQzBt+MOMOhOP-V+v�P-V ^ x Y MUT\cl+W�P-q v Z T�\]NQqO\cl M9^_W W�K+M p ^ Y \cT�^_W�\cT Z �9~{M:�CMUTg^cp/\ Y N}Wg^cqOpRMUN l+T�MU�CMOVCW W�K+P-N v]\C^cpEn T�\]b Y MOPRV+v^cqgK+PRM:�CMOX P-bfbfMOX+PR^_W�MOp Z ��J K+M P-V+P-W�PR^cp�^cV�^cp Z W�PRqO^cp'��\cT � T�MU�CM#^cp-MOXDW�K+M M��uW�MUV+NQP-�CM nwt+V+X+PRV+v^cV+X8W�PRb M1T�MOz{t+PFT�MObfMUV W�NkV+MOMUX+MOX PRV \cT�X+MUTyW�\ l+T�\{X+t+qUMsNQzBt+MOMOhOP-V+v+��^cN���MUpRp�^cNaW�\ t+V+X+MUT 0N�W�^cV+X zBt+MON�W�P-\]V+NjqO\]V+qUMUT�V+PRV+v�V+\]V+pRP-V+M#^_T�P-WQPRMONkPRV8x Y M:T�NO��N�l@MOqUP-x�q#^cp-p Z PRN�NQt+MONyNQt+qgK5^cNax Y MUTX+\clm^cVCW�T�MOpR^_W�PR\]V+NQK+PFl�N/W�\1b t+pFW�P-l�K+\cW�\]VfTQMONQ\]V�^cV+qOMk^cV+X9MOV+M:T�v Z WQTg^cV+N�nwMUT Y MUW ��MUMOV X+\clm^cV WP-\]V+N�� J K+P-NyTQMU�uP-NQMOX�v]\C^cpeP-Nkb t+qgK V�^_T�T�\���MUT P-V�NQqU\cl@Ms^cV+X�PRNyM��{l@MOqUWQMOX W�\ Y M t+NQMOnwt+p�W�\nwtuTQWQK+MUTHT�MUNQM#^_T�qgK�t+V+X+MUTQW�^ � MOV�PRV�W�K+PRN�^_T�M#^ �

A �8��� ;=�F> �$G*

� W��L^cN X+MUqOPRX+MOX5W�K�^_WyW�K+M l+T�\��uPRb9^_WQMsv]\C^cp ��\]t+p-X Y M W�\�P-V �CMON}W�PRvC^_W�M ^cV+X�T�MUl \cTQW\]V V+\]V+pRP-V+M#^_Tk\cl+W�PRqO^cp"M� @MUqUW�NyPRV�x Y MUTQN��1JLK+PRNkNQMOq:W�PR\]V8\]n�W�K+M W�K+MONQP-NyX+P-NQqOt+NQN�MONjW�K+M bfMO^ 0NQtuTQMObfMOVCW9\]nk^ lm^_TQWQPRqOt+pR^_TfV+\]V+pRP-V+M#^_T�PFW Z �4W�K+M�W�K+PFT�X \cT�X+MUTfV+\]V+pRPRV+MO^_T9NQt+NQqOM:l+W�P Y P-pRP-W Z ��\]n\cl+W�P-q#^cpex Y MUTQN W�K�^_W ^_T�M X+\cl MOX���P-W�K�T�^_T�M M#^_T�W�K PR\]V+N��fJLK+MsW�K+MON�PRN1N�W�^_W�MON1^�K Z l@\cW�K+MUNQPRNW�K�^_WkK+P-v]K+p Z X+\cl MOX90 x Y MUT�N��HP-pRp!l+T�\��uP-X+M nw\cT ^cV M � qOPRMOVCWyNQz{t+MUMOhOPRV+v�bfMOX+P-t+b2�kIap-W�K+\]t+v]KW�K+M1^cqUW�t�^cp�NQz{t+MOMUhOPRV+v&��PRp-p�V+\cW Y M l+T�\BX+t+qOMOX ^_WHWQK+PRNHW�P-bfMc��P-WHPRN�PRVCW�MOV+X+MOX�W�\fN�K+\�� W�K�^_WK+P-v]K+p Z 0HX+\cl@MUX�x Y MUTQN�HP-pRpel+T�\��uP-X+Mfp ^_T�v]M V+\]V+pRP-V+M#^_T�PFW�PRMONjNQt+qgK�^cNjW�K+PFT�X \cT�X+MUT NQt+NQqOM:l+W�P 0Y P-pRP-W Z �2IaX+X+PFW�PR\]V�^cp�T�MONQM#^_TQq6K PRV�W�K+M x�MOp-X qU\]t+pRX p ^_W�MUTktuWQPRpRP-hOM1W�K+M P-V+nw\cT�b9^_W�P-\]V`l+T�\ �{PRX+MOXY Z W�K+PRN�bfM#^cNQtuT�MUbfMOVCW WQ\sW�MON}W�W�K+Mjnwt+pRp�K Z l@\cWQK+MONQPRN��

JLK+M�X+MOqOP-NQPR\]V W�\�T�MONQM#^_TQq6K x Y M:T�NE^_T�\]NQM�nw\cT�NQM:�CMUTg^cpBTQM#^cNQ\]V+N���JLK+M�x Y MUT�\cl+WQPRq�v Z T�\�0NQqU\cl@M �L^cN/WQK+M2l+T�PRb9^_T Z ^cV+X \ Y �uP-\]t+N�bf\cW�PF�c^_W�P-\]VsW�\jl�tuT�NQt+MkNQz{t+MUMOhOPRV+v P-Vfx Y MUT�N��/JLK+MUT�MK�^#�CM Y MOMUV�NQM:�CMUTg^cp lm^_l MUT�N � T�P-WQWQMOV \]V WQK+MaNQt Y �}MOqUW ����� ���� � �� � � � ����� � � � � � ��� � �� � � ��� ��� � �aJ K+M5� ��| M��ul MUT�PRb MOV Wa^cp-T�M#^cX Z K�^cNal+T�\ �CMUX8WQK�^_Wy^ x Y MUTyPRN2^ b MOX+PRt+b q#^_lm^ Y pRM\]n l+TQ\{X+t+qOP-V+v NQz{t+MOMUhOMOX pRP-v]K W��eIap-p�M��ul MUT�PRb MOV WQNEW�\jl+T�\{X+t+qOMHz{t�^cXuTg^_W�tuTQM2NQz{t+MUMOhOPRV+v K�^��CMT�MUz{t+P-TQMOX K+P-v]K�l \���M:T pR^cNQMUT�N�� J K+MON�M�pR^cNQMUT�N l+T�\��uP-X+MOX W�K+M�PRVCW�MOV+N�M�x�MOp-X+N WQK�^_W ^cp-pR\���MOXpR^_T�v]M1V+\]V+pRP-V+M#^_T2l+T�\BqOMONQN�MONaW�\9\{qOqUtuT��2JLK+M n ^cqUW2W�K�^_W2PRVCW�MOV+NQM x�MOp-X+Nk^_T�M T�MOzBt+P-T�MUX bf^ � MONx Y MUT�Nj^cV ^_W�WQTg^cqUW�PF�CM \cl+W�PR\]V.� � P Y MUT�Nk\# @M:TjvcTQM#^_W�MUTkl@\cWQMOV WQP ^cp"nw\cTyV+\]V+pRP-V+M#^_TyPRVCW�MUTg^cq:W�PR\]VW�K�^cV q#^cV Y M ^cqgK+P-MU�CMOX P-V Y t+p � qUT Z N�Wg^cp-Ny^cN ^9T�MONQt+pFW \]n4W�K+MOP-TyNQbf^cpRpeqO\cT�M NQP-hOM ^cV+X pR\]V+vp-MOV+vcW�K+N��EJLK+PRN�bfMO^cV+N4W�K�^_W/p ^_T�v]M ��t9� X+MOV+NQPFW�PRMUN�q#^cV Y MHl+TQ\{X+t+qOMOX�^cV+X9nwtuTQWQK+MUT�bf\cT�MHNQt+N 0Wg^cP-V+MOX \ �CMUTyp-\]V+v�X+P-N�Wg^cV+qOMUN�� JLK+Ms^ Y P-pRPFW Z W�\ b9^cPRVCWg^cPRV8^cV PRVCW�MOV+N�M Tg^cX+PR^_W�PR\]V�x�MOp-X�\��CMUT^9pR\]V+v�pRMUV+vcW�K b M#^cV+N2W�K�^_Wy^9x Y MUTkl+T�\��uP-X+MON ^9v]\B\{X8bfMOX+P-t+b nw\cTax�MOpRX+NkW�\ PRVCW�MUTg^cq:WjP-V.�

���

Page 63: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

ikP-�CM:T�v]MOV+qOM1\]n�W�K+Mjl�t+b l Y M#^cb PRV`q:T Z N�W�^cpRN q#^cV�X+PRN�WQtuT Y W�K+M1V+\]V+p-PRV+M#^_THPRVCW�MUTg^cq:W�PR\]V.�6� V^ NQP-V+v]pRMabf\BX+M2x Y MUTLW�K+M2l�t+b l3��\]t+p-X Y Mknw\cT�qOMOX W�\ T�MOb9^cP-V PRV9W�K+Max Y MUT��/JLK+M2x Y MUT q#^cVW Z l�P-q#^cpRp Z�Y M�bf^cVBt+n ^cqUWQtuT�MOX b \cT�M9qO\]N�W M� MOqUW�PF�CMOp Z WQK�^cV qUT Z N�Wg^cp-N�� � P Y M:T�N ^_TQMfT�M#^cX+PRp Zb9^cX+MkP-V�pRMUV+vcW�K+N WQK�^_W2^_T�Mkp-\]V+v]MUT�WQK�^cV`^cV Z q:T Z N�W�^cp@W�K�^_WHqU\]t+pRX�M:�CMUT Y Mjbf^cVBt+n ^cqUWQtuT�MOX.�[ \]V+v]MUT pRMUV+vcW�K+N l+T�\��uP-X+M9pR\]V+v]MUT P-V WQMUTg^cqUW�P-\]V W�PRb M � MU�CMUV5pR\]V+v]MUT1WQK�^cVDl+TQ\ �{PRX+MOX5nw\cT Y ZqUT Z N�Wg^cp-N2l�p ^cqOMUX�PRV q#^#�uPFW�PRMON ��� [ \]V+v]MUTyPRVCW�MUT�^cqUW�PR\]V pRMUV+vcW�K+Nkq#^cV�^cp-NQ\ \# @NQM:WyWQK+M TQMOz{t+PFT�M�0bfMUV Wjnw\cT ^cV P-V WQMOV+NQM N�\]tuT�qOM#� | \BX+MON�W NQ\]tuTQqOMON qO^cV b9^cPRVCWg^cP-V�K+PRv]K ��t9� X+MUV+NQP-W�P-MON1\��CMUTp-\]V+v]MUT X+P-N�Wg^cV+qOMUN W�\�^cqgK+PRMU�CM W�K+M�N�^cbfM V+\]V+pRP-V+M#^_T M� @MOqUWQNsl+T�\BX+t+qOMOX ��P-W�K�K+PRv]K�l@\���MUTNQ\]tuTQqOMON \ �CMUT NQK+\cT�Wsq:T Z N�W�^cp�pRMOV+vcWQK+N�� � n MU�CMOV�pR\]V+v]MUT PRVCW�MUT�^cqUW�PR\]VDW�P-bfMfPRN X+MON�P-T�MOX>�EW�K+Mx Y MUT2q#^cV Y Mjnwt+NQPR\]V`N}l�pRPRqUMOX�W�\snw\cT�b ^ x Y MUT�T�MONQ\]V�^_WQ\cT��

IaV+\cWQK+MUTL^cXu�_^cV Wg^cv]M�W�K�^_W�x Y M:T�N�NQK+\]t+pRX9K+\]p-X9\ �CM:T Y t+p � \cl+W�PRqON/PRN�P-VfW�K+MOP-T�^ Y PRpRPFW ZW�\9b PRV+PRb PRhOMyNQPRv]V�^cp�pR\]NQN�MON��aI N Z N�W�MOb WQK�^_WaPRN2X+MUNQPRv]V+MOX qO\]b l�p-MUW�MOp Z P-V�x Y MUT+��PRp-p!^#�C\]PRXp-\]NQNQMONy^cNQNQ\BqOP ^_WQMOX)�HPFW�K`l+T�\clm^cvC^_W�P-\]V8WQKuT�\]t+v]K Y t+p � \cl+W�P-q#^cp"MOp-MObfMOVCW�N��2��K+PRp-M x Y MUT�NkX+\K�^#�CM�^_W�W�MOV t�^_W�PR\]V pR\]NQNQMUNsn T�\]b ^ Y NQ\cT�l+W�PR\]V ^cV+X NQq#^_W�W�MUT�P-V+v+�4W�K+MON�M`^_T�M Y MUPRV+v TQMOX+t+qOMOX.�r�tuTQT�MOVCW�p Z x Y MUT1P-Nj\]V+Ms\]n/W�K+M n ^cN}W�MON�W vcT�\���PRV+v�x�MOpRX+N PRV�\cl+WQPRqON��frL\]V+N}Wg^cV WjT�MONQMO^_T�qgK5PRNP-b l+T�\��uPRV+vk^cV+X M��{lm^cV+X+PRV+vjx Y MUT / N4^ Y P-pRPFW�PRMON�� � P Y MUTEPRNeT�M#^cX+P-p Z ^cX�^_l+Wg^ Y p-M�W�\kNQMObfP-qO\]V+X+t+q�0W�\cTkpR^cNQMUT�Nk^cV+X8P-V W�MUvcTg^_W�MOX MOpRMUqUWQT�\�0 \cl+W�PRq1W�MUq6K+V+\]p-\]v Z �aI x Y MUTyq#^cV Y M t+NQMUX W�\9l+T�MUNQMUTQ�CM^1NQzBt+MOMOhOMUX�NQP-v]V�^cp �eIapFW�K+\]t+v]K ^_WQW�MOV t�^_W�P-\]V9pR\]NQNQMUN�N�W�PRp-pM��+PRN}W#�BW�K+M Z b9^ Z Y Ma\# @N�MUW Y Z W�K+M^ Y P-pRP-W Z \]n�x Y MUT WQ\`b9^cPRVCWg^cP-V5^`NQPRv]V�^cp4PRV5\]V+Mfb \{X+M#� � P Y MUT PRN qO\]b lm^cqUW#� ��M��+P Y pRMc�e^cV+XM#^cN Z W�\ PRVCW�MOvcTg^_WQMyP-V WQ\s^cV Z N Z N�W�MOb � � WLNQMUMObfN�W�K�^_WLvcT�M#^_WQMUTLV+\]V+pRP-V+M#^_T M� @MOq:W�NLNQK+\]t+pRX Y M^cqgK+PRM:�c^ Y p-MsP-V x Y M:T�N ^cV+X W�K t+NyW�K+M:T�MsN�K+\]t+pRX Y M vcTQM#^_W�MUTyl@\]NQN�P Y PRp-P-W Z \]n4NQz{t+MOMUhOPRV+v�pRPRv]KCWn T�\]bdNQbf^cpRp>NQ\]tuT�qUMON2PRV�qO\]b lm^cqUW N Z N�W�MOb N��

r�MUTQW�^cPRV8PRNQN�t+MON ^cN�NQ\{qOPR^_W�MOX��HPFW�K8NQz{t+MUMOhOPRV+v�PRV�x Y M:T�Njb t+N�W Y M ^cX+XuT�MONQNQMUX PRV8W�K+MnwtuW�tuTQM#� JLK+MUT�M PRNy^ TQMOz{t+PFT�MObfMOVCWynw\cTkl�K�^cNQMsbf^_W�qgK+PRV+v PRV \cT�X+MUTkW�\�v]MUWkW�K+M��L^#�CM P-V WQMUT 0^cqUWQPR\]V`\]n�^fNQMUqO\]V+X8\cTHW�K+PFT�X�\cT�X+MUTaV+\]V+p-PRV+M#^_THl+T�\{qOMUNQN��2JLK+M T�MUz{t+P-TQMObfMOVCW�N2\]V`W�K+Mjx Y MUTW�\ Y Myt+N�MOX`^cN�W�K+MkbfP �+P-V+v bfMOX+PRt+b b t+N}W Y MkX+MUW�MUTQbfPRV+MOX.�EIaV+\cW�K+MUT P-b l@\cTQW�^cV W�P-NQNQt+MaW�\Y M X+MUW�M:T�bfPRV+MUX�PRNLW�K+M WQTg^cV+N}�CMUT�NQM1b \{X+Mkl+T�\cx�pRMj\]ne^ NQzBt+MOMOhOMOX8N�W�^_W�M#��I lm^_T�W�PRqOt+pR^_THN�PRhOM^cV+X NQK�^_l@M qU\cT�M b9^ Z V+MOMOX8W�\ Y M X+MU�CMUpR\cl@MUX P-V \cT�X+M:TaW�\9l+T�MONQMUT��CM WQK+M N�z{t+MOMOhUMOX�bf\BX+M^cN P-W l+T�\clm^cvC^_W�MON��

A �F4 � ;=�F> �$5KM� ��N���������@�F���F�'*

� V�W�K+M x+TQN�WkNQMOqUWQPR\]V8P-W ��^cN2l@\]PRVCW�MOX8\]tuWaW�K�^_W2NQz{t+MOMUhOPRV+v q#^cV Y M1l+TQ\{X+t+qOMOX���P-W�KNQMUqO\]V+X�^cV+X8W�K+PFT�X8\cT�X+MUTkl+T�\{qUMONQNQMON�� JLK+MONQMs^_T�M1W�K+M \]V+p Z V+\]V+pRP-V+M#^_TkM� @MUqUW�NyN�W�t+X+PRMUX M�� 0W�MUV+NQP-�CMOp Z Y MOqO^ct+NQMH^cNeW�K+M \cT�X+MUTEP-V+qUT�M#^cNQMUNEW�K+M M� MOqUW4v]MUW�N�NQb9^cp-pRMUT��"J K+MLbf\]N�Wel+TQ\]bfPRV+MOVCW

� �

Page 64: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

V+\]V+p-PRV+M#^_T�PFW Z P-N WQK+MUT�MOnw\cT�MjMOP-WQK+MUT2NQMUqO\]V+X`\cT W�K+P-T�X�\cT�X+MUT��

JLK+MkX+MOqOP-NQPR\]V�W�\sM��ul�pR\cTQMyV+\]V+p-PRV+M#^_TQP-W�P-MONLPRV x Y MUT�N pRMO^cX+N W�\ W�K+Myz{t+MUN�W�PR\]V>� �}��K�^_WW Z l MON \]nHV+\]V+pRPRV+MO^_T�P-W�P-MON qO^cV Y M`nw\]t+V+X P-V ^ x Y MUT � � �aVCW�P-p T�MUqOMOVCW�p Z P-W"�L^cN v]MUV+MUTg^cpRp Z^cvcT�MUMOX�W�K�^_W�\]V+p Z \{X+X \cTQX+MUT�N�t+NQqOMUl+W�P Y PRp-P-W�P-MON-��\]t+p-X K�^#�CM V+\]V+hUMUT�\ �_^cpRt+MUN�P-V�x Y M:T�N��� P Y MUT�NL^_TQM2v]MOV+MUTg^cp-p Z qOP-T�qUt+p ^_T�q Z pRP-V+X+MUT�N�\]n�^cbf\cTQl�K+\]t+N/b9^_W�MUT�PR^cp � �kp ^cNQN�P-N/W�K+Mab9^_WQMUT�P ^cpt+NQMUX l+TQMOX+\]bfPRV�^cVCW�p Z Y MUq#^ct+NQM8P-W K�^cN9pR\�� p-\]NQN WQTg^cV+N�bfPRNQN�PR\]V qgK�^_Tg^cqUW�M:T�PRN�WQPRqON ^cV+X q#^cVY M l+T�\BX+t+qOMOX PRV �CM:T Z pR\]V+v�pRMOV+vcWQK+N��1I v]p ^cNQNyPRNy^ bfMOX+PRt+b WQK�^_WjP-Ny^�N�W�^_W�MsN�\]bfM���K+MUT�MY MUW ��MOMOV�^ pRP-z{t+PRX�^cV+X�^ NQ\]pRP-X.�EiktuT�P-V+v W�K+Myb9^cV t+n ^cqUW�tuT�P-V+vsl+T�\BqOMONQNHWQK+Mjb9^_WQMUT�P ^cp-N�W�K�^_WqO\]bsl+T�PRNQM`WQK+M v]pR^cNQN�^_T�M�qO\B\]pRMOX �CMUT Z zBt+PRq � p Z � I WQKuT�MOM8X+PRbfMUV+NQPR\]V�^cp2bf^_WQT�P � q#^cV Y Mnw\cT�b MOX�\]V+p Z \ �CMUTa^fNQK+\cTQW2Tg^cV+v]M��aJ K+Mjl+T�\{qOMUNQNkqO\]V W�T�P Y tuW�MUN2W�\fW�K+M ^cbf\cT�l�K+\]t+N2V�^_W�tuT�M\]n�W�K+M9bfMUX+PRt+b2( � \8pR\]V+v`T�^cV+v]Mfl@MUT�P-\{X+P-qOP-W Z M��+PRN}W�N��`ikt+MfW�\�PFW�N pRP-z{t+PRX90 pRP � Msl+T�\cl MUTQW Z �^ qO\]V+X+PFW�PR\]V � V+\���V*^cNfPRVC�CMUT�N�PR\]V N Z b bfMUWQT Z M��uPRN�WQN�(`W�K+M`x Y M:T9l@\]NQNQMUNQNQMON�^ qOMOVCW�MUT�\]nP-V �CMUTQNQPR\]V.� � \cT bf^_W�MUT�PR^cpRN W�K�^_W M��+K+P Y PFW NQt+qgK ^`l+T�\cl@M:TQW Z ��WQK+M�M��ul@MUqUW�MOX NQMOqO\]V+X�\cT�X+MUTV+\]V+p-PRV+M#^_T NQt+N�qOMUl+W�P Y PRpRPFW Z PRNfhUMUT�\�� � V � � � � ����� � � ��W�K+M8^_T�v]t+bfMUV W9P-Nfl+T�MONQMUV W�MUX ^cNnw\]p-pR\��HN��4JLK+M NQMOqU\]V+X`\cT�X+MUTHV+\]V+pRPRV+MO^_T�l \]p ^_T�P-h#^_W�PR\]V�PRN v]P-�CMUV YBZ

� � � � IU W # Z � # � � �%��K+MUT�MyW�K+M1^_l+l�p-PRMOX�x�MOpRX`P-N�v]PF�CMOV Y Z

� � � � � ��� � � � � � �� n"W�K+M1N�PRv]V`\]n"W�K+M MOpRMOq:WQT�PRqjx�MOpRX2��M:T�M W�\fqgK�^cV+v]Mc�W�K+M1NQP-v]V`\]n"W�K+M1P-V+X+t+qOMOX�l@\]pR^_T�PRh#^_WQPR\]Vb t+N�W�^cpRNQ\ qgK�^cV+v]M Y MOqO^ct+NQM�W�K+M bfMOX+PRt+b l \]NQNQMONQN�MON�PRVC�CMUT�NQP-\]V N Z bfbfMUWQT Z � J K+M V+M��T�MUp ^_W�P-\]V3��\]t+p-X Y M

� � � � � U W # Z � � � � � � � # %Y tuW�W�K+PRNLT�MOX+t+qOMUNHW�\

� � � � � U W # Z � # � � � �� V`\cT�X+M:Tanw\cTHW�K+MjV+\]V+pRP-V+M#^_T2l@\]pR^_T�PRhO^_W�PR\]V W�\fMOzBt�^cp�PFW�N V+MOvC^_W�P-�CM_�mW�K+MjNQMOqO\]V+X8\cT�X+M:T2V+\]V90p-PRV+M#^_T�NQt+NQqOM:l+W�P Y P-pRP-W Z b t+N�W�MOz{t�^cp�hOMUTQ\��

*�MOqOMOVCW�p Z ���� ������ � � � � �� � � � ��� � �K�^cN�NQK+\��HV9W�K�^_W4x Y MUT�N�qO^cV l+TQ\{X+t+qOMaM � qOPRMUV WNQMUqO\]V+X K�^_TQbf\]V+PRq#�-� W1PRN Y MUpRPRM:�CMOX5W�K�^_W N Z bfbfMUWQT Z 0 Y TQM#^ � P-V+v`\cT�vC^cV+PRhO^_W�PR\]V�^cp�l+T�\{qUMONQNQMON\BqOqOtuT��LJLK+M1ijr l@\]p ^_TQPRh#^_W�P-\]V�n T�\]b ^cV�PRVCW�MOV+N�M Y M#^cb PRN�W�K+\]t+v]K W�W�\ Y MjT�MON}l@\]V+NQP Y pRM nw\cTT�MO^_TQTg^cV+v]PRV+v bf\]p-MOqOt+pRMUN�P-V WQ\H^�l@MUTQPR\{X+P-q4N}WQT�t+qUW�tuTQM#�eJLK+PRN�^cpRpR\���N@l�K�^cNQM/b9^_WQq6K+P-V+v Y MUW ��MOMUV^kl�t+b l9^cV+XfN�PRv]V�^cp+W�\ \BqOqOtuT4nw\cT�NQMUqO\]V+X9\cT�X+MUTEl+T�\{qUMONQNQMON��/JLK+MHNQMUqO\]V+X9K�^_T�bf\]V+P-q Y t+P-pRX+Ntul�\ �CMUTyb9^cV Z K+\]tuT�NyPRV8W�K+M T�MUl@\cT�W�MOX�M��ul@M:T�PRbfMUV W�Ny^cpFW�K+\]t+v]K�^ ��NQMOMUX+PRV+v���M� @MOqUW���P-W�KNQMUqO\]V+X K�^_T�bf\]V+P-q PRVul�tuWjK�^cN Y MOMOV X+MOb \]V+N�WQTg^_W�MUX W�\�N�l@MUMOX tul�WQK+PRNkl+T�\{qOMUNQN�� IaV+\cW�K+MUT

� �

Page 65: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

n ^cqUWQ\cT WQK�^_W q#^cV qO\]VCWQT�P Y tuW�M W�\8PRV+qUT�MO^cNQPRV+v8W�K+M�NQMOqO\]V+X \cT�X+MUT V+\]V+pRP-V+M#^_T N�t+NQqOMUl+W�P Y PRp-P-W ZP-Nfx Y MUT v]MO\]b MUWQT Z � ~Bl@MOqOPR^cp-W Z x Y MUT�N�^_T�M`V+\�� b9^cV t+n ^cqUW�tuTQMOX �HPFW�K �c^_T�P-\]t+NfqO\cT�M8^cV+XqOpR^cX+X+PRV+vDv]MO\]bfM:WQT�PRMUN�� Se\]p ^_T�P-h#^_W�PR\]V bf^cPRVCWg^cPRV+P-V+v x Y MUT�N q#^cV*K�^#�CM MUpRpRPFl+W�PRqO^cpH\cT ��i ��0NQK�^_l MOX qO\cTQMON���r�\]V+X+t+qUW�PRV+v T�\{X+Ns^cV+X�X+\]t Y pRM�qU\cT�MON q#^cV Y M l�pR^cqOMOX P-V�x Y MUT�N���JLK+MONQM^cV+P-NQ\cWQT�\cl�P-qLx Y MUT�N Y T�M#^ � qOMOVCWQT�\]N Z bfbfMUW�T Z �!Iap-NQ\jN}WQTg^cPRV Y M:W ��MOMOV W�K+M qO\cT�M�^cV+XfqOpR^cX+X+PRV+vq#^cV�T�MONQt+pFWHP-V�NQMOqU\]V+X�\cT�X+MUT2V+\]V+p-PRV+M#^_T�M� MOqUW�N��

� V�W�K+PRN W�K+MONQP-NHP-W �L^cN�X+MOqOP-X+MOX`W�\ N}W�t+X Z W�K+P-T�X�\cT�X+MUT�V+\]V+pRPRV+MO^_T�P-W Z �+qgK�^_Tg^cqUW�M:T�PRhOMUXY Z WQK+MjW�K+PFT�X`\cT�X+MUTHV+\]V+pRP-V+M#^_T2NQt+N�qOMUl+W�P Y PRpRPFW Z ��U W X[Z ��ikMON�l�P-WQM W�K+M ��\cT � X+MONQqUT�P Y MOX8P-V�W�K+Mlm^_Tg^cvcT�^_l�K�^ Y \ �CMc��NQMUqO\]V+X�\cT�X+M:THM� MOqUW�N�^_T�MyV+\cW�^cV�MOVCW�PFT�MOp Z t+V+X+M:T�N�W�\B\{X�l�K+MUV+\]bfMOV+\]V.�� WkPRNy^cp-NQ\�M��ul@MUV+NQP-�CM W�\ v]MUWyNQ\]bfM \]n�W�K+MON�MsV+M���MUTjx Y MUT�Nynw\cTkT�MONQM#^_TQq6K l�tuTQl@\]N�MON�� � \]tuT 0�L^#�CM�bfP �+PRV+v5P-NfW�K+M�X+\]bfP-V�^cV W9l+T�\BqOMONQN q#^_T�T�PRMOX*\]tuW PRV x Y MUT�NO��NQt+qgK ^cN Y Z W�K+M)� �L|T�MUNQM#^_T�qgK�W�MO^cb � �

��� ��������� � � � ��� � � �4J K+P-NLPRN ^cpRNQ\s^ l@\cl�t+p ^_T bfM:W�K+\{X W�K�^_WLK�^cN Y MOMOV

NQt+qUqOMONQNQnwt+p-p Z t+N�MOX�PRV�NQM:�CMUTg^cp�NQz{t+MOMUhOPRV+v9M��{l@MUTQPRbfMOVCW2P-V��_^_T�PR\]t+N2b MOX+P ^ � � \cT2q Z pRP-V+XuT�PRqO^cpx Y MUT�N1W�K+M WQK+P-T�X5\cT�X+M:T NQt+NQqOMUl+WQP Y PRp-P-W Z N�K+\]t+pRX Y M WQK+M9p ^_T�v]MON}W��3� V5n ^cqUW1PRV5\]V+M ^_TQW�P-qOpRM ��� ���� � � � � � �� � � � W�K+M2W�K+PFT�X9K�^_T�bf\]V+P-q/�L^cN�T�M:l@\cTQW�MUX WQ\1vcT�\�� M��{l@\]V+MOVCW�P ^cp-p Z �HPFW�KfW�P-bfM

^_W�W�K+M M��ul MOV+NQM�\]nW�K+M�NQMOqO\]V+XfK�^_TQbf\]V+PRq#�"J K+M W�PRbfM�N�q#^cpRM nw\cT4WQK+PRN�l+T�\{qOMUNQN%�L^cNEbfP-VBtuW�MUN��

� V�p-\{\ � P-V+vfnw\cT2x Y MUT�N2W�K�^_W2l \]NQNQMON�Nap ^_T�v]M1V+\]V+p-PRV+M#^_TQP-W Z � PFW/�L^cN2nw\]t+V+X8W�K�^_WHb9^cV90t+n ^cqUWQtuT�MUT�NaX+\9V+\cWaP-V WQMOV WQPR\]V�^cpRp Z l+TQ\{X+t+qOM1x Y MUT�Nanw\cTaW�K+MOPFTaV+\]V+pRP-V+M#^_T�PFW Z � � P Y MUT�NHq#^cV Y Mb9^cX+M9\]tuW \]n�l�pR^cN�W�PRqUNO��pRPRzBt+PRX+NO��^cV+X�v]p ^cN�NQMON�� IaN bfMOVCW�PR\]V+MUX ^ Y \ �CM9v]pR^cNQN PRN1WQK+M�b \]N�W��PRX+MOp Z t+NQMOX.� J K+M bf\]N�W�P-b l@\cTQW�^cV W v]pR^cNQN�nw\cTQbfPRV+v�MOpRMUbfMOVCW�N�^_TQM W�K+M V+\]V+bfMUW�^cpRN PRVvcT�\]tul�N�� � � 0 I � � � 0 I ��^cV+X � 0 I \]n/W�K+M l@MUT�P-\{X+P-q Wg^ Y p-M"��K+PRqgK qU\]b Y P-V+M1��P-W�K \�� Z v]MUV W�\nw\cT�b \��uPRX+M1v]pR^cNQNQMON � ��� � ��� � � � � � � � � �� � � � �� �� ��� � ��o/p-MObfMOVCW�N/��P-W�K+P-V�W�K+MON�M vcTQ\]tul�NO�NQt+qgK�^cNH~{PRp-PRqO\]V>� �kMUT�b9^cV+P-t+b`� � \cT�\]V>��^cV+X�S/K+\]N�l�K+\cT�\]t+N�nw\cT�b W�K+Myb9^cPRV�X+\clm^cV WQNHt+NQMOXP-V�bf\]N�WLx Y MUT�N��/J K+M Z nwt+V+qUWQPR\]V`W�\ v]P-�CMkW�K+Mjx Y MUT�qO\cT�M1^cV+X�qOp ^cX+X+P-V+vslm^_TQW�P-qOt+p ^_T�PRV+X+P-qOMON\]n�T�MOn Tg^cqUWQPR\]V.�

JLK+M/W�K+PFT�X \cT�X+MUT!l+T�\{qOMUNQNQMONeq#^_T�T�PRMOX \]tuW"PRV x Y MUT�NeX+MONQq:T�P Y MOX ^ Y \��CM6��MUT�M4l+T�\{X+t+qOMUXP-V �CMUT Z N�b9^cpRp"qU\cT�MON��HPFW�K �CMUT Z K+PRv]K l \���MUT pR^cNQMUTyl�t+b l�N��s�aV+p Z PRVCW�MOV+NQM l�t+b l�NyqO\]t+pRXP-V+X+t+qOMap ^_T�v]MHV+\]V+pRPRV+MO^_T ^cqUW�PR\]V n T�\]b W�K+M2N�b9^cpRp^cbf\]t+VCW�N�\]n>X+\clm^cVCW�N�PRV9W�K+M2qU\cT�MON�\]n>W�K+Mx Y MUT�N���IdK+PRv]K+p Z 0 X+\cl@MOX5x Y M:TsqU\]t+pRXDqO\]V+qOMOPF�c^ Y p Z l+T�\BX+t+qOM p ^_T�v]MUT1V+\]V+pRPRV+MO^_T�P-W�P-MON1W�K�^cVt+V+X+\cl MOX x Y MUT�Nat+NQP-V+vfW�K+M N�^cbfMjN�WQT�MUV+vcW�K�l�t+b l�x�MOpRX.� � V`W�K+M1p ^cN}WaNQMU�CMUT�^cp Z M#^_T�NHNQ\]bfMp-\�� 0 p-\]NQN x Y MUT�NfX+\cl MOX ��P-W�K ^cV ^cNQNQ\cT�W�bfMOVCWf\]n Tg^_T�M�0 M#^_TQW�K P-\]V+N K�^#�CM Y MOMOV l+T�\BX+t+qOMOX.�JLK+MONQM8K+PRv]K+p Z X+\cl@MUX*x Y MUT�N NQK+\�� N�WQT�\]V+v�^ Y NQ\cT�l+W�PR\]V pRM:�CMOpRN9P-V*W�K+M`�{PRNQP Y pRM8^cV+X V+M#^_TP-V+n Tg^_T�MOXfT�MUv]PR\]V+N�^cpFW�K+\]t+v]KfpR\���pR\]NQN'�HP-V+X+\���N�M��uPRN�W%�HK+MUTQM2W�K+Ma^_WQW�MUVBt�^_W�P-\]VfPRN/NQPRbfP-p ^_T�W�\W�K�^_W \ Y NQMUTQ�CMUX5PRV t+V+X+\cl MOX5x Y MUT�N�� | t+qgK�^_WQW�MOVCW�P-\]V K�^cN Y MOMOV5v]P-�CMUV W�\�K+P-v]K+p Z 0 X+\cl@MOXMUT Y PRt+b ^cV+X V+MO\{X Z bfPRt+b x Y MUT�N���JLK+MONQMLx Y M:T�NE^_T�MLqOtuTQT�MOVCW�p Z Y MOP-V+vyX+M:�CMOpR\cl MOX nw\cT�t+NQM�^cNpR^cNQMUT�NE^cV+X p ^cNQMUT4^cb l�p-P-x�MUTQN��"I*qO\cTQT�MOq:W4N�MOpRMOq:W�PR\]V \]nmx Y MUTEX+\clm^cV W4^cV+X l�t+b l �L^��CMUpRMOV+vcW�K

� �

Page 66: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

qO\]t+p-X*l+TQ\ �{PRX+M8W�K+M8K+PRv]K��_^cpRt+M8\]nkW�K+P-TQX�\cT�X+M:T�NQt+N�qOMUl+W�P Y PRpRPFW Z NQ\]t+v]K W�� � \cT M��+^cb l�pRM_�MUT Y PRt+b X+\cl@MOX�x Y MUT�N�K�^��CM Y MUMOV NQt+qOqUMONQNQnwt+p-p Z t+N�MOX ^cN�p ^cNQMUTQN�^_W ���10 0 �� � ILW�WQK+PRN�L^#�CMOp-MOV+vcW�K ^1p ^_TQv]MHW�K+P-TQX9\cT�X+MUT�NQt+N�qOMUl+W�P Y PRpRPFW Z PRN�P-V �C\]pF�CMOX.�EJ K+M�� ��| M��{l@MUT�P-bfMOVCW�t+NQMOX^�x Y MUT qO\]b l \]NQMOXD\]n�l�tuT�M nwt+NQMOX�NQPRp-PRq#^ ��J K+Mf�_^cpRt+M nw\cT P-W�N WQK+P-T�XD\cT�X+MUT N�t+NQqOMUl+W�P Y PRp-P-W ZP-N�� � � # # W�\ � � � # X � #

� # � � � � ������ �� � � � � � Z q6K+\B\]NQPRV+vD^ K+PRv]K+p Z X+\cl@MUX x Y MUT ^cV+X

Y Z ��\cT � PRV+v�^_WyWQK+M ^_l+l+T�\cl+TQP ^_W�M l�t+b l�L^��CMUpRMOV+vcW�K P-WyNQK+\]t+p-X Y M l@\]N�NQP Y p-M W�\�v]MUWjK+PRv]KNQzBt+MOMOhOP-V+vfX+t+MjWQ\f^sN}WQT�\]V+v]MUTHV+\]V+pRPRV+MO^_THqO\]tul�p-PRV+vfb MOqgK�^cV+PRNQb2�

JLK+MLv]\C^cpRN�\]n�W�K+M TQMONQM#^_T�qgKsn T�\]b�W�K+PRN�l@\]P-V W$��MUT�MLW�\j\ Y W�^cPRVs^kK+P-v]K+p Z 0�X+\cl@MOX x Y MUT^cV+X�W�\9X+MON�PRv]V ^cV�M��ul MUT�PRb MOV WaWQ\9bfM#^cNQtuT�M1^cV P-V+qUT�M#^cN�MOX V+\]V+p-PRV+M#^_TkN�t+NQqOMUl+W�P Y PRp-P-W Z ^_Wk^qOM:TQWg^cPRV3�L^#�CMOpRMOV+vcWQK.�

� W1�L^cNfX+MOqOP-X+MOX W�K�^_WfMUT Y PRt+b10 X+\cl@MOX x Y M:T�N&��\]t+pRX bf^ � M�v]\{\BX q#^cV+X+P-X�^_W�MON9nw\cTP-V+N�l@MOq:W�PR\]V.�/�kV+MkT�M#^cN�\]V3�L^cN�W�K�^_WLW�K+MUNQN ��MUT�MaW�K+Mkx+T�N�WLTg^_T�M�0 M#^_TQW�K x Y M:T�NH^cXu�CM:TQW�PRN�MOX Y Z^ �CMOV+X+\cT��yI N�MOqO\]V+X TQM#^cNQ\]V�W�\9PRVC�CMON�WQPRvC^_W�M MUT Y PRt+b x Y MUT�N+�L^cN2W�K�^_WkiaTg^_l MUT [ ^ Y NaK�^cXpR^cNQMUT X+MU�{PRqOMUN ^��_^cPRpR^ Y pRM W�K�^_W MObfPFWQW�MOX�PRVD^�N�l MOqUWQT�^cp4T�MOv]P-\]V W�K�^_W1qU\cTQT�MON�l \]V+X+MOXDW�\`W�K+M^ Y NQ\cT�l+W�PR\]Vs^cV+X ��\cTQMONQqOMOV+qUM�T�MOv]P-\]V+N�\]nmW�K+M�x Y MUT���Iap-W�K+\]t+v]K ^kN�^cb l�p-M �L^cN�V+\cW/^#�_^cPRp ^ Y p-Mn T�\]b W�K+M/�CMOV+X+\cT#� ^cNQN�PRN�Wg^cV+qUM �L^cN"T�MOqOMUP-�CMOX n T�\]b W ��\a\cWQK+MUT�NQ\]tuT�qOMUN���I � 0�0 bfMUWQMUT"N�^cbsl�pRM\]nyMUT Y P-t+b X+\cl@MOX x Y MUT �L^cN9T�MUqOMOP-�CMUX�n T�\]b J�MOX | \cT�N�M \]n � T�\��HV �aV+P-�CM:T�NQP-W Z � JLK+PRN�L^cN l+T�\{X+t+qUMOX PRV W�K+MUP-Tfb \{X+P-x�MUX qgK+MObfP-q#^cp 0'�c^_l \cTfX+MUl \]NQP-W�P-\]V � | r �ki � p ^ Y � I Z M#^_TpR^_W�MUT�^jN�^cb l�pRM \]n>K+PRv]K+p Z qU\{X+\cl@MUX Z WQW�M:T Y PRt+b10 MUT Y P-t+b x Y MUT �L^cNET�MOqOMOPF�CMOX9n T�\]b *HPRqgK�^_T�XJ!t+b bfPRV+MOp-pRP{^_W/iaTg^_l MUT [ ^ Y N��EJLK+PRN�x Y MUT'�L^cNEN�l@MOqUP ^cpRp Z b9^cX+M YBZ J!t+bfb PRV+MOp-pRPu^cV+X o/pRPR^cN~{V+PFW�hOMUT�����P-W�K�W�K+MONQMyx Y MUT�N�P-W ��\]t+p-X Y Mkl@\]N�NQP Y p-MjW�\ M���^cb PRV+MkV+\]V+pRP-V+M#^_THM� @MOqUWQN���JLK+MONQMx Y MUT�N2^cV+X�\cW�K+MUT�N�qO\]t+pRX Y M b M#^cNQtuT�MOX�nw\cTHW�K+PFT�X�\cTQX+MUT2NQt+N�qOMUl+W�P Y PRpRPFW Z �

A � A � �#�$�������� � �$��� �6����� U W X[Z � �ON������ �E;=��>?�� �����E� NF�

IaqUqO\cT�X+PRV+vsW�\f^ T�MU�uP-M�� \]n!W�K+MjpRP-WQMUTg^_W�tuT�MkW�K+MUTQM1^_T�MyW ��\fqO\]bfbf\]V �L^ Z NLW�\fbfMO^ 0NQtuTQMfW�K+M W�K+PFT�X5\cT�X+MUT NQt+N�qOMUl+W�P Y PRpRPFW Z \]n�W�K+MfN�^cbsl�pRM#��J K+Msx+T�N�W bfMUWQK+\{X P-N ^cVDPRV+X+P-TQMOqUWbfMO^cNQtuT�MObfMUV W#� �HK+P-qgK5PRN ^�b \{X+P-x�qO^_W�PR\]V \]n�W�K+M bfM:W�K+\{X X+MUNQqUT�P Y MOX Y Z � � � � �� � � ���� � � ��� � � �aW�\�bfM#^cNQtuTQM U?W X[Z \]nyNQMObfP-qO\]V+X+t+qUW�\cT 0 X+\cl@MUX v]p ^cNQN�MON�^_W�p-\�� l@\���MUT�M��+qOPFWg^_W�P-\]V.�JLK+M Z X+MUWQMUT�bfP-V+M2W�K+Mab9^cv]V+P-WQt+X+Mc�Bl�K�^cNQM_��^cV+X�T�MUN�l@\]V+NQMaW�P-bfMH\]n"U?WYX[Z"t+NQP-V+v PRV+nw\cT�b9^_WQPR\]Vn T�\]b ^�l�K�^cNQM9qU\]V �}t+vC^_W�M Y MO^cb l+T�\BX+t+qOMOX Y Z nw\]tuT 0 �L^#�CM9bfP �uPRV+v��s��K+PRp-MsW�K+P-N1bfMUWQK+\{Xq#^cV Y Mjt+NQMOX`P-V Y t+p � b9^_WQMUT�P ^cp-NO�uP-V�x Y M:T2P-W q#^cV�\]V+p Z9Y Mjt+NQMOX`\]V�^sb t+p-WQPRbf\BX+MaN�^cb l�pRM��I&N�PRV+v]pRMsbf\{X+M x Y MUT1\]V+p Z ^cpRpR\���N \]V+Mfbf\BX+Ms\]n�l+TQ\clm^cvC^_W�PR\]V.( JLK+MUT�MUnw\cT�M W�K+MUTQM&��\]t+pRXY M2V+\5�L^ Z W�\1W�MUpRp�W�K+M2X+P MUT�MOV+qUM Y MUW ��MOMOV9W�K+M�l�K�^cNQMaqO\]V �}t+vC^_W�M �L^#�CMk^cV+XfW�K+MHTQM ��MOqUW�MUX�L^#�CM Y MOq#^ct+N�M W�K+M Z ��\]t+p-X`K�^��CMkW�\ Y M P-V�W�K+MjN�^cbfMkbf\BX+M#�

� �

Page 67: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+MyNQMOqO\]V+X�bfM:W�K+\{X>� ��K+PRqgK �L^cN qgK+\]NQMOV>�mPRN�^sX+PFT�MOqUW�bfM#^cNQtuTQMObfMOVCW�� � W�PRN Y ^cNQMOX\]V W�K+M ��\cT �9Y Z ��� ��aN�W�M:T Y MUTQv���� �� ���� � � � � � � � � � ����� ��JLK+MypR^cNQMUT Y MO^cb W�K�^_WLPRNLNQMUV WP-V W�\ W�K+M x Y MUTjN�^cb l�p-M q:T�M#^_W�MON ^ WQK+P-T�X K�^_T�bf\]V+PRq � l \]NQNQP Y p Z ^�N�MOqO\]V+X ��� I WyW�K+M MOV+X \]nW�K+Msx Y MUT W�K+M Y M#^cb P-N1NQMOVCW W�KuT�\]t+v]K�^�x�pFW�MUT1W�\�p-MUW \]V+p Z W�K+M9X+MUNQP-T�MUXDWQK+P-T�XDK�^_T�bf\]V+P-qlm^cNQN��/JLK+PRN Y M#^cb&PRN�WQK+MOV�N�MOV W P-V W�\ ^ bf\]V+\BqgKuT�\]b9^_W�\cT / N/P-Vul�tuW�l@\cTQW#�u^cV+X WQK+My\]tuW�l�tuWLPRNNQMUV WHPRVCW�\f^ l�K+\cW�\]b t+p-W�PFl�pRPRM:T WQt Y M ��K+PRqgK ��PRp-p Y MjqO\]V+V+MOqUW�MUX�W�\f^cV`^cV�^cp Z hUMUT��

� W ��^cNaV+MOqOMONQNQ^_T Z W�\9t+V+X+MUT�N}Wg^cV+X WQK+M1l�K Z NQPRqONkP-V �C\]pF�CMOX�PRV�W�K+PFT�X�K�^_T�bf\]V+P-q1v]MOV90MUT�^_W�PR\]V Y MOnw\cT�M ^cV Z M��ul@M:T�PRbfMUV W ��^cNHl@MUTQnw\cT�bfMOX.� � Z X+M:T�P-�{PRV+v9^fnw\cT�b t+pR^ nw\cT2W�K+M WQK+P-T�XK�^_T�b \]V+PRq l \���M:TsM��ul@MUqUW�MOX�n T�\]b W�K+M9x Y MUT P-W5��\]t+p-X Y Mfl@\]NQN�P Y pRM9W�\�qO^cpRqOt+pR^_W�MfW�K+M MOn 0nwMOq:W�P-�CM1�_^cpRt+M1nw\cTaWQK+P-T�X8\cT�X+MUTkN�t+NQqOMUl+W�P Y PRp-P-W Z n T�\]b M��ul MUT�PRb MOV W�^cp!X�^_Wg^ �HJ K+M X+MUTQP-�_^_W�PR\]VN�W�^_TQW�N�\]tuW ��P-W�K9W�K+MkqOpR^cNQNQPRqO^cp [ \cTQMOV WQhy\]N�qOPRp-p ^_W�\cT�b \{X+MOpnw\cT WQK+MyMUz{t�^_W�P-\]V9\]n�bf\cWQPR\]V9nw\cT^cV8^_W�\]b PRq MUpRMOqUW�T�\]V8PRV8^cV8MOpRMUqUWQT�P-q x�MOpRX.� � \]V+p-PRV+M#^_THT�MON�W�\cTQPRV+v9nw\cT�qOMUNj^_TQM ^cX+X+MOX8W�\fW�K+MMOzBt�^_W�PR\]V.��^ NQMOqU\]V+X�\cT�X+MUT W�MUTQbd^cV+X`^ W�K+P-T�X�\cT�X+MUTLW�MUTQb2�EJ K+Mj^cX+X+P-W�P-\]V�\]n�W�K+MON�MjW�MUTQbfNT�MUNQt+p-W�N PRV5^�V+\]V+pRPRV+MO^_T X+P MUT�MOVCW�P ^cpEMOzBt�^_W�PR\]V.�fo4z{t�^_W�P-\]V+Nj\]n4W�K+PRNyW Z l@M ^_T�M X+P � qOt+pFW W�\NQ\]pF�CMHM��+^cqUW�p Z NQ\ ^yl@MUTQWQtuT Y ^_W�PR\]VfWQMOqgK+V+PRz{t+MaP-N�^_l+l�p-PRMOX.�EJLK+PRN�bfM:W�K+\{X9^cN�NQt+bfMON/WQK�^_W�W�K+MK+P-v]K+MUT W�K+M \cT�X+MUT W�M:T�bfN ^_T�M9qU\]V+NQMOqOtuW�PF�CMOp Z N�b9^cpRp-MUT��`JLK+M MOz{t�^_WQPR\]V5PRN1x+TQN�W NQ\]p-�CMOX Y ZV+MOv]p-MOqUW�P-V+vfW�K+M1V+\]V+p-PRV+M#^_TaW�M:T�bfN2^cV+X�N�\]p-�uP-V+v9nw\cT2W�K+M1hUMUT�\�0 \cTQX+MUTy^_l+l+T�\��+PRbf^_W�PR\]V.� JLK+PRNNQ\]p-tuW�PR\]V PRNyW�K+MOV NQt Y N}W�P-W�tuWQMOX Y ^cq � P-V WQ\�W�K+M MUz{t�^_W�P-\]V Y tuW��P-WQK ^�V+\]V+p-PRV+M#^_TjW�MUT�b �sIx+T�N}W/\cT�X+M:T�NQ\]p-tuW�PR\]VsPRNE\ Y Wg^cPRV+MOX.� � T�\]b W�K+MLx+T�N�W�\cTQX+MUT/N�\]pRtuW�P-\]VsW�K+M�V+\]V+pRPRV+MO^_T4l \]p ^_T�P-h#^ 0W�P-\]V+NH^cV+X�NQt+NQqOMUl+WQP Y PRp-P-W�P-MON2^_TQM X+MUx�V+MOX.�LJLK+Mjl \]p ^_T�P-h#^_W�P-\]V�P-N W�K+MUV�NQt Y N�W�PFW�tuW�MOX`P-V WQ\ W�K+M�L^#�CM2MOzBt�^_W�PR\]V ^cNL^1XuTQP-�uP-V+v W�MUTQb2�eI NQ\]pRtuWQPR\]V9nw\cT�W�K+MHWQK+P-T�X K�^_T�bf\]V+P-qHP-N/W�K+MOV X+MUT�PF�CMOX.�rL^cpRqOt+pR^_W�PR\]V�X+MUWg^cP-pRN�^_T�M N�K+\���V`PRV�W�K+M nw\]p-pR\��HP-V+vsN�MOqUW�P-\]V.�

A �YT � KM����N��8�:���� H * �&�8N�NF����O � !#���)���F� �I����N � �'��� * ����9 � �$������>��)���F� �

JLK+MLMOz{t�^_WQPR\]V \]nm^kV+\]V+p-PRV+M#^_TE\]NQqUPRpRpR^_W�\cTeq#^cV Y M � T�P-W�W�MOV ^cNenw\]pRp-\���Net+NQPRV+vj^2l@\���MUTNQM:T�PRMON W�\sTQMUl+T�MONQMUV W2WQK+MjV+\]V+p-PRV+M#^_T�l@\cW�MOVCW�PR^cp � T�MON�W�\cTQPRV+v nw\cT�qOM1\]V�W�K+MjMUpRMOqUW�T�\]V ���

� # �� � # � � #� � � � # � # � � X � X � �� � ! ��� � � � ! � � � ! � � %��K+MUT�M � P-NsW�K+M�X+PRN�l�pR^cqOMObfMUV W \]n2W�K+M�MOp-MOqUWQTQ\]V � \cTsPR\]V �:� � � PRNsWQK+M�pRP-V+M#^_Tf\]N�qOPRp-p ^_W�\cT / NT�MUNQ\]V�^cV W�n T�MOz{t+MUV+q Z � � # % � X ^_T�MHV+\]V+p-PRV+M#^_T/qO\{M � qOP-MOV WQN�\]n W�K+MH\]N�qOPRp-p ^_W�\cT / NEl \cW�MOVCW�P ^cp �{^cV+X� ! ��� � � � ! � � � ! � �yPRN W�K+M PRVul�tuW x�MOp-X5XuT�P-�{PRV+v`W�K+Mf\]N�qOPRp-p ^_W�\cT�� � T�\]b WQK+MfMOz{t�^_WQPR\]V \]V+Mq#^cV9X+MUX+t+qOMaW�K�^_W � # K�^cN�t+V+P-WQN�\]n>PRVC�CMUT�NQMap-MOV+vcW�K ^cV+X9P-V �CMUTQNQM2W�PRb M�NQzBt�^_T�MOX>�+^cV+X � X K�^cNt+V+PFW�N�\]n!PRVC�CMUT�NQMjpRMOV+vcW�K�NQz{t�^_T�MUX`^cV+X`P-V �CMUTQNQMjW�P-bfMkNQz{t�^_TQMOX.�

� PFT�N�WLNQ\]pF�CMaW�K+MkpRPRV+MO^_TLMOz{t�^_W�P-\]V � NQMUW � # % � X �� �/nw\cTLW�K+MkhOMUT�\�0 \cT�X+MUTH^_l+l+T�\��+PRbf^ 0� &

Page 68: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

W�P-\]V�NQ\]p-tuW�PR\]V>� � # ( � # �� � # ��� #� � � �� � ! ��� � � � ! � � � ! � � �JLK+MjWQTQP ^cp>NQ\]p-tuW�PR\]V�PRN

� # � ! � � � � � ! � � � ! � � �NQ\]pF�uP-V+v�� � �

� � #! � ! ��� � � � ! � � � ! � � ��� #� � ! ��� � � � ! � � � ! � � � �� � ! � � � � � ! � � � ! � �� � #! � ! ��� #� � ! � �� � !

� ! �� � !� #! � � #�NQ\ W�K+M hUMUT�\ \cTQX+MUTa^_l+l+T�\��+P-b9^_W�P-\]V�NQ\]p-tuW�PR\]V�PRN

� # �� � !� #! � � #� ��� � � � ! � � � ! � � �� \�� ��Mj^cpRpR\�� � # ^cV+X � X WQ\ Y MyV+\]V+hOMUTQ\ ^cV+X�t+NQM � # W�\sx�V+X � !��� # �� � # ��� #� � � � # � � # � # � � X � � # � X � �� � ! ��� � � � ! � � � ! � � �t+NQP-V+v W�K+MyqO\]NQP-V+M NQzBt�^_T�M1^cV+X�qOt Y M1P-X+MOVCW�P-W�P-MONLW�\ Y T�P-V+v \]tuW W�K+M K�^_TQbf\]V+PRqaW�MUTQbfN

� #! ��� � # � � ! � � � ! � � �� � #! �F� � ��� � # � � � ! � � � � ! � ��� %

� X! ��� � X � � ! � � � ! � � �-� X! � + ��� � � � ! � � � ! � � � � � � � + � ! � � + � ! � � � %W�K+Mkx+T�N�WH\cT�X+MUTHV+\]V+pRPRV+MO^_THMOzBt�^_W�PR\]V Y MOqU\]bfMON

� # �� � # � � #� � � �� � ! ��� � � � ! � � � ! � �� � #� � #! � + � X- � X! � � � � � ! � � � ! � �

� � #� � #! ��� � � � � ! � � � � ! � � � � X-� X! ��� � � + � ! � � + � ! � � �� M��{W�^cNQNQt+bfMyW�K+MyW�T�P ^cp>NQ\]p-tuW�PR\]V�PRN

� ! � � � � ! � � � � � ! � � � ! � � � � # � � � � � � ! � � � � ! � � � � X � � � � + � ! � � + � ! � � �Ian W�M:T�Wg^ � P-V+v1W�K+MkX+MUT�P-�_^_W�PF�CMON�\]n>W�K+MkqO\]b l@\]V+MUV W�N�\]n � !�\]V+M �HP-pRp v]M:W ^ V+M�� MOz{t�^_WQPR\]V PRV��K+PRqgK�qU\]NQPRV+MkW�MUT�b N \]V�MOPFW�K+MUT NQPRX+M���PRpRp>bf^_W�qgK�tul � � \�� �}t+N�WHN�\]p-�CMknw\cTLW�K+MjqU\{M � qOPRMOVCW�N� � % � # % � X � � #� � � � � #� � #!

��(

Page 69: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� � #� � - � #! � � # � � #� � #!� � #� � � � #! � � X � � X- � X! �

� P-V�^cpRp Z �]W�K+M x+T�N�W/\cT�X+MUTL^_l+l+T�\��+P-b9^_W�P-\]VsNQ\]p-tuW�PR\]Vsnw\cT�W�K+M�X+PRN�l�pR^cqOMObfMOVCW�\]nW�K+M2V+\]V+pRP-V+M#^_T\]NQqUPRpRpR^_W�\cT PRN

� ! � � # � # � #!� � #� � # � � #! � � #� � #� � � !� � � #! � � #� � # ��� � � � ! � � � ! � �� � # � # � #!� � # � - � #! � � #� � � � #! � � #� � # ��� � � � � ! � � � � ! � �� � X � X � X!-�� X � � � #! � � #� � � � #! � � #� � X ��� � � + � ! � � + � ! � ���K+MUT�M1W�K+M qU\{M � qOPRMOVCW�Na\]n"W�K+M qU\]NQPRV+M1W�M:T�bfNa^_T�M � ! � � # �@^cV+X � X ^cV+X�W�K+M1ijr W�MUT�b PRN

� � �A �FS � KM����N��8�:���� � ��N���@��%&�)���F� �

JLK+M1l@\]pR^_T�PRhO^_W�PR\]V`q:T�M#^_W�MOX)��P-W�K+P-V�^fb9^_W�M:T�P ^cp�PRNHTQMOp ^_W�MUX`W�\fW�K+M \]NQqOP-pRpR^_W�\cT2MOzBt�^ 0W�P-\]V.�

� ��� %��K+MUT�M P-N/W�K+MaV t+b Y MUT�\]n>X+PFl@\]pRMUN/l@MUTLt+V+PFW��C\]pRt+b Mc� � P-N/W�K+M2MOp-MOqUWQTQ\]V � \cT�PR\]V ��qgK�^_T�v]Mc�^cV+X � P-N WQK+M MOp-MOqUWQT�\]V � \cT�PR\]V ��X+PRN�l�pR^cqOMObfMOVCW��

� \cT W�K+MjV+\]V+p-PRV+M#^_THb9^_W�MUTQP ^cp'�� � � ��� ! � � � � � � � � ! � � � � � � ! � � � � + � ! � �A � � ��� NF�'���@�8���"��* � ���:����> ��N��F� Q

U U W�! Z � ��U W # Z � � # U WYX[Z ��������#

Page 70: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+Mjl \]p ^_T�P-h#^_W�PR\]V�q#^cV�^cpRNQ\ Y M M��ul+T�MON�NQMOX`W�KuT�\]t+v]K�\cW�K+MUT�lm^_Tg^cbfMUW�M:T�N

� U � � ���K+MUT�M�WQK+M`pRP-V+M#^_TfNQt+N�qOMUl+W�P Y PRpRPFW Z W�MUTQb U U W�! Z P-Nf^ X+PRb MOV+NQPR\]V+p-MONQN l+T�\cl@MUT�W Z \]n2W�K+Mp-PRV+M#^_T�b9^_W�MUTQP ^cp � � \cT W�K+MjV+\]V+p-PRV+M#^_THb9^_W�MUTQP ^cp'�

� � � �� � � U W�! Z � � U W # Z � # � U W X[Z � X ������� � �Se\]pR^_T�PRh#^_WQPR\]V9b t+N�WLK�^#�CMjt+V+PFW�NL\]n�qU\]t+pR\]b Y N�l@MUT bfMUWQMUTLNQz{t�^_TQMOX�N�\ W�K+P-N�nw\cT�qOMONLW�K+MkV+\]V90p-PRV+M#^_T NQt+N�qOMUl+W�P Y PRpRPFW�PRMUNLU W # Z ^cV+X(U?W X[Z1WQ\�K�^#�CM�t+V+P-WQN�\]nkbfM:W�MUT�Nfl MUT �C\]p-W ^cV+X bfMUWQMUT�NNQzBt�^_T�MOX�l MUT �C\]p-W�N NQz{t�^_TQMOX�T�MON}l@MOqUWQP-�CMOp Z �

JLK+M NQt+NQqOM:l+W�P Y P-pRP-WQPRMON q#^cV Y M�M��ul+T�MUNQNQMOX P-V�WQMUT�bfN \]nLW�K+M�V+\]V+pRPRV+MO^_Ts\]N�qOPRp-p ^_W�\cT / Nx+T�N}W 0 \cT�X+M:Ta^_l+l+T�\��+P-b9^_W�PR\]V�NQ\]p-tuW�PR\]V.(

U W�! Z � � ! � � � � ! �� � � ! � � !� � � ! � #� � � � � #! � � #� � %U W # Z � � � ! � � � � � ! �� � � #! � � #� � � #! � X � #� � � # � � - � #! � � #� � � � #! � � #� � # %U WYX[Z � + � ! � � � + � ! �� � � X! � � X� � � X! � � X� � � X - � � � #! � � #� � � � #! � � #� � # �

A � � � � G� � �'� � � � � � !#���)�������

� Vf\cTQX+MUT�W�\yl+T�MOX+PRq:W�W�K+M Y MOK�^��{PR\cT/\]n W�K+M�WQK+P-T�X9K�^_T�b \]V+PRq �L^��CM l+T�\{X+t+qUMOX �HPFW�K+PRVW�K+MLMUT Y PRt+b x Y MUTO�BNQ\]pF�CM�W�K+M �L^��CMLMOzBt�^_W�PR\]V ��P-W�Ks^yXuTQP-�uP-V+vaW�MUT�b2�"J K+P-NEnw\cTQqOPRV+vjnwt+V+qUW�PR\]V\]n"W�K+M MOz{t�^_W�P-\]V2�HP-pRp Y MjW�K+M V+\]V+pRP-V+M#^_T2l@\]pR^_T�PRhO^_W�PR\]V�\]n"W�K+M MUT Y P-t+b PRV`TQMON�l@\]V+N�M1W�\fW�K+MP-Vul�tuWHx�MOp-X.�

JLK+M X+M:T�P-�_^_W�PR\]V Y MOv]P-V+N ��P-WQK | ^ � ��MUpRp / N�MUz{t�^_W�P-\]V+N

� �� , ,, � �� �� � �� i ii �� � � �� � S SS �� � � �� � � � U � �� � S SS�� � � �IaN�NQt+bfM ^fK+\]bf\]v]MOV+MU\]t+NO�@V+\]V+b9^cv]V+MUWQPRq bfMOX+P-t+b W�\�^cp-pR\�� UE�����>^cV+X W�\9N�Wg^ Z

qO\]V+N}Wg^cV W��HPFW�K�TQMON�l@MUqUWHW�\ � �� �� "

Page 71: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� �� � � � ��� � � � # , ,,� � # � �� � ��, ,,� � �� � � � � U � � #�� ��� � # � � � � ��� � � � #QS SS � � � �� � #� M��{WLWg^ � MyWQK+M qOtuT�p�\]n!WQK+M ^ Y \ �CMjMOz{t�^_W�P-\]V+NH^cV+X�qO\]b Y PRV+MkW�K+MOb2�

� �� � � �� � � �� � �� � � � � U � � # � ��� � # � �� � � ��� � � � #QS SS � � � �� � # ��^cV+X Y Z t+NQPRV+vsW�K+My�CMUqUW�\cT�PRX+MOVCW�P-W Z �

� �� � � �� � � �� � �� � � �� � � �� � � � �� # � ��^_TQTQP-�CMj^_W WQK+M �L^#�CM MOzBt�^_W�PR\]V�nw\cTa^ �L^#�CMjXuT�PF�CMOV Y Z ^ V+\]V+pRP-V+M#^_THb MOX+PRt+b2�

� �� # � �� �� � � ��� � � �� � # � ��� � # � � #QS SS � � � �� � #� V \cT�X+M:TfW�\ v]MUWf^�T�\]t+v]K ^_l+l+T�\��+P-b9^_W�PR\]V�\]n2W�K+M`V+\]V+p-PRV+M#^_TQP-W Z V+MUMOX+MOX*nw\cTfW�K+M

x Y MUTaW�K+M ^cV�^cp Z NQPRN�PRN2N�PRb l�p-P-x�MOX.��IaNQNQt+bfM WQK�^_W2W�K+M1x Y M:TkPRN2\]V+M X+P-bfMOV+NQP-\]V�^cp!^cV+X8V+\]V90qO\]V+X+t+q:W�PRV+v�� IapRNQ\�^cNQNQt+bfM W�K�^_W ^cpRp�x�MOp-X+Nf^_T�M�l�p ^cV+M �L^��CMUNf^cV+X W�K�^_W W�K+MUTQM�PRN l�K�^cNQMb9^_WQq6K+P-V+v Y M:W ��MOMOV bf\{X+MON�� � \���^fN�q#^cp ^_T2WQPRbfM�0 N�lm^cqOM MOzBt�^_W�PR\]V�nw\cTaW�K+M1bf\cW�P-\]V`\]neW�K+MW�K+PFT�X�K�^_TQbf\]V+PRqyqUT�M#^_WQMOX`PRV�W�K+M X+P-MOpRMUqUWQT�P-qjq#^cV Y M���T�PFWQW�MOV.�

� # � � � �� # � # � �� � # � # � � � � �� � #

JLK+M�XuTQP-�uP-V+vyWQMUT�b`� � � � � � � ��PRp-p Y MLW�K+M�V+\]V+p-PRV+M#^_TEl@\]pR^_T�PRhO^_W�PR\]V � � � �E~{P-V+qOM WQK+M�P-V W�M:T�MON�WP-N PRV5W�K+M9W�K+P-TQX�K�^_TQbf\]V+PRqfnw\cT W�K+P-N M��ul MUT�P-bfMOVCW \]V+p Z �ep-MUW W�K+M9MOzBt�^_W�PR\]VDqO\]VCWg^cPRVDW�MUTQbfNn T�\]b � � + � ! ���

� � + � ! � U W X[Z � + � ! ��� � � X! %��K+MUT�MyW�K+M P-Vul�tuW�x�MOp-X � pR^cNQMUT�p ^ct+V+qgK+MOX�PRVCW�\ W�K+Mjx Y MUT ��PRN

� ! � ! ��� � � � ! � � � ! � � �JLK+MjWQTQP ^cp>NQ\]p-tuW�PR\]V�nw\cT�W�K+P-N�MUz{t�^_W�P-\]V�\]n!W�K+MkW�K+PFT�X`K�^_T�bf\]V+P-q�/ NLbf\cWQPR\]V.(

� � � X � X � ��� � � + � ! � � + � ! � � � � X � � � � � + � ! � � + � ! � �Ian W�M:TjN�t Y N�W�P-WQtuW�PRV+v�PRV WQK+M M��ul+T�MON�NQPR\]V+Njnw\cT � X � � � � � � ��^cV+X � ! � � MOMUl�P-V+v�\]V+p Z W�K+M + � !W�M:T�bfN �:�CMU�_^cpRt�^_WQPRV+vjWQK+MHX+MUT�PF�c^_WQP-�CMONO�B^cV+XsWQK+MOV9qO\]b Y PRV+P-V+vyW�M:T�bfNO� NQ\]p-�CMLW�K+M�MOz{t�^_W�P-\]V Y Z

� �

Page 72: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

MOzBt�^_W�PRV+v qO\]N�PRV+M W�MUT�b N �HPFW�K8qO\]NQPRV+M W�M:T�bfNk^cV+X NQPRV+M W�MUTQbfN �HPFW�K NQPRV+M W�MUTQbfN��yJ K+M W ��\T�MUNQt+p-W�NH^_T�MyNQK+\���V Y MOpR\��� �� � � X � � � �

+� � ! U W X[Z � X!

�� � � X � � � � � �I2l+l�p Z PRV+v W�K+M Y \]t+V+X�^_T Z qO\]V+X+P-WQPR\]V+N nw\cTHW�K+Mkx Y MUTO�P-V�\cW�K+MUT���\cT�X+NO�

� X � � � � � X � � � � ��snw\cT � ���� � � X � � � � �� � � X � � � � ��snw\cT � ��

%W�K+MyNQ\]p-tuW�PR\]V�\]n!W�K+MkW�K+P-T�X�K�^_T�bf\]V+PRq+�L^#�CM P-N�nw\]t+V+X Y Z PRVCW�MOvcTg^_WQPRV+v�(

� X � � � � + � � ! U W X[Z � X! �� X � � � � �� �� V W�K+PRNjNQPRb l�p-P-x�MOX�^cV�^cp Z NQPRNO��W�K+M W�K+P-T�X K�^_T�bf\]V+P-qsvcT�\���Njp-PRV+M#^_T�p Z �HPFW�K�X+P-N�Wg^cV+qOM

WQT�^��CMOp-MOX�^cV+X�K�^cN�^ X+PFT�MOqUW X+MUl MOV+X+MOV+qOM \]V�W�K+MkP-Vul�tuW x�MUpRX#/ N �L^#�CMkVBt+b Y M:T � WQKBt+N �L^#�CM�0p-MOV+vcW�K �:�>W�K+MsqOt Y M \]n4W�K+M PRVul�tuWjx�MOpRX#/ N ^cbsl�pRP-WQt+X+Mc��^cV+X�\]V WQK+MsbfMUX+PRt+bM/ NkWQK+P-T�X \cT�X+MUTNQt+N�qOMUl+W�P Y PRpRPFW Z �

A � � � ����'��� � ���O* ������E����� � ���?��@� �E�'���

� P-v]tuT�MD��3DN�K+\���N�WQK+M M��ul@M:T�PRbfMUV W9W�K�^_W �L^cN t+NQMUX nw\cT�^�X+PFT�MOqUW�bfM#^cN�tuT�MObfMOVCW\]nkW�K+M8W�K+P-T�X�\cT�X+MUT�NQt+NQqUMUl+W�P Y P-pRPFW Z \]nyW�K+M8MUT Y PRt+b x Y MUT�� � V�W�K+M M��{l@MUT�P-bfMOVCW�^�pR^cNQMUTY M#^cb �L^cN�N�MOV W�n T�\]b ^�l \���MUT�nwt+pkp ^cNQM:T�NQt+qgK ^cN�^ � X.( �I/� PRVCW�\DW�K+M MUT Y PRt+b x Y MUT���5M9M��ul@MUqUW�MOXDNQMOqU\]V+X ^cN5��MUpRp�^cN1WQK+P-T�XDK�^_T�bf\]V+P-qfv]MOV+MUT�^_W�PR\]V ��P-W�K+P-V W�K+Mfx Y MUT \��CMUT ^qOM:TQWg^cPRV W�PRbfM P-V W�M:TQ�c^cp � �� ���� � � � � � �� � � � � J K+M�W�K+P-T�X K�^_T�bf\]V+PRq�\]nHP-V WQMUT�MON�W PRV WQK+PRNM��{l@MUTQPRbfMOVCW���\]t+pRX�K�^��CM Y MOMUV PRV W�K+M t+pFWQTg^#�uPR\]p-MUWkPRn/^ � X.( �I/�&^_W ��� � 2 �� K�^cX Y MOMOVt+NQMUX.� � P-T�N}WkP-W/��^cNaV+MOqOMONQNQ^_T Z W�\9NQM:lm^_Tg^_W�M \]tuW2W�K+M1WQK+P-T�X8K�^_T�bf\]V+P-q nw\cT�b W�K+M1x+T�N�Wk^cV+XNQMUqO\]V+X`K�^_T�bf\]V+P-qON YBZ x�p-WQMUT�PRV+v��4JLK+MOV�W�K+P-N�\]tuWQl�tuW�lm^cNQNQMOX�W�KuT�\]t+v]K8~{\BX+PRt+b ~u^cpRP-q Z pR^_W�MNQ\]p-tuW�PR\]V�W�\ftul@qU\]V �CMUT�WkP-WHWQ\ W�K+M �{PRNQP Y pRMjT�^cV+v]M ��K+MUT�M P-W���\]t+pRX Y M lm^cNQNQMUX8WQKuT�\]t+v]K`W�K+Mv]pR^cNQN�W�t Y M \]n"l@\���MUTab MUW�MUT�N�\cT2l�K+\cW�\]b t+p-WQP-l�pRP-MUT�N�� � V`W�K+Mjx�V�^cp!M��{l@MUT�P-bfMOVCWa^fX+P @MUT�MUV WpR^cNQMUT �L^cNHt+NQMUX.��JLK+PRN �HP-pRp Y MyX+MONQqUTQP Y MUX�PRV�WQK+M V+M��{WHNQMUqUW�PR\]V.�

� �

Page 73: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � � � � � � � � ����� U W X[Z �

JLK+Mjl \���MUTH\]n�W�K+MyWQK+P-T�X`K�^_TQbf\]V+PRqax�MOp-X`PRN

� X � � #X ��

� � � � � ��# � � # � U?W X[Z ��# � X !2�- � # ! � � � # %\cT#��NQ\]pF�uP-V+vsnw\cT�NQt+NQqOM:l+W�P Y P-pRP-W Z �

U W X[Z �+� !� �

� � � ��

��� X �� X ! �

� V�^ VBt+bfM:T�PRq#^cp>M���^cb l�p-Ma\]n�W�K+MkM��{l@MUTQPRbfMOVCW � bfP-VBt+N�W�K+Mktul qO\]V �CM:T�NQPR\]V�n ^cqUW�\cT�N �:�^ � X.(! /I/� p ^cNQM:TsP-N t+NQMOX ^_W � ! ��� � 2� �� �HPFW�K�^cV P-Vul�tuW l \���MUT \]n � ! � � ��� W�\XuT�PF�CM W�K+M MUT Y PRt+b x Y MUT+�HPFW�K8^`� �� �� qO\cT�Mc�@\��CMUTy^_l+l+T�\��+P-b9^_W�MOp Z � � � � W2PRNanw\]t+V+X�W�K�^_WP-V \cT�X+MUTsW�\ bfM#^cNQtuT�M�^cV \]tuWQl�tuW � X � � � ^ �_^cpRt+M�\]n U?W X[Z 2 �,3{� � � ��� #�! � � � ��� ���\]t+p-X Y M V+MOMOX+MUX.�

� �

Page 74: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� � � ����� �/g�� *����� < %!�]�C�� �`�>�m�-;��

T �8��� �V@��N8� �6�������Q � ��� �$G� �E�'����*

,k^#�uP-V+v��\cT � MOX \]tuW ^ T�\]t+v]K ^_l+l+T�\��uPRb9^_WQPR\]VDnw\cT9^ bfPRV+P-b9^cp/bfMO^cNQtuTg^ Y pRM U?WYX[ZY ^cNQMUX�\]V WQK+MfqOp ^cN�NQPRq#^cpEM��{l�p ^cV�^_W�P-\]V5\]n�K�^_T�bf\]V+PRqsv]MOV+MUTg^_WQPR\]V5PRV ^`bfMOX+PRt+b���W�K+MfV+M��uWN�WQMUl2�L^cNLW�\sx�V+X`^sp ^cN�MUT2nw\cT W�K+Mjx+TQN�WHM:T Y PRt+bdx Y MUT��

JLK+M M:T Y PRt+b x Y MUT n T�\]b � T�\���V ��^cNjW�K+M x+T�N�Wjx Y MUT M���^cbfP-V+MOX�P-V W�K+Msp ^ Y � � \cWb t+qgK3��^cN � V+\���V�^ Y \]tuW�W�K+Max Y M:T���K+MOV�PFW ^_TQT�PF�CMOX.�EJ ��\ X�^_Wg^1l�pR\cWQN ��P-WQK�^_W�W�MOV t�^_W�PR\]V^cV+X TQMOn Tg^cqUW�PF�CM/P-V+X+M��>� NQK+\���V1P-V x�v]tuT�MH���u����MUT�M4X+MOpRPF�CMUT�MOX �HPFW�KjW�K+MEx Y MUT���J K+MET�MOn Tg^cqUWQP-�CMP-V+X+M��`l+T�\cx�p-M1NQt+v]v]MON}W�N2W�K�^_WHWQK+M x Y MUTkP-N2vcTg^cX+MOX�P-V+X+M��.� Ian W�MUT2M���^cbfP-V+PRV+v W�K+M1x Y MUTHW�P-lt+V+X+MUTs^�bfP-qUT�\]NQqO\cl MfW�K+M9qO\cT�M NQP-hOM&�L^cN nw\]t+V+XDW�\8pRPRM NQ\]bfM���K+MUT�M Y M:W ��MOMOV*� � ^cV+X ��0bfP-qUT�\]V+N�� � MOnw\cT�M W�K+Mjq#^cpRqUt+p ^_W�P-\]V+NHPRV�W�K+M pR^cN�W2NQMUqUW�PR\]V-��MUT�M1X+\]V+M_�PFW/�L^cN W�K+\]t+v]K W�W�K�^_WNQP-V+qOM/W�K+MEx Y MUT"K�^cNe^HNQb9^cp-p]qUT�\]NQN 0 NQMOq:W�PR\]V>�]MU�CMUV ^HNQMObfP-qO\]V+X+t+qUW�\cT!p ^cNQM:TeNQK+\]t+pRX Y M�^ Y p-M4W�\^cqgK+PRM:�CMLWQK+M�K+PRv]K l@\���MUTEX+MOV+NQPFW�PRMUNEV+MUMOX+MOX P-V \cT�X+MUT�W�\ Y T�P-V+vj^ Y \]tuW�V+\cW�PRqUM#^ Y pRMLV+\]V+pRP-V+M#^_TW�M:T�bfN��eI N�MObfPRqU\]V+X+t+qUW�\cT�X+P-\{X+M2pR^cNQMUT4W�K�^_W�K�^cX Y MOMOV �}l�PRvcW�^cPRpRMUX � � qO\]V+V+MUqUW�MOX9W�\ ^yx Y MUTnw\cT!\cl+W�PRb t+b \]tuWQl�tuWeqO\]tul�p-PRV+v � ��^cN!qO\]V+V+MOq:W�MOX W�\HW�K+M/N�l@\B\]pB\]nuM:T Y PRt+b x Y MUT���JLK+M�X+P-\{X+MpR^cNQMUT4MObfP-W�W�MOX Tg^cX+P-Wg^_WQPR\]Vs^_WH� �,0 0kbfP-qUT�\]V+N$��K+PRqgK7�L^cN4^_W4WQK+M l M#^ � \]nW�K+M�^ Y NQ\cTQl+W�P-\]Vfnw\cTMUT Y PRt+b2�sJ K+M X+PR\BX+M \]V+p Z MObfP-W�W�MOX ^�qO\]tul�pRMsbfPRp-pRP �L^_WQW�N Y tuW P-W��L^cN Y MOp-PRMU�CMOX W�K�^_WjWQK+PRNbfM:W�K+\{X bfP-v]K W!N�W�P-pRpBl+TQ\{X+t+qOM��{PRNQP Y pRM�\]tuWQl�tuW � vcT�MOMOV �"^_W"WQK+M�MOV+Xs\]n+W�K+M/N�l@\B\]p �eJLK+M�PRVul�tuWNQP-v]V�^cp%�L^cN ^_W�W�MOV t�^_W�MOX Y tuW P-W1W�tuTQV+MOXD\]tuW W�K�^_W ^cV Z vcT�MOMOV5W�K�^_W���^cN Y MOP-V+v�l+T�\{X+t+qOMUX�L^cN Y MOP-V+vsT�MO^ Y NQ\cT Y MUX�\cT��L^cN$�}t+N�W2W�\B\"��M#^ � WQ\ bfM#^cN�tuT�M#�EIaV+\cW�K+MUT2b MUW�K+\{X�PRVC�C\]p-�{PRV+v^ K+PRv]K+MUT�l@\���MUT�p ^cNQMUT���\]t+pRX Y MjV+MOMOX+MOX.�

JLK+MfqgK�^cpRp-MOV+v]M7�L^cNjW�K+MOV5W�\�x�V+XD^�l \���M:T�nwt+p�p ^cN�MUT W�K�^_W��\]t+pRX5\cl MUTg^_W�M ^_W1W�K+M^_l+l+T�\cl+TQP ^_W�M ��PRV+X+\��HN PRVDW�K+M9x Y M:T / Ns^ Y NQ\cTQl+W�P-\]V N}l@MOqUW�T�t+b NQ\ WQK�^_W W�K+M�\]tuW�l�tuW WQK+P-T�XK�^_T�b \]V+PRq ��\]t+p-X�V+\cW Y My^ Y NQ\cT Y MOX�^cNLP-W ��^cN Y MOPRV+v v]MOV+MUTg^_WQMOX.��JLKuT�MOMyp ^cNQM:T�N�W�K�^_W ��MUT�MM��+^cbfPRV+MUX���M:T�M/bfMUX+PRq#^cp]pR^cNQMUT�N�n T�\]b ^ p-\{q#^cpcTQMONQM#^_T�qgK pR^ Y W�K�^_W ��M ��MUT�M4v]P-�CMOVkl@M:T�bfPRN�NQPR\]VW�\9t+N�M#�j�kV+M p ^cN�MUT+�L^cNk^ � X.(! /I/� p ^cN�MUTy^_W � � � 2 ��(2JLK+PRN ��^cNaV+\�v]\B\{X Y MOq#^ct+NQM W�K+MW�K+PFT�X�K�^_T�bf\]V+P-q �L^cN2WQ\{\fqOp-\]NQM W�\fWQK+M x Y MUT�/ Nk^ Y NQ\cTQl+WQPR\]V�l@M#^ � ��IaV+\cWQK+MUTap ^cN�MUT �L^cNk^cVoET�(! ~�� �*p ^cN�MUTE^_W � � ��- ��("JLK+PRN ��^cNeV+\av]\{\{X Y MOq#^ct+NQM ^_W"WQK�^_WeK+PRv]K��L^#�CMOpRMUV+vcW�K W�K+MUT�MP-NeV+\kl+TQ\clm^cvC^_W�PR\]V W�KuT�\]t+v]K W�K+M�x Y MUT / N�NQP-pRP-q#^2K+\]N�W���JLK+MLp ^cN�WepR^cNQMUT �L^cN�^+,a\]pRb PRt+b �I/�^_W � �R� � ���4IaV�M��ul MUT�PRb MOV W �L^cNLW�\ Y Mj^_WQW�MObsl+W�MOX�t+NQPRV+v W�K+PRNLp ^cN�MUT��EI l+T�\ Y p-MOb ^_T�\]NQMX+t+M W�\ W�K+M n ^cqUWkW�K�^_WkW�K+PRN+�L^cNj^�b MOX+PRq#^cp!p ^cNQMUT�� J K+M qO\cTQMsNQP-hOM \]n4W�K+M x Y MUT \]tuW�l�tuW \]nW�K+P-NHpR^cNQMUT/��^cN2^_T�\]t+V+XM- � � �� ��P-WQK`^ V t+bfMUT�P-q#^cp�^_l@MUT�W�tuT�M1\]n � � �]� �/JLK+M1MUT Y PRt+bdx Y MUTN�^cbsl�pRM9K�^cX�qO\cT�M9NQP-hOMON \]n�^_TQ\]t+V+X�W�MUV bfP-qUT�\]V+N5��P-W�K�^�V t+bfMUT�P-q#^cp�^_l@M:TQW�tuT�M \]n�^ Y \]tuW

� �

Page 75: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

������������ � � � � ��� � � ���

� �,09�eJ K+M Tg^cX+P ^cV+qUM�W�K+MO\cTQMOb l+TQMOX+PRqUWQN4W�K�^_WEW�K+MUT�M �HP-pRp Y M�^jpR^_T�v]MLl@\���MUT�p-\]NQN/P-VsWQT Z PRV+vkW�\qO\]tul�p-M2^ Y M#^cb Y MUW ��MOMOVfW�K+MUNQMHqO\cTQMON��$*2^cX+PR^cV+qOM � W�K+M l \���MUT/l MUT/t+V+PFW�^_TQM#^ ^cV+X l@MUT/t+V+P-WNQ\]p-PRX�^cV+v]pRM �/PRNL^ qO\]V+N�Wg^cVCW#�uP-V�^cV \cl+W�P-q#^cp N Z N�W�MUb2�4~{PRV+qOM Y \cWQK WQK+M2W�MON�W�x Y MUT / N ^_T�MO^ ^cV+XV t+bfMUT�P-q#^cpE^_l@MUT�W�tuT�Ms^_T�MsN�b9^cpRp-MUTkW�K�^cV W�K+\]N�M \]n4WQK+MspR^cNQMUTyx Y MUT / NjW�K+M qO\]tul�p-PRV+v ��PRp-p Y Mp-\�� ��J K+MHpR\���V t+bfMUTQPRq#^cpm^_l@M:TQW�tuT�M2b M#^cV+N4W�K+M:T�M2PRN/^ pR\��*NQ\]pRP-X9^cV+v]pRM�PRV7��K+PRqgK9p-PRv]KCW/q#^cVY M ^cqOqOMUl+W�MUX.��� neW�K+M1W�MON}Wyx Y MUTkPRNab \ �CMOX8n ^_TkMOV+\]t+v]K ^��L^ Z NQ\�^cN2W�\ Y M ^ Y pRM1WQ\ ^cqOqOMUl+W^cp-p W�K+MapRMUV+N�p-PRv]KCW�PRVCW�\ P-W�N�NQ\]p-PRX�^cqOqOM:l+Wg^cV+qOMj^cV+v]pRMc�uW�K+MUV�W�K+MkN�l \cWLNQPRhUM���\]V#/ W b9^_W�qgK9W�K+Mx Y MUT / N qO\cT�My^_T�MO^ � � \cTLW�K+MkbfMOX+PRqO^cp@p ^cNQM:T#�+W�K+Mal@\���MUT�n T�\]b&W�K+Myp ^cNQMUT P-N qU\]V Wg^cP-V+MOX`P-V�^cV^_T�MO^ 0 NQ\]p-PRX ^cV+v]pRM1l+T�\BX+t+qUW \]n � � � ���,2 �D� ����� � # � � � JLK+M W�MON�Wkx Y M:T���PRp-p"\]V+p Z ^cqOqOMUl+Wl \���M:TkqO\]V W�^cPRV+MOX��HPFW�K+PRV8PFW / Na^_TQM#^ 0 NQ\]p-PRX ^cV+v]pRM1l+TQ\{X+t+qUW#� � � ��� �D� ��� !�# � # � � � �HK+P-q6KP-N�^ Y \]tuW�^ � � p-\]NQN��4~{PRV+qOMkW�K+MON�M���M:T�Mjb MOX+PRq#^cp p ^cNQMUTQN n TQMOz{t+MOVCW�p Z t+N�MOX�P-V�T�MUNQM#^_T�qgK`^cV+XNQtuTQv]MUT Z W�K+M:T�M��L^cNaV+\ �L^ Z W�\ v]MUWaP-V+NQPRX+M W�K+M pR^cNQMUTy^cV+X8vC^cPRV ^cqOqOMUNQNaW�\fW�K+M qO\]pRp-PRb9^_WQMOXY M#^cb2�

��P-WQK+PRV W�K+MjpR^cN�W Z M#^_T W�K+MjN�MOqO\]V+X�x Y MUT2NQ^cb l�pRM �L^cNLT�MOqUMOP-�CMOX.�%*HP-q � J!t+b bfPRV+MOp-pRPl+T�\��uP-X+MOXDt+N��P-W�KD^`K+M#^#�uP-p Z X+\cl@MOX5x Y M:T n T�\]b o4pRP/~{V+P-W�hOM:T / N pR^ Y � *HtuW�v]M:T�N ��� ����JLK+PRNV+M�� x Y MUT��L^cNy^�qO\BX+\cl@MOX� kWQW�MUT Y P-t+b10 oET Y PRt+b NQPRV+v]p-Msbf\BX+M1x Y MUT � ^_W � �10 �� �+��P-WQK�^qO\cTQM�N�PRhOM�\]n + �,0 �� ^cV+X ^8VBt+bfM:T�PRq#^cp�^_l@MUTQWQtuT�M�\]n � � �]� � ��J K+M:T�M3��MUT�M�^cpRNQ\ N�^cb l�p-MONn T�\]b&WQK+MaN�^cbfM2l+T�MOnw\cTQb �HPFW�K p ^_T�v]MUTLqU\cT�MkNQPRhOMUN tul�W�\J3 �� �4JLK+MyqU\]V+qOMOVCWQTg^_W�P-\]V�\]n�W�K+MX+\clm^cVCW�N%��^cN/b t+qgKfvcT�M#^_W�M:T/W�K�^cV WQK�^_W/P-V W�K+MLx+T�N�W�M:T Y PRt+b x Y MUT��EJLKuT�\]t+v]K W�K+MUP-T�N}l@MOqOPR^cp

���

Page 76: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

x Y MUT b9^cV t+n ^cqUW�tuT�P-V+v�l+T�\BqOMONQN ^�K+PRv]K5qO\]V+qOMUV WQT�^_W�PR\]V x Y MUT5�L^cNjXuTg^���V.� � W / NyqO\cT�Mfv]pR^cNQNqO\]VCWg^cP-V+N���0 � � � #�� X Y Z ��MOPRv]KCW/^cV+X � �,+ � � � #�� X Y Z ��MOPRv]KCW��"��P-W�K1*HPRq � / NE^cNQNQP-N�Wg^cV+qOMW�K+M�x+T�N}WEx Y MUTEn T�\]b � T�\��HV��L^cN�X+MUW�M:T�bfPRV+MUX>�CWQKuT�\]t+v]KsqU\]b lm^_T�PRN�\]V \]n^_WQW�MUVBt�^_W�P-\]V X�^_Wg^u�W�\8qO\]VCWg^cP-V ^ Y \]tuW � �R��3 � � � #�� X Y Z ��MOP-v]K W�� JLK+M K+PRv]K+MUT qO\]V+qOMUV WQT�^_W�PR\]V�\]n�X+\clm^cVCW�NNQt+v]v]MUN�W�NaW�K�^_WkW�K+MUT�M���PRp-p Y M bf\cTQM V+\]V+pRPRV+MO^_Tj\]N�qOPRp-p ^_W�\cT�NHPRV8W�K+M qO\{X+\cl MOX b MOX+PRt+b ^cV+XW�K t+NHvcTQM#^_W�MUT�K�^_T�bf\]V+P-qjv]MOV+M:Tg^_W�PR\]V>����K+PRqgK`P-N W�K+MjN�^cbfMy^cNHNQ^ Z PRV+vs^ K+PRv]K+MUT U?WYX[Z �

������������� � � � � ��� � � � � � � � ��� � � ���

| \cT�M9P-V+NQPRv]KCW��L^cN vC^cP-V+MOX YBZ ^cp-NQ\`T�MU�{PRM���PRV+v ~{V+PFW�hOMUT / N1lm^_W�MOVCW�� � � � � �� � � �� � ��NQK+\���PRV+v�WQK+Mf^ Y NQ\cTQl+WQPR\]V N�l@MOq:WQT�t+b \]n4W�K+M Tg^_T�M�0 M#^_TQW�K�PR\]V+Nk\ �CM:T1^ �HP-X+MsN�l MOqUWQTQt+b \]n�L^#�CMOp-MOV+vcW�K+N�� JLK+PRNyX�^_Wg^ �L^cNkbf\cT�M ^cqOqOtuTg^_WQM W�K�^cV ^cV Z l+T�MU�uP-\]t+NjX�^_W�^ W�K�^_WyK�^cX Y MOMOV^#�c^cP-p ^ Y p-M#� � T�\]b W�K+M ^ Y NQ\cTQl+WQPR\]V N�l@MOq:WQT�t+b nw\cTEMUT Y PRt+b��]NQK+\���V P-V x�v]tuTQM � �u�C^cVs^_WQW�MUb l+W�L^cN/b9^cX+MHW�\ qgK+\{\]N�Mk^ l�t+b l �L^��CMUpRMOV+vcW�K9nw\cT ��K+PRqgK9W�K+M2W�K+PFT�X9K�^_T�bf\]V+P-q/��\]t+p-X9V+\cW Y M^ Y NQ\cT Y MOX�^cV+X ��\]t+p-X ^cpRN�\ Y MsP-V WQK+M �{PRNQP Y pRM PRn�l@\]NQN�P Y pRM�� I Y NQ\cTQl+W�P-\]V \]nEW�K+M l�t+b l Y ZW�K+MsX+\clm^cV W1^cN���MOpRp4^cN Y Z W�K+M v]pR^cNQNjK+\]N}W�L^cNj^�b9^ �}\cTyqO\]V+qOMUTQV.�fIaV+\cW�K+MUTjPRb l \cTQWg^cVCWn ^cqUWQ\cT"��^cN W�K+M�^ Y PRp-P-W Z W�\8l�PRq � ^)�L^��CMUpRMOV+vcW�K�Tg^cV+v]M�nw\cT"��K+PRqgK WQK+MUT�M�M��+P-N�W�MOX ^ pR^cNQMUTW�K�^_W�L^cN q#^_lm^ Y pRM9\]nLK+PRv]K90'l@\���MUT \cl@M:Tg^_W�PR\]V>��^cV+XDnw\cT ��K+PRqgK5W�K+MUT�M �L^cN ^cqOqUMONQN W�\�W�K+M

� �

Page 77: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� �� � � � � ��� � � � � � � ��� ��� ��� ���� � � � ��� �

qO\]p-pRP-b9^_W�MOX Y MO^cb2�

� MOPRv]K+P-V+v ^cp-p W�K+MONQMyn ^cqUW�\cTQN W�K+M Y MUN�W q6K+\]P-qOM��L^cN WQK+M � X.( �I/� \cl@M:Tg^_W�PRV+vs^_WLW�K+M� �.+u��� �� WQT�^cV+NQP-W�P-\]V.��JLK+PRN p ^cNQMUT1PRN q#^_lm^ Y p-Mf\]nLK+PRv]K l@MO^ � l@\���MUTQN5�HK+MOV � 0 N ��P-WQq6K+MUX^cV+X � \cTHbf\{X+MypR\Bq � MUX.��o4T Y P-t+b P-N�WQT�^cV+N�lm^_T�MOVCW2W�\sP-W�N�nwt+V+X�^cbfMOVCWg^cp ��^��CMOp-MOV+vcW�K8^cV+X`PFW�NW�K+PFT�X5K�^_T�bf\]V+P-q P-N1PRV W�K+Ms�uPRN�P Y pRM � �uP-\]pRMUW �alm^_TQW1\]n�W�K+MfN�l MOqUWQT�t+b ��IaqUWQt�^cpRp Z W�K+M WQK+P-T�XK�^_T�b \]V+PRq�PRN�NQpRP-v]K WQp Z W�\LW�K+M/NQP-X+M4\]nBW�K+MEW�Tg^cV+NQbfP-NQNQPR\]Vyl@M#^ �aY tuW!MOV+\]t+v]K1NQK+\]t+p-X Y M�lm^cNQNQMUX^_WeK+P-v]K l@\���MUT���IapRN�\anw\cTE^kN�PRV+v]pRM�0 bf\BX+M�p ^cNQMUTeWQK+M Y M#^cb�N}l@\cW�NQP-hOM �HK+MUVsnw\BqOt+NQNQMOXsNQK+\]t+pRXY MjX+P Tg^cqUWQPR\]V�p-PRbfPFW�MOX�^cV+X�PFW�N ^_T�M#^ 0 NQ\]pRP-X`^cV+v]pRMkl+T�\BX+t+qUWHN�K+\]t+pRX Y M1^_l+l+T�\��+P-b9^_W�MOp Z � # �JLK+PRN/�_^cpRt+MHnw\cT�W�K+M � X.(! /I/� P-N�^_l+l+T�\��+PRbf^_W�MOp Z ���,3�+]� � ��� ��� !�# � # � � � � ~{MOM2q#^cp-qOt+p ^_WQPR\]V+NP-V*V+M��uW9NQMUqUW�PR\]V.� � J K+P-N9PRNfqO\]bslm^_Tg^ Y pRM�WQ\DWQK+M Y 0 o4T W�MON�W9x Y MUT �HK+P-q6K K�^cN ^ �_^cpRt+M� qO^cpRqOt+pR^_W�MOX n T�\]b P-WQN qO\cT�M�NQPRhUM�^cV+X � � I�� � \]n � � �u�+u� � � ��� !�# � # � � � IapRN�\ \]n2V+\cW�M�PRNW�K�^_W�W�K+M Z WQW�MUT Y P-t+b P-\]V�\]V+p Z ^ Y NQ\cT Y Na^_W��L^#�CMOpRMOV+vcWQK+Na^_T�\]t+V+XD� �� ^cV+X�PRNH\cWQK+MUT ��PRNQMWQT�^cV+N�lm^_T�MOVCW���JLK+Myp ^cN�W PRbsl@\cTQWg^cVCWLn ^cqUW W�\ V+\cW�MjP-N WQK�^_W WQK+MUT�M P-N ^cV`^ Y NQ\cTQl+WQPR\]V�l M#^ � ^_W^ Y \]tuW2W�K+M NQMOqO\]V+X K�^_T�bf\]V+P-q � 2&0 � � � ���aJLK+M PRb l \cTQWg^cV+qOM1\]neW�K+P-NHl@MO^ � �HP-pRp Y M NQK+\��HVP-V�W�K+MjV+M��uW�NQMOqUWQPR\]V.�

*�MOqOMOVCW�p Z W�K+M`^_l+l+T�\cl+T�P ^_WQM�p ^cN�MUT7�L^cNsnw\]t+V+X.� SeMUT�bfP-NQNQP-\]V �L^cN v]PF�CMOV W�\ t+NQM�^� X.( �I/� p ^cNQM:T9^_W [ P-V+qO\]pRV [ ^ Y \cTg^_W�\cT�P-MON���J K+P-N pR^cNQMUTsPRNs^ � t�^cV WQTQ\]V+P � �]��3 � X.(! /I/�pR^cNQMUTy\cl@MUT�^_W�PRV+v�^_WkW�K+M � �,+u��� �� WQTg^cV+NQPFW�PR\]V.� � WyK�^cNy^ � 0 N �HPFW�qgK+MUT1P-V�PFW�Naq#^#�uP-W Z � J K+M

� &

Page 78: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

pR^cNQMUTyl+T�\{X+t+qOMUN ^ Y \]tuWs�sW�\M0 �L^_W�W�NjP-VDr�� \cl@MUTg^_WQPR\]V�X+M:l@MOV+X+P-V+v�\]V�K+\�� ^cqUqOtuTg^_W�MOp ZPFW�N�P-V W�Tg^cq#^#�uP-W Z l�P-MOqOMONH^_T�M ^cp-PRv]V+MOX.����K+MOV � 0 N ��P-W�qgK+MOX>�mP-W l+T�\{X+t+qUMONa^ Y \]tuWj� b PRpRp-P �}\]t+p-Ml MUTjl�t+p-NQMc� �HPFW�K l�t+p-NQM p-MOV+vcW�K+Ny\]n�^ Y \]tuW � � � V�^cV+\]NQMOqO\]V+X+N��fJLK+PRNybfM#^cV+Nj^ Y \]tuW 0 � �\]n�l@M#^ � l@\���MUT��

T �F4 � �#���6���7NF�O* * �8� �ON D����$��Q

� V8l+T�MUlm^_Tg^_WQPR\]V nw\cTyWQK+M M��ul@M:T�PRbfMUV WaW�\ bfMO^cNQtuT�M W�K+M W�K+P-TQX \cT�X+M:TjN�t+NQqOMUl+W�P Y PRp-P-W Z\]nkW�K+M8x Y MUT�N�^cb l�p-MON�^�qO\]V+qUMUT�V ��^cN�Tg^cP-NQMOX�^ Y \]tuW�V+\]V90 K�^_TQbf\]V+PRq \]tuWQl�tuW�n T�\]b W�K+Mx Y MUT��`JLK+MONQM9X+\cl MOX x Y M:T�N ^_T�M l+T�\BX+t+qOMOX�nw\cT t+NQM9P-V p ^cNQM:T ^cb l�pRPFx�MUT�N ^cV+X5\]N�qOPRp-p ^_W�\cT�N��~{MOqU\]V+X�K�^_T�b \]V+PRq�v]MOV+MUT�^_W�PR\]V K�^cN Y MUMOV*l+TQ\{X+t+qOMOX�PRV N�Wg^cV+X�^_TQX WQMOpRMOqU\]bfb t+V+PRq#^_W�P-\]V+Nx Y MUT � �� ��� � � �� � � �� � � � ��� � � ��J K+M�PRVCW�MUTQMON�WsPRVDl�tuT�M�K�^_TQbf\]V+PRq9v]MOV+M:Tg^_W�PR\]V�PRV�W�K+Mx Y MUT9pRMUX W�\5^cV ^cV�^cp Z NQP-NsW�K�^_W1�L^cN qU\]b l�pRP-bfMOVCWg^_T Z W�\�WQK+M`qOp ^cN�NQPRq#^cp�l�P-qUW�tuT�M`\]n2WQK+P-T�XK�^_T�b \]V+PRqkv]MOV+MUTg^_WQPR\]V.�

I N�WQT�\]V+v l M#^ � M��+P-N�W�N�P-V W�K+M5^ Y N�\cTQl+W�PR\]V N�l@MOq:WQT�t+b \]n WQK+M MUT Y P-t+b ^_W�\]b ^_W^ Y \]tuWV2&0 � � �� JLK+PRNkqO\cT�T�MON�l \]V+X+NyW�\�^fT�M#^cpeN�W�^_W�M nw\cTkW�K+M ^_W�\]b PRV���K+PRqgK W�K+M MOV+M:T�v ZP-N�� # �+� � ��K+MUT�M � P-N�W�K+M l�t+b l n T�MOzBt+MOV+q Z � � W`P-N � V+\���V W�K�^_W�PRn W�K+M x Y MUT`PRNl�t+b l MOX �HPFW�K5pRP-v]K W W�K�^_W K�^cX�^ �L^��CMUpRMOV+vcW�KD\]n=2&0 � � � WQK+MOVDP-W5��\]t+p-X Y M ^ Y NQ\cT Y MOX.�� \cT4WQK+PRN4x Y MUT�M��{l@MUTQPRbfMOVCW/WQK+M�l�t+b l&��^cN/NQMOp-MOqUW�MUX ^_W2�+u��� � ��EJ K+P-N/qO\cT�T�MON�l \]V+X+N�W�\1^WQT�^cV+N�lm^_T�MOVCW"T�MOv]P-\]V1PRVyW�K+M/x Y MUT���~{\]bfM/^ Y NQ\cTQl+W�P-\]V��PRpRpC\BqOqOtuT Y Z W ��\�0 l�K+\cW�\]V1l+T�\BqOMONQN�MON��� WyPRNyK+MOp-l�nwt+p�W�\�qO\]V+NQP-X+MUT ^ �uP-T�W�t�^cpeN�Wg^_W�M ^_W � ! � � ^ Y \��CM W�K+M vcT�\]t+V+X N}Wg^_W�M#� � PFT�N�W\cT�X+M:THl@M:TQW�tuT Y ^_W�P-\]V`W�K+MO\cT Z ��PRpRp>l+T�MUX+PRqUW�WQTg^cV+NQPFW�PR\]V+N Y MUW ��MOMUV ^cV`^_W�\]bM/ NLMOV+M:T�v Z N�W�^_W�MONnw\cTk\]V+M l�K+\cW�\]V.�j~{MOqO\]V+X \cT�X+MUTkl@M:TQW�tuT Y ^_W�P-\]V�W�K+MO\cT Z v]PF�CMON2T�P-NQM W�\fWQTg^cV+NQPFW�PR\]V+Nanw\cTkW ��\l�K+\cW�\]V+N�( K+MUV+qOM W�K+M PRX+M#^f\]nE^ �{P-TQW�t�^cp�N�Wg^_WQM#�HJLK+M1W�P-bfMjW�K�^_WHW�K+M1MOp-MOqUWQT�\]V+NaN}l@MOV+X PRV8^�{P-TQW�t�^cp�N�W�^_W�MsP-N P-V �CMUTQNQMOp Z l+T�\cl \cTQW�PR\]V�^cpeW�\�W�K+M MOV+M:T�v Z X+P @MUTQMOV+qOM Y M:W ��MOMOV W�K+MsK+PRv]K+MUT^cV+X�vcT�\]t+V+X�N}Wg^_W�MON�� JLK+PRN�PRNa^ qU\]V+NQMOz{t+MUV+qOM \]n!W�K+M5,aMOP-NQMOV Y MUTQv��aV+qUMUTQWg^cP-V W Z S4T�P-V+qOP-l�p-M#�JLK+MHMOV+M:T�v Z p-MU�CMOp�X+P ^cvcT�^cb nw\cT4\]tuT�N Z N�W�MUb P-N4NQK+\���VfPRV x�v]tuTQM � � �eIaVfP-V W�M:T�MON�W�P-V+v T�MON�t+p-W\]n/WQK+PRNkW�K+MO\cT Z PRNkW�K�^_WyW�K+Msl+T�MUNQMOV+qOM9\]n�^�qgK�^cV+v]MfPRV \cl+W�PRq#^cpelm^_W�K�pRMOV+vcW�K � ^cV+X�W�K t+N1^l�K�^cNQM qgK�^cV+v]M � Y M:W ��MOMOV �L^��CMUN NQMOVCW WQKuT�\]t+v]KDn T�MOM N�lm^cqOM�^cV+X ^�WQTg^cV+N�lm^_T�MUV W bfMOX+P-t+bNQK+\���N W�K+PRNjM� @MUqUW��9JLK+Msl�K�^cNQM X+MOp ^ Z \cT NQpR\���PRV+v�X+\���V5M� @MOq:W1\]n�W�K+MspRPRv]KCWjPRN X+t+MsW�\`^X+MOpR^ Z WQPRbfM P-V ��K+PRqgK W�K+M MOp-MOqUWQT�\]V+N���MUTQMsM��uqOP-WQMOX tul�PRVCW�\ W�K+PRNk�uPFTQW�t�^cp"N�W�^_W�M ^cV+X W�K+MOVXuT�\cl+l MOX Y ^cq � X+\���V>� Y MUq#^ct+NQMaW�K+PRN/pRMU�CMOp X+PRX V+\cW�qO\cTQTQMON�l@\]V+X W�\ ^cV�^ Y NQ\cTQl+WQPR\]V9l@M#^ � PRVW�K+Myb9^_W�M:T�P ^cp ��J K t+Na^cV Z bf^_W�MUT�PR^cp �HP-pRp>K�^#�CM1^ �uP-T�W�t�^cp>N�Wg^_W�Mj^_W�MU�CMUT Z �L^#�CMOpRMUV+vcW�K.�

� n"W�K+M M:T Y PRt+b x Y MUTkP-NHl�t+b l@MUX���P-WQK�NQt � qOP-MOVCWkMOV+MUT�v Z ^_W �+u��� � � � �HK+M:T�M1W�K+Mb9^_WQMUT�P ^cp PRN"W�Tg^cV+N�lm^_T�MOVCW�W�K+MOV W�K+MLMOpRMUqUWQT�\]V+N�\]n+W�K+M�X+\clm^cVCW4N�K+\]t+pRX Y M�Tg^cPRN�MOX W�\y^a�{P-TQWQt�^cp

� (

Page 79: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� �� � �� � ��� � � � � � ��� � � � � � � � � � � � �

� ��� � � � ��� � �� � �

N�W�^_W�M#��*2^_WQMsMOzBt�^_W�PR\]V+N+��PRp-pev]\ �CMUTQV ^9l@\cl�t+p ^_WQPR\]V�N�K+PRn WjPRVCW�\�WQK+PRNk�uP-T�W�t�^cp"N�Wg^_WQM#�5� n/W�K+Ml�t+b l x�MOpRX PRNsPRVCW�MOV+NQM�MUV+\]t+v]K � P � M#� W�K+MUT�M`^_T�M`MOV+\]t+v]K l�K+\cW�\]V+N � W�K+MOV ^�l MUT�qOMOVCWg^cv]M\]naW�K+M�M��uqOP-WQMOX MOpRMUqUWQT�\]V+NO��^cN9v]\��CMUT�V+MOX Y Z W�K+M�V+M�� Tg^_W�M`MOzBt�^_W�PR\]V+NU� ��PRp-p Y M�M��+qOPFW�MOXW�\�^cV MOV+MUTQv Z X+P MUT�MOV+qOM8W�K�^_W qO\cT�T�MON�l \]V+X+N WQ\DW ��PRqOM`WQK+M8l�t+bsl�n TQMOz{t+MOV+q Z � K�^cpRnkW�K+M�L^#�CMOp-MOV+vcW�K ���DJLK+PRN MOV+MUT�v Z p-MU�CMOp�PRN ^cV ^ Y NQ\cTQl+W�P-\]V pRM:�CMOpL^cV+X P-V W�K+M l+T�MONQMUV W q#^cNQMc�4PRN^�T�MO^cp�N�W�^_W�M#� ~{\5V+\�� ^�l@\cl�t+pR^_W�PR\]V q#^cV Y M`vcT�\��HV ^_W W�K+M`NQMOqU\]V+X*MUV+MUT�v Z p-MU�CMOp ��IvcT�MO^_W�MUTjVBt+b Y M:T \]n/WQK+MONQM MUpRMOqUW�T�\]V+N���PRp-peV+\�� Y MsM��uqOP-WQMOX Y Z bf\cT�M PRV+qO\]bfP-V+v9l�K+\cW�\]V+N��JLK+\]NQM1W�K�^_Wk^_TQM M��+qOPFW�MOX)��PRpRp Y M1T�^cPRNQMOX�W�\ ^9p-MU�CMOp � X � + � � ��K+MUT�M1WQK+M1l@\]NQNQP Y PRp-P-W Z \]nnwtuTQWQK+MUT M��+qOPFWg^_W�PR\]V8P-NyV+MUv]pRPRv]P Y pRM#�jI K+PRv]K l MUT�qOMUV Wg^cv]M \]n�W�K+MONQM MOpRMUqUWQT�\]V+NyNQK+\]t+pRX X+MOq#^ ZTg^cX+PR^_W�P-�CMUp Z WQ\ WQK+M vcT�\]t+V+X p-MU�CMOp�^cV+X�l+T�\BX+t+qOM WQK+P-T�X8K�^_T�bf\]V+P-q#�yJ K+MUNQM T�^_W�M MOz{t�^_WQPR\]V+NNQK+\]t+p-X�^cpRN�\sl+T�MOX+P-qUWHWQK+My�_^cpRt+Mj\]n�U?WYX[Z �

� \cTk^ � X.(! /I/� p ^cN�MUT+�HPFW�K�lm^_Tg^cbfMUWQMUT�N�( � �+u��� � � �"� � � l MUTal�t+pRNQM_��^cV+X ^l�t+p-NQM p-MOV+vcW�K�\]n"^ Y \]tuW � � � � � �uW�K+M nw\]p-pR\��HP-V+v T�MUNQt+p-W�N�b9^ Z9Y M M��ul@MUqUW�MOX.(

SeMO^ � l \���MUT�(� � � � � ��� � � X �

� � � � � � � � � 0 ���� t+b Y MUTH\]n�l�K+\cW�\]V+N�(

� � � � � � ! � � � � � � � !� �� � � � ����X2 �,2 � 2 � � � � X + ��� � �

���.+u��� � � � ��� I2 �,2 +&0 0 � � � ! � � � � � � �� � � � � �

� #

Page 80: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� n�W�K+MUTQM ^_T�MfW�K�^_W b9^cV Z l�t+bsl�l�K+\cWQ\]V+N l MUT � � �`V�^cV+\]NQMOqU\]V+X+N W�K+MUVDWQK+MUT�M�^_T�M+ �.+u��3#� �5� � � l�K+\cW�\]V+NHl MUTanwMOb W�\]NQMUqO\]V+X`W�K�^_WH^_T�M1MOp-PRv]P Y p-MyWQ\fM��+qUP-W�MyW�K+M MOp-MOqUWQTQ\]V+NHW�K�^_WK�^#�CM2^cpFT�M#^cX Z Y MOMUV9M��+qOPFW�MOX YBZ ^jl+T�MU�{PR\]t+NEl�K+\cW�\]V.�eI nwMOb W�\]NQMUqO\]V+X � � ��� ! N ��PRN/^_l+l+T�\�� 0P-b9^_W�MOp Z W�K+M pRP-nwMUW�PRb M \]nE�{P-TQW�t�^cpeN}Wg^_W�MON Y MUq#^ct+NQMsWQK+Msp-PRnwMUW�P-bfM PRNkP-V �CMUTQNQMOp Z l+T�\cl \cTQW�P-\]V�^cpW�\�W�K+M n TQMOz{t+MOV+q Z ��K+PRqgK PRNjKBt+V+XuTQMOX+N \]n�J!MUT�^cK+MUTQW�h#� IaNjp-\]V+v�^cNjMUV+\]t+v]K l�K+\cW�\]V+N q#^cV^_TQTQP-�CMLW�\jT�M � M��+qOPFW�MLW�K+MHMOp-MOqUWQTQ\]V+N/PRVsW�K+M x+TQN�W/�{P-TQW�t�^cp�N�W�^_W�M � �HPFW�K+PRVsnwMOb W�\]NQMOqO\]V+X+N ��W�K+MOVW�K+\]N�MjMOp-MOqUWQTQ\]V+N ��PRp-p Y MyM��+qOPFW�MOX�tul`PRVCW�\ W�K+MkT�M#^cp � bfM:Wg^cN�Wg^ Y p-M ��N�Wg^_W�MaW�K�^_W qO\cTQTQMON�l@\]V+X+NW�\2WQK+ML^ Y NQ\cTQl+W�P-\]V Y ^cV+X ^_WeW �HP-qOM�W�K+M�l�t+b l n T�MUz{t+MOV+q Z �eILWeW�K+P-N"l@\]PRVCWePFW�NQK+\]t+pRX Y MLM#^cN Z �Y MOq#^ct+NQM \]nW�K+MLM��{W�MOV+X+MOX pRPRnwM:W�PRbfM_�cW�\y^cvC^cPRV M��+qOPFW�M�W�K+MLMOpRMUqUWQT�\]V+NEPRVCW�\kW�K+M�K+P-v]K+MON�WEN�Wg^_WQM#�JLK+PRN�N�Wg^_W�MjNQK+\]t+pRX�K�^#�CM ^ NQK+\cT�W2MOV+\]t+v]K�p-PRnwMUW�P-bfMyNQ\ W�K�^_WHP-W2N�K+\]t+pRX`Tg^cX+PR^_W�M X+\��HV �L^_T�X^_W W�K+MkW�K+P-T�X�K�^_T�bf\]V+PRq Y MOnw\cT�M PFWHqO^cV Y MyM��+qUP-W�MOX`^cvC^cPRV.�

JLK+M�P-b l@\cT�Wg^cV W lm^_Tg^cbfM:W�MUT�N PRVC�C\]p-�CMOX PRV W�K+P-N V+M�� ^cV�^cp Z NQP-N qgK+MOq � ��P-W�K�W�K+\]NQMP-V5\]tuT1l+T�MU�{PR\]t+N ^_l+l+T�\��+P-b9^_W�M qO^cpRqOt+pR^_W�PR\]V+N1nw\cT W�K+P-T�XDK�^_T�b \]V+PRq#� � V W�K+PRN V+\]V+qOpR^cNQNQP-q#^cp^cV�^cp Z NQP-N�P-njW�K+M x Y MUT�PRN l�t+b l@MOX K�^_T�X+MUT#�aW�K+MUTQM ��PRpRp Y M�bf\cTQM l�K+\cW�\]V+N�^��_^cPRpR^ Y pRM�W�\M��uqOP-WQM W�K+M MOpRMUqUWQT�\]V+N�� �}njW�K+M�X+\clm^cVCW`qO\]V+qUMOV W�Tg^_W�PR\]V P-N�P-V+qUT�M#^cN�MOX PRV WQK+M x Y M:T�W�K+MOVW�K+M:T�M-��\]t+p-X Y M�bf\cT�M l@\cW�MOVCW�PR^cp MUpRMOqUW�T�\]V+N W�\ Y M�M��+qOPFW�MOX Y Z WQK+M`PRV+qO\]b PRV+v8l�K+\cW�\]V+N��IaV PRV+qUT�MO^cNQM P-V�qO\]V+qOMUV WQT�^_W�PR\]V N�K+\]t+pRX3�}t+N�W PRV+qUTQM#^cNQM W�K+Ms^ Y NQ\cTQl+WQPR\]V�l M#^ � Nj^cqUT�\]NQNyW�K+MN�l MOqUWQTQt+b � V+\fNQK+P-n W ����J K t+N2W�K+M1V+M�� l�P-qUW�tuT�M1qU\]b l�pRP-bfMOVCW�N�W�K+Mjl�PRqUW�tuTQM W�K�^_W2NQ^ Z NHW�K�^_WW�K+M W�K+PFT�X�K�^_T�b \]V+PRq5��PRpRpeX+M:l@MOV+X tul \]V W�K+M PRVCW�MOV+N�P-W Z \]n4W�K+M nwt+V+X�^cbfMOVCWg^cpex�MOpRX�^cV+X ^qO\]b Y P-V�^_W�PR\]Vs\]n W�K+MHbf^_W�MUT�PR^cpRN�qO\]V+qOMOVCWQTg^_WQPR\]V � WQKBt+N�^ Y N�\cTQl+W�PR\]Vsl@M#^ � N �E^cV+X PRVul�tuW�x�MOp-X>���K+PRqgK`qO\cT�T�MON�l \]V+X�W�\ U?W X[Z �

T � A � ��Q"* ���� � �'* �F9 �

Ian WQMUT1W�K+Msnw\cT�b t+p ^cN1K�^cX Y MOMOV5X+MUT�PF�CMOXDn T�\]b W�K+MO\cT Z ^cV+X W�K+M Y ^cNQP-qfN Z N}W�MOb T�M�0zBt+P-T�MOb MOV WQNaK�^cX Y MOMOV bfMUW#�mW�K+M \]V+p Z \ Y N�Wg^cqOp-M1W�K�^_W2T�MObf^cPRV+MOX)�L^cN2W�K+M l+T�M:lm^_Tg^_W�PR\]V8\]nW�K+M p ^ Y M��{l@MUT�P-bfMOVCW�� �aNQPRV+v Y ^cN�PRqf\cl+W�P-qONO�e^`N�PRb l�p-M \cl+W�P-q#^cp4N Z N�W�MUb �L^cN1X+MUNQPRv]V+MOX�nw\cTW�K+M p ^ Y Wg^ Y p-MsW�\�bfMOMUW N Z N�WQMOb N}l@MOqOPFx�q#^_W�P-\]V+N ^cV+X W�\�^cqOqO\]bsl�pRPRN�K�W�K+M bf^cPRV \ Y �}MOqUWQP-�CM

�W�\sb M#^cNQtuT�MyW�K+MyWQK+P-T�X`\cTQX+MUTHN�t+NQqOMUl+W�P Y PRp-P-W Z \]n�W�K+Mjx Y MUT��

ikMON�PRv]V \]n/WQK+M \cl+W�P-q#^cp Y MOV+qgKDN Z N}W�MOb nw\{qOt+NQN�MOX5\]V�W ��\�^_T�MO^cN�( � �aqO\]tul�pRP-V+v`W�K+MpR^cNQMUT Y M#^cb&PRVCW�\ WQK+M2x Y MUTLN�^cbsl�pRM2^cV+X � �4N�MUlm^_Tg^_W�P-V+v1W�K+Manwt+V+X�^cbfMOVCWg^cp n TQMOz{t+MOV+q Z n T�\]bW�K+MyK+PRv]K+M:T2K�^_T�bf\]V+P-qON��

� "

Page 81: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� � � � ���� � � � � � ����� ��� � � � � � ��� �� �

� V�\cT�X+MUT�W�\ qUTQM#^_W�My^ pR^_T�v]M ��t9� X+MOV+N�P-W Z PRV+NQP-X+MaW�K+Max Y MUT qO\cT�M_�+M � qOP-MOVCWHqO\]tul�p-PRV+v\]n/WQK+Mfp ^cNQM:T bf\{X+M PRVCW�\�WQK+M x Y MUT1PRN MUNQNQMOVCW�P ^cp � *H\]t+v]K Tg^cX+P-\]bfMUWQT�P-qsqO^cpRqOt+pR^_W�PR\]V+N���MUT�MX+\]V+M W�\ NQK+\�� PRn�W�K+M N Z N�WQMOb ��\]t+pRX�^cqOqO\]b l�p-PRNQK�W�K+P-NaWg^cN � � J K+M� Y 0 oETkW�MON�Wkx Y M:TjK�^cXW�K+M1WQ\]t+v]K+MON�WyN�l@MUqOP-x�q#^_WQPR\]V+NaW�\9bfMOM:W��kJ K+M W�KuTQ\]t+v]Kul�tuWj\]neW�K+P-N2x Y MUT � t+N�PRV+v9W�K+M 2 ��qO\cTQM � ��^cNHq#^cp-qOt+p ^_W�MUX

� � #��K+MUT�M �P-N W�K+M ^cqOqOMUl+W�^cV+qOM ^cV+v]pRMy\]n�WQK+Mjx Y M:T�(

� � � � ! � � � � � � � ! � � �]� � � � � �]� � � � �� � �� �]� � � � �]� � �R��0G- � �� � � #

- � � � + � � � � ! ! � #

� � I- �,+&3 � � � � !�# � # � � � �� \cT ^5qO\]pRp-PRb9^_WQMOX p ^cNQM:T Y M#^cb`� ^5pRMUV+N&�HPFW�K W�K+M�qO\cTQT�MUqUW�VBt+bfM:T�PRq#^cpH^_l@MUT�W�tuT�M8q#^cV Y MqgK+\]NQMOV W�\1nw\BqOt+N�W�K+M Y M#^cb P-V W�\1WQK+M2W�MON�W�x Y MUT / N�qO\cT�M/��P-W�K+P-VfW�K+Mk^cqOqOM:l+Wg^cV+qOMk^cV+v]pRM�� � \cT^ NQPRV+v]p-Mjbf\BX+MjpR^cNQMUT W�K+M Y M#^cbdN�l@\cWHNQPRhUM���K+MOV`nw\BqOt+NQNQMOX8NQK+\]t+p-X Y MyX+P Tg^cqUW�P-\]V�p-PRbfPFW�MOX^cV+X`PFW�N�^_T�M#^ 0 N�\]pRPRX�^cV+v]pRMkl+T�\{X+t+q:W2NQK+\]t+p-X Y Mj^_l+l+T�\��+PRbf^_W�MOp Z

� � � � # ���,3G- � � � � !�# � # � � � �JLK+M5^_T�M#^ 0 NQ\]pRP-X ^cV+v]pRM l+T�\{X+t+q:W�\]n W�K+M pR^cNQMUT�PRN`qO\]bslm^_Tg^ Y pRM8W�\ W�K+M ^_T�M#^ 0 N�\]pRPRX ^cV+v]pRMl+T�\BX+t+qUW2\]n�W�K+Mjx Y MUT��

JLK+M � t�^cVCWQT�\]V+P ��p ^cNQMUT�K�^cN�^ �j^ct+NQNQPR^cV Y M#^cb \]tuWQl�tuW�� J K+P-N�P-N9W�K+M � � � # #bf\BX+M#��JLK+PRN WQTg^cV+N}�CMUT�NQM9bf\BX+M9K�^cN \]V+p Z \]V+M TQ\]t+V+X N�l \cW ^cV+XDPRN1W�K+M9M#^cN�PRMON�W W�\2��\cT ���P-W�K.���y^ct+NQNQP ^cV Y M#^cb MUz{t�^_W�P-\]V+NHq#^cV`l+T�MUX+PRqUWaW�K+Mjl+T�\clm^cvC^_W�PR\]V�n T�\]b W�K+M Y M#^cb �L^cPRN}W��� \cTkW�K+PRNkp ^cN�MUT#��W�K+M Y M#^cb �L^cP-N�W#��^cqOqO\cT�X+P-V+v�W�\ W�K+M b9^cV t+n ^cqUW�tuT�MUTO� �L^cNkp-\{q#^_W�MUX ^_WkW�K+Mn T�\]VCW/^_l@MUTQWQtuT�ML\]nW�K+MLp ^cN�MUT4^cV+X K�^cXf^kX+P ^cb MUW�MUT�\]n � � � � �d^cV+Xs^knwt+pRp�X+P-�CMUTQv]MOV+qOM�^cV+v]pRM\]n � � � � � � � � � \cT WQK+MONQMjW ��\sx�v]tuT�MON�WQK+M*2^ Z p-MOPRv]K Tg^cV+v]M���\]t+pRX Y M � � � � 2 ��

I [ MUP-W�hybfPRq:T�\]NQqO\cl Mj\ Y �}MOqUWQP-�CMypRMOV+N �L^cNHt+NQMUX�W�\ nw\BqOt+N�WQK+M Y MO^cb P-V WQ\ W�K+Mkx Y MUTqO\cTQM#�EJ K+Map-MOV+N�K�^cNL^ VBt+bfM:T�PRq#^cp ^_l@MUT�W�tuT�Ma\]n � �.- �1^cV+X�^1l@\���MUTL\]n � � � � � T�\]b WQK+MapRMOV+Nl \���M:T1�c^cp-t+MfP-W PRN � V+\���V W�K�^_WjW�K+Mfnw\{qO^cp/pRMUV+vcW�K5PRN� � � �eNQ\`W�K+Mfp-MOV+N1b t+N�W K�^#�CM9^cV^_l MUTQW�tuT�Mj\]n"^ Y \]tuW + � � � � �/J K+MyN�l@\cWHNQPRhUMjnw\cT2^snw\{qUt+NQNQMOX�y^ct+NQNQP ^cV Y M#^cbdPRN

��� ��� � 3 � � �� �

Page 82: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� \cT ^`N�l \cW NQP-hOMf\]nL^ Y \]tuW 2 �� �"WQ\`b9^_W�qgK�W�K+Msx Y MUT qO\cTQMc�!W�K+M Y M#^cb X+PR^cbfMUW�M:T1b t+N�WY M ^ Y \]tuW � � � + � � ^_W2W�K+M p-MOV+N��HJ K+P-N2X+\{MONaV+\cWHx�pRp�W�K+M MOVCW�P-T�M p-MOV+N2NQ\fWQK+M � I �HP-pRp Y Mp-MONQN�W�K�^cV � �.- � �eikP-�{PRX+P-V+v WQK+Manw\{q#^cp@p-MOV+vcW�K�PRVCW�\ W�K+M Y MO^cb X+P ^cbfMUWQMUTL^_W�W�K+Map-MOV+NLv]P-�CMONL^V t+bfMUT�P-q#^cp�^_l@MUT�W�tuT�M N�pRPRv]KCW�p Z p ^_T�v]MUT W�K�^cV�W�K+Mjx Y MUT / N��

I Y M#^cb M��{lm^cV+X+MUT&�L^cN t+NQMOX WQ\�M��{lm^cV+X W�K+M Y M#^cb X+P ^cbfM:W�MUTsn T�\]b W�K+M-�L^cP-N�WW�\ W�K+M�V+MOqOMON�N�^_T Z NQP-hOM8^_W WQK+M�bfPRqUTQ\]NQqO\cl@M�\ Y �}MOqUW�PF�CM#� JLK+M�^cqUW�t�^cp Y M#^cb lm^_Tg^cbfMUWQMUT�N��M:T�M1NQp-PRv]KCW�p Z X+P MUT�MOVCWan T�\]b W�K+\]NQM1N�l MOqOPFx�MOX>��^cN��L^cN�W�K+M ^cqUW�t�^cp�pR\Bq#^_W�P-\]V`\]n"W�K+M Y M#^cb�L^cP-N�W�� ILWQW�MObsl+W�NaW�\�qO^cpRqOt+pR^_W�M W�K+M Y M#^cb �L^cPRN}W���P-WQK ^ � V+PRnwM MOX+v]M l+T�\ �CMUX�X+P � qOt+p-WjNQ\W�K+M Y M#^cb�M��{lm^cV+X+MUT%��^cN�^cX �}t+N�W�MOX ^cNEV+MUqOMONQN�^_T Z � [ \]NQN�MONEWQKuT�\]t+v]K WQK+M�pRMOV+NQMUN'��M:T�M ^ Y \]tuW��0 l@MUT�qUMOV W����2l+W�PRb9^cp>qU\]tul�pRPRV+vsPRN W Z l�PRq#^cp-p Z ^_TQ\]t+V+X 0 � l MUT�qOMOVCW��

� � � � � � � ��� � � � � � � � � � ��� � � �

�aVCW�P-p@W�K+MjpR^cNQMUT Y M#^cb��L^cN nw\{qUt+NQNQMOX`P-V WQ\sW�K+Mkx Y MUT�MU�CMUT Z ^_W�W�MOb l+W �L^cN b9^cX+MaW�\b9^ �uPRbfP-hOM�WQKuT�\]t+v]Kul�tuW����5MkM��ul MOqUW�MOX�W�K+Mk\]tuWQl�tuW Y M#^cb n TQ\]b W�K+Max Y MUT W�\ qO\]VCWg^cPRV�V+\cW\]V+p Z W�K+M2l�t+b l n TQMOz{t+MOV+q Z9Y tuW ^cpRNQ\1W�K+MaN�MOqO\]V+X�^cV+X WQK+P-T�X9K�^_T�b \]V+PRqON�\]n>W�K+M2l�t+bsl �EILWW�K+P-N�l@\]P-V WLW�K+Man T�MUz{t+MOV+qOP-MONHb t+N�W Y MaNQMUlm^_Tg^_WQMOX.�/ikt+MaW�\ W�K+MaNQb9^cp-p�_^cpRt+MONLnw\cT V+\]V+pRP-V+M#^_TNQt+N�qOMUl+W�P Y PRpRPFW�PRMUNO�{W�K+MaX+MON�P-T�MOX�NQP-v]V�^cp b9^ ZsY Ma\ �CM:T�V+PRV+Ma\cT�X+M:T�N�\]n�b9^cv]V+P-W�t+X+MHpR\���MUT�W�K�^cVW�K+M l�t+b l Y MO^cb2�yJ!\ NQMUlm^_Tg^_W�M W�K+M n T�MUz{t+MOV+qOP-MONjWQK+M Y M#^cb b t+N�W Y M lm^cNQN�MOX W�KuTQ\]t+v]K�^vcTg^_WQPRV+v��1I l+T�PRN�b ��^cNjV+\cWjqgK+\]NQMOV Y MOq#^ct+NQMs\]n4N�lm^cqUM pRP-bfP-W�^_W�PR\]V+Na^cV+X pR\�� X+PRN}l@MUT�N�PR\]V.�JLK+MLvcTg^_W�PRV+vab t+N�W�V+\cW Y M�X+MON�WQT�\ Z MOX YBZ WQK+MLl�t+bsl Y M#^cb2��� M t+N�MOXf^cV ,/0�� �abf\]V+\BqgKuT�\�0b9^_WQ\cTkn T�\]b � V+N�WQT�t+bfMUV W�N ~{I � � V+q#� W�K�^_Wyt+NQMONj^ Y pR^chOMOX qO\]V+q#^#�CM K+\]pR\]vcT�^_l�K+PRq vcTg^_W�P-V+v��JLK+Mk^_l@MUT�W�tuT�MaK�^cNL^cV n � � \]n"+ �101^cV+X�^ nw\{q#^cppRMOV+vcWQK�\]n�� � � � � �4JLK+PRN�bfM#^cV+N4W�K�^_W�W�K+M^_l MUTQW�tuT�M9\]n�WQK+MfvcTg^_W�P-V+v�PRN1\]V+p Z5� � �.2 � ��`JLK+M9z{t+\cW�MUX W�KuT�MONQK+\]p-XDnw\cT p ^cNQMUT1X�^cb9^cv]M�L^cN 0 �"��^_WQW�NLl@MUTHNQz{t�^_T�MyqOMOVCW�P-bfMUW�MUT��

� Vj\cT�X+MUT�W�\ l+TQ\cW�MOqUW�W�K+MEvcTg^_W�PRV+v+��W�K+M�l�t+b l1b t+N�W Y MEx�pFW�MUT�MOX \]tuW��!I b t+pFW�PRpR^ Z M:T�MOXX+P-MOpRMOq:WQT�PRq2x�p-b K�^cN�W�\{\ p-\�� ^1l@\���MUT q#^_lm^ Y PRp-P-W Z ^cV+X ��\]t+p-X�^cp-NQ\ Y pR\{q � K�^_T�bf\]V+PRqUN��EJ K+MP-X+M#^cp@x�p-W�M:T�P-NH^ K+PRv]K l@\���MUT�X+PRqgKuT�\]P-qyx�pFW�MUT�\cT�^ K�^_T�b \]V+PRq Y M#^cb N�l�pRPFWQW�MUTLb9^cX+Mknw\cT�K+PRv]Kl \���M:TjpR^cNQMUTy\cl+W�P-qON��yJ K+M qO\C^_WQPRV+v qgK+\]PRqOM b t+N�Wy^cpRp-\�� nw\cTy^�K+P-v]K8W�Tg^cV+NQbfPFWQWg^cV+qOM \]n�W�K+MK+P-v]K+MUT K�^_T�bf\]V+P-qON Y MOq#^ct+NQMfW�K+MUP-T l@\���MUT1PRN1NQ\�p-\��j�e^cN��MOpRp/^cN1nw\cT K+PRv]K T�M ��MOqUWg^cV+qOM \]nW�K+M�l�t+b l�n T�MOz{t+MUV+q Z � ,aM#^_WL^ Y NQ\cT Y P-V+v x�p-W�MUTQN6�HP-pRp^cpRNQ\5��\cT � ��P-W�K9p-\���MUT�l�t+b l9l \���M:T�N��

[ ^cNQMUTjX�^cb9^cv]M W�\�W�K+M x Y MUT1n TQ\]b WQK+Msl�t+b l Y M#^cb PRNj^ N�l@MOqUP-x�q#^_W�P-\]V�W�K�^_W��L^cN^cp-NQ\aWg^ � MOV PRVCW�\y^cqOqO\]t+VCWEPRV W�K+M�X+MONQP-v]V.�EJ ��\al+T�\BqOMONQN�MON Y Z ��K+PRqgK p ^cNQMUT�P-V+X+t+qOMOXsX�^cb9^cv]Mq#^cVD\BqOqOtuTs^_T�M9NQP-b l�pRMfK+MO^_W�PRV+v Y Z ^ Y NQ\cTQl+W�P-\]V�^cV+X�MUpRMOqUW�T�\]V ^#�_^cp ^cV+qgK+M#�8JLK+M�K+MO^_W�PRV+vl+T�\BqOMONQNkb9^ Z qO^ct+NQM l+TQ\ Y pRMObfNaP-neW�K+M W�P-l�Na\]n�W�K+M x Y MUTj^_T�M V+\cWa�CM:T Z qOp-M#^cV.��� V n ^cqUWkW�K+M

� �

Page 83: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

x+T�N}W"PRV+qgK \]nuW�K+MEx Y MUT�/ N"\]tuW�M:TeqO\C^_W�P-V+vHPRN�N�WQT�PFl+l@MOX N�\aP-W �HP-pRpCV+\cW Y tuT�V tul X+t+M�WQ\HpR\Bq#^cpRP-hOMOXK+M#^_WQPRV+v�� J K+MsMOpRMUqUWQT�\]V�^��_^cp ^cV+qgK+M P-NyWQK+M bf\]N�WkP-b l@\cT�Wg^cV WyX�^cb9^cv]M l+T�\BqOMONQN�� � \cTy�CM:T ZK+P-v]K8l�K+\cWQ\]V ��t9�uMONkPR\]V+P-h#^_W�PR\]V�qO^cV \BqOqOtuTyX+tuT�P-V+v WQK+M1W ��\ l�K+\cWQ\]V�^ Y NQ\cT�l+W�PR\]V�l+T�\BqOMONQN^cV+X W�K+PRN�q#^cV Y T�PRV+vy\]V W�K+MLMOpRMOq:WQT�\]Vf^#�_^cp ^cV+qgK+M#��JLK+PRN�X�^cb9^cv]M�l+T�\BqOMONQNEPRVCWQT�\BX+t+qOMON/N�K+\{q ��L^#�CMONH^cV+X�M��{l�pR\]NQPF�CMy�_^_l@\cT�P-h#^_W�P-\]V�PRVCW�\ W�K+Mjbf^_W�MUT�PR^cp �

I NQqgK+MOb9^_W�P-qH\]n@W�K+M�qO\]b l�pRM:W�MHN Z N�W�MOb X+MONQP-v]V9PRN/N�K+\���V PRV x�v]tuT�M �]� ��J!\ W�MON}W�W�K+MK Z l \cW�K+MONQP-N W�K�^_W qO\]V+qUMOV W�Tg^_W�PR\]V�NQK+\]t+pRX�X+MUW�MUT�b PRV+MVU W X[Z�l�pR^cV+N ��MUT�Myb9^cX+MaW�\sW�MUN�WLW�KuT�MOMx Y MUT�N��@W�K+M K+P-v]K8qO\]V+qOMOVCWQTg^_W�P-\]V2 Y 0 o4Tax Y MUT#� WQK+M pR\���MUTkqO\]V+qOMUV WQT�^_W�PR\]V8o4Tax Y MUT#�>^cV+X ^N�W�^cV+X�^_T�X�W�MOp-MOqO\]bfb t+V+P-q#^_W�PR\]V+N�x Y MUT��

����������� � ������������� � ��� � � � �� � � � � ���

� �

Page 84: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

T �YT � ��Q"* ���� �#�'��* �P��� � �P� Q

IaN�lm^_TQW/\]n W�K+M�TQMONQM#^_T�qgKfl+T�\BqOMONQN/P-W'�L^cN/V+MOqUMONQN�^_T Z W�\ X+M:W�MUT�bfP-V+M ��K�^_W/WQK+MHNQMOV+N�P 0W�PF�uPFW Z \]nuW�K+M�b M#^cNQtuT�MOb MOV W"N Z N�WQMOb ��\]t+p-X Y M#��JLK+PRN�lm^_Tg^cbfMUW�M:T ��\]t+p-Xs^cp-pR\��Dl+T�MOX+PRq:W�PR\]V+NW�\ Y M2b9^cX+M2^ Y \]tuW/WQK+M2b9^cv]V+P-WQt+X+M2\]n@W�K+MHW�K+PFT�X9\cT�X+MUT�NQt+NQqOMUl+WQP Y PRp-P-W Z nw\cT/W�K+MHx Y M:T�N�W�K�^_W��\]t+p-X Y M�M���^cbfP-V+MOX.�eJ!\yX+MUW�MUTQbfPRV+M�W�K+M NQMOV+NQPFW�P-�{P-W Z \]n�W�K+M bfM#^cNQtuT�MUbfMOVCW4N Z N�W�MUb X+MONQPRv]VPFW/b t+N�W Y Ma^cN � MOX �}��K�^_W�PRN�W�K+M2b PRV+PRb t+b U W X[Z �c^cp-t+MHV+MOMUX+MOX>�unw\cT�^jv]P-�CMOVsPRVul�tuW�l \���M:T#�W�\ � NQMOM�/+W�K+MaW�K+PFT�X�K�^_TQbf\]V+PRq � � JLK+MyvcT�M#^_W�MON}W l M#^ � l�t+pRN�Myl \���M:TH^#�_^cPRp ^ Y p-Mkn T�\]b&W�K+M � �N ��P-WQq6K+MUX p ^cNQM:T1N Z N�W�MOb q#^cV Y M q#^cp-qOt+p ^_WQMOX.� �aNQP-V+v�W�K+MsX+MUT�PF�CMOX nw\cT�b t+p ^ �HK+P-qgK�T�MOpR^_W�MON� � � �:��U?W X[Z��e^cV+X � � + � �:��W�K+MfbfP-V+PRb t+b bfM#^cNQtuT�^ Y pRM U?W X[Z2q#^cV Y Mfnw\]t+V+X Y Z t+N�PRV+v�W�K+M� V+\���V bfP-V+PRb t+b �c^cp-t+Msnw\cT � � + � ���sJLK+M bfP-V+PRb t+b �c^cp-t+M nw\cTjW�K+P-T�X�K�^_T�bf\]V+PRq P-N �}t+N�WW�K+M � �{PRNQP Y PRp-P-W Z p-PRbfPFW /{\]n�W�K+MyM Z Mjnw\cTLW�K�^_W �L^#�CMOp-MOV+vcW�K.�4J K+P-N�N Z N�W�MOb / N�l+T�PRbf^_T Z X+MUWQMOqUW�\cT��\]t+p-X Y MjW�K+MjKBt+b9^cV�M Z M#�

T �FS � � �ON8�&��NF�)��������� � ����� � � � ��

� V5W�K+M M��{l@MUT�P-bfMOVCW W�K+M9l@\���MUT \]nLW�K+M p ^cNQM:T PRN ^cV�PRb l \cTQWg^cVCW1T�MOzBt+P-T�MOb MOV W���� V\cT�X+M:THW�\ l+T�\{X+t+qUM ^spR^_T�v]Mal@\cl�t+p ^_WQPR\]V�P-V�W�K+MyK+PRv]K+MUTHMOV+MUT�v Z p-MU�CMOpRN PRV�W�K+M ^_WQ\]bfNL\]n!W�K+MX+\cl MOX9x Y MUT#�uWQK+MUT�Mab t+N�W Y M2b9^cV Z l�K+\cW�\]V+NL^#�c^cP-p ^ Y p-M#�"� PFW�K�^ � � N �HPFW�qgK+MUT PRVfW�K+MapR^cNQMUTq#^#�uPFW Z P-W�PRNLT�MOz{t+PFT�MOX�WQ\ q#^cp-qOt+p ^_W�MkW�K+Mkl@M#^ � l \���M:THl@M:THl�t+pRN�M#�

����������� � � � � ���� � � � ��� � �� � � ���� � ��� � � �

� P-v]tuT�M � +fNQK+\��HNaW�K+M N�MUW�tul W�\ X+MUW�MUT�b PRV+M1W�K+M1l M#^ � l \���M:T��+�}V�W�K+M qO^cpRqOt+pR^_W�PR\]VW�K+M � � N ��P-WQq6K+M:T PRN1NQM:W1W�\8^�qOM:TQWg^cPRV5l�t+p-NQM T�MUl MUW�PFW�PR\]V5n T�MUz{t+MOV+q Z � S6* � ���!JLK+M ^#�CMUTg^cv]M

� �

Page 85: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

l \���M:T2PRN�bfM#^cNQtuTQMOX ��P-W�K�^ l@\���MUTHbfMUW�M:T2^_W W�K+M n TQ\]V W2^_l@MUTQWQtuT�M#��IaV�^_WQW�MOV t�^_W�MOX Y M#^cbn T�\]b W�K+M Y ^cq � ^_l@MUTQWQtuT�M�PRN�NQMOVCW�PRVCW�\a^�l�K+\cW�\BX+PR\BX+M#� � MOnw\cT�M�MUV W�M:T�PRV+vaW�K+M�^_l MUTQW�tuTQM�\]nuW�K+Ml�K+\cW�\BX+PR\BX+M WQK+M Y M#^cb PRNanwtuT�W�K+MUT ^_WQW�MOV t�^_W�MOX YBZ t+NQP-V+v�V+MUtuWQTg^cpeX+MOV+NQPFW Z x�p-W�MUTQN��1JLK+MONQMx�pFW�MUT�N�l+T�\cW�MUqUWLW�K+Myl�K+\cWQ\{X+PR\BX+Mkn T�\]b Y MOP-V+vsNQ^_W�tuTg^_W�MOX Y Z W�K+M Y M#^cb ^cV+X W�KBt+N � MOMUl�W�K+MbfMO^cNQtuT�MObfMUV W4PRV WQK+M�X+P-\{X+M�/ N/pRP-V+M#^_T � qO\cTQT�MUqUW ��TQMOv]PR\]V.��JLK+M�l�K+\cW�\BX+PR\BX+M�/ N4\]tuWQl�tuW�P-N4NQMUV WP-V W�\ ^cV�\]NQqUPRpRp-\]NQqO\cl M���K+MUT�M WQK+Myl�t+p-NQM NQK�^_l M q#^cV Y M M���^cbfP-V+MOX.�

JLK+M NQqO\cl Mst+NQMUX�L^cNy^cX+MOzBt�^_W�M � ^ bfPRqUTQ\{qgK�^cV+V+MOp!l�pR^_W�M NQqO\cl@M���\]t+p-X K�^#�CM l+T�\�0X+t+qOMUX�^sNQK�^_T�l@MUTHPRb9^cv]M �4WQ\ pR\B\ � ^_W W�K+Myl�t+p-NQM N�K�^_l@M#�4IapRp@W�K+M � � N �HPFW�qgK+MOX � \cT � v]PR^cV W / �l�t+p-NQMONLbfM#^cNQtuTQMOX3��MUT�My^ Y \]tuW�W�K+MaNQ^cbfM �HP-XuW�K.�EJ K+M Z ��MUT�My^cpRb \]N�W �y^ct+NQNQP ^cV�PRV NQK�^_l Mc���P-W�K8W�K+MsM��+qOM:l+W�PR\]V \]n/NQp-PRv]KCW�p Z p-\]V+v]MUTjW�^cPRpRNk\]V W�K+MsX+\���V+NQPRX+M#�sJLK+M � t+pRp"��PRXuW�K>� ,k^cpRn| ^ � � � � , | ��bfMO^cNQtuT�M nw\cT4W�K+MLl�t+pRN�M��HP-XuW�K7�L^cNEt+NQMOX.��Iap-pul�t+pRNQMON'��MUT�MH^_l+l+T�\��+PRbf^_W�MOp Z2 � � V�^cV+\]NQMOqO\]V+X+N��

D ��> NF�6�

� � � � � � � � � � �

� 0 ~ �HPFW�qgK�S6* � I2�CMUTg^cv]MkSe\���MUT ~{qO\cl@MjSeMUT�P-\{X ��������

� � � � �� ��,ah � � � � � @N � � V+N � � � �2 � � � �.- �2 � 2 � � +&3�+ �.+09�,2 � �,+ ��� � 2 � � +]� �-�� � � �R��0 � - � 2 � � -&2 �+ � � � �R� � + � � 2 � � 0#� 2� � � � � �&0 - � � 2 � � 3�2 �� � � � � � � � 2 � 2 � � � � � �� �10 � �13 0 ��� � � 2 � � �]� 0 �� �,+ � �13 � + + � � 2 � � + � �]�� �R� � �13 � � �sb N 2 � � �]�2 2&3

J�\sq#^cp-qOt+p ^_WQMjW�K+Mkl@M#^ � l \���M:T#�

� � � � � � � � � � � � ������� � � � � � � � ! � � � � � � �� � � � � � � � � � ������� ��

� �

Page 86: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��K+MUT�M � PRNLW�K+Mjl MUT�PR\BX�\]n!WQK+M��L^#�CMOnw\cT�b \cT �� ��� �JLK t+NO� � � � � � � � �� �

�������� � � ��� � �

o ��^cb l�p-MON ^_T�MjN�K+\���V.�

JLK+M�pR\���MON}W�S%* � NQMUW�W�PRV+v�^#�c^cP-p ^ Y pRM�\]V WQK+M � � N ��P-WQq6K+M:T�P-N�� � � ,ah#� � \cT9WQK+PRNl�t+p-NQM�Tg^_W�M ^cV+Xsnw\cT�W�K+M=2 � �cV+N"l�t+p-NQM���PRXuW�K ^cV+X W�K+M 3 � �cb � ^#�CMUTg^cv]M�l@\���MUT#�Cq#^cp-qOt+p ^_WQPR\]V+NX+MUWQMUT�bfP-V+M WQK+M bf^ �+PRb t+b l@M#^ � l \���M:TjW�\ Y M��]���.2 2&3 � � � � WyP-Nkl \]NQNQP Y pRM W�\�M��uW�M:T�V�^cpRp ZWQTQPRv]v]MUTEW�K+M � � N ��P-W�qgK+MUT/W�\1pR\���MUT/S6* � N Y tuW�W�K+M�b9^ �+P-b t+b l@\���MUTL^#�_^cPRp ^ Y p-M�N�K+\]t+pRX9V+\cWY M b t+qgK�K+P-v]K+MUT��2I bf\BX+M p-\{q � MOX8p ^cNQM:T ��\]t+pRX Y M W�K+M V+M��{W2l+Tg^cqUW�P-q#^cp!N}W�MUl8W�\9PRV+q:T�M#^cNQMW�K+Mkl@MO^ � l�t+p-NQM l \���M:T��

IaN ^5NQP-X+M�V+\cW�Mc� P-W �L^cN9nw\]t+V+X W�K�^_W9W�K+M � � N ��P-W�qgK+MUT�K�^cX�^5b9^ �+P-b t+b S4t+pRNQM*�MUl@MUWQP-W�P-\]V � TQMOz{t+MOV+q Z � S%* � �e\]n�3 �10 � ,ah#�eIaV Z S6* � X+P ^cp-MOXfPRV ^ Y \��CM�W�K+P-N4�_^cpRt+M ��\]t+pRX\]V+p Z l+T�\{X+t+qUM l�t+pRN�MON�^_W W�K+P-N�^_l+lm^_T�MOVCW�b9^ �uPRb t+b TQMUl@MUWQP-W�P-\]V*Tg^_WQM#� JLKBt+N�^cpRp Y M#^cb^cp-PRv]V+bfMOVCWyX+\]V+M ^_WyW�K+M K+PRv]K S6* � \]n%��K�^_W ��^cNyW�K+\]t+v]KCWyW�\ Y M���0 � ,ah � ^�K+PRv]K�S%* �p-M#^cX+N1W�\�^�pR\���MUT l@M#^ � l@\���MUT � �L^cN ^cq:W�t�^cpRp Z X+\]V+M ^_W 3 �,0 � ,ah���IavC^cPRV>�!V+\cW�MfW�K�^_W ^cp-p^cp-PRv]V+bfMOVCW1K�^cX5W�\ Y M9X+\]V+M&�HPFW�K W�K+M � � N ��P-W�qgK+MUT \]V Y MUq#^ct+NQM P-W P-N ^cVD^cqO\]t+N�W�\ � \cl+WQPRqN ��P-WQq6K+M:T�^cV+X W�K t+N �HP-pRpHN}W�MOMUT W�K+M Y MO^cb W�\D^cV ^cV+v]p-M2�HK+MUV*W�tuTQV+MOX \]V.� IapRN�\�V+\cWQMc�W�K+Msn T�MOzBt+MOV+q Z \]n4W�K+M � � N ��P-W�qgK+MUT P-N V+\cWyW�K+M n TQMOz{t+MOV+q Z \]n/W�K+M ^cqO\]t+N�W�P-q1�L^#�CM � �HK+P-q6KX+MUWQMUT�bfP-V+MON Y M#^cb&^cV+v]pRM � Y tuWLP-V+N�W�M#^cX9W�K+Man T�MUz{t+MOV+q Z ^_W ��K+PRqgK9l�t+pRN�MON ^_T�M2l+T�\{X+t+qUMOX Y Zt+NQP-V+v W�K+M � � N �HPFW�qgK+MUT��

T � � � D�����@���M�O �E�����8� ����� � ��@* �F� �

SeM:TQW�tuT Y ^_W�P-\]V W�K+MO\cT Z �L^cN�t+NQMOX P-V1qgK�^_l+W�MUT?+ WQ\2X+MUT�PF�CM4W�K+M/WQK+P-T�X1K�^_TQbf\]V+PRq�l@\���MUT^cN�^snwt+V+qUWQPR\]V`\]n!WQK+Myx Y MUTa^cV+X�WQK+M p ^cN�MUT��

� � + � � � � � � � # � � # � U W X[Z � # � � � � X2�- � # ! � � � � � ��� ��� � # �

� V lm^_TQW�P-qOt+p ^_T#�Cnw\cTEW�K+M � t�^cVCWQT�\]V+P �sp ^cNQMUT � � ���.+u��� @b �e\cl MUTg^_W�P-V+v � � N ��P-WQq6K+MUX^_WyW�K+M bfPRV+P-b t+b S%* � \]n�� � �-,ahc��W�K+Msb9^ �+P-b t+b l@M#^ � l@\���MUT PRN � � � � � ��� � �]���,2 2&3� � � � \cTyWQK+Msx Y M:T#�!^cN ^cV�M��+^cb l�pRM qO\]V+N�PRX+MUT1^ � 0 �109qOb N�^cb l�p-Ms\]n Z WQWQMUT Y PRt+b"0 MUT Y P-t+b

� �

Page 87: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

X+\cl MOX`NQP-pRPRqO^sv]p ^cN�N ��P-W�K�^sqO\cTQMjX+PR^cbfMUW�MUT�\]n"^_l+l+TQ\��uPRb9^_W�MUp Z 2� @b2(

� � + � � � � � � � � �]� + � � � X � � U W X[Z� � � � # �,aM:T�Mc�CW�K+M WQK+P-T�Xs\cT�X+MUT�N�t+NQqOMUl+W�P Y PRp-P-W Z PRNEPRV b � N�t+V+P-W�NE\]n b MUW�MUT�NENQzBt�^_T�MOXsl MUT/�C\]pFW

NQzBt�^_T�MOX.� � \cT4qU\]b lm^_T�PRN�\]V1��P-W�K W�K+MHqUv]N4N Z N�W�MOb � MUpRMOqUW�T�\ N�W�^_W�PRqLt+V+P-WQN ��t+N�M�W�K+M nw\]pRp-\���PRV+vqO\]VC�CMUT�N�PR\]V.�

U W X[Z� � � ��� - � � � ��� U W X[Z� � � �JLK t+NO�

� � + � � � ��� � 0 �,2&3 ��� � # X � U W X[Z� � � � # �T � � � � ��* ��> ��N��F� Q � � �6�P�

� V+PFW�P ^cp-p Z PRV�W�K+M�b M#^cNQtuT�MOb MOV W N Z N}W�MOb W�K+M�X+MUWQMOqUW�\cT nw\cT W�K+PFT�X K�^_T�b \]V+PRq�pRPRv]KCW��\]t+p-X Y M�WQK+M`KBt+bf^cV M Z M#� [ ^_W�M:T ^�l�K+\cW�\]b t+p-W�PFl�pRP-MUTsWQt Y M2��\]t+p-X Y M`t+NQMUX WQ\ v]MUW ^zBt�^cV W�PFWg^_W�PF�CM4x�v]tuT�M#� � V \cT�X+MUTeWQ\ � V+\�� W�K+M�p-\���MUN�W"l@\]N�NQP Y p-M��c^cp-t+M�\]nOU W X[Z W�K�^_WePRN!q#^_lm^ Y pRM\]n Y MOPRV+v bfM#^cNQtuT�MUX �HPFW�K�WQK+M M Z Mc�m\]V+M V+MUMOX+N2W�\ t+N�MjW�K+MjM Z M�/ N �uP-NQP Y P-pRP-W Z p-PRbfPFW x�v]tuTQM1^_WW�K+PFT�X�K�^_TQbf\]V+PRq#�EJLK+PRN �c^cp-t+Mjb t+N�W W�K+MOV Y M qO\]VC�CMUTQWQMOX`PRVCW�\st+V+P-W�N�\]n ��t9� � �D^_WQW�N ���

JLK+M2bfP-V+PRb t+b �uP-NQP Y P-pRP-W Z \]n�^cV9\ Y �}MOqUW�W�\jW�K+MaX�^_T � ^cX�^_l+W�MOX KBt+bf^cV9M Z M2PRN/v]P-�CMOV^cN ^_l+l+TQ\��uPRb9^_W�MUp Z 0 � � ��� � [ t+b MOV+N l@M:T bfMUW�M:T1NQzBt�^_T�MOX l@M:T N�W�MUT�^cX+P ^cV � � � � � � � � � ��������� � � � �aJLK+PRN2Tg^cX+PR^cV+qOM1�c^cp-t+M q#^cV8PRNaqO\]VC�CMUTQWQMOX P-V WQ\ ^ ��t9�`�c^cp-t+M YBZ t+NQPRV+v W�K+MX+MUx�V+PFW�PR\]V�\]n�Tg^cX+PR^cV+qOM#�

� # �� � � � � � � � � �

� \cT2^ p ^cNQM:T#�

� � � � � � # � � # � � � � � - - � � � � # ��� � + � � � � ! X � # � � �NQ\

� � 0 ��� � � � � � ��� � + ��� � � ! X � � �,2&3 ��� � � # # � � � � � �J�\`qO\]VC�CMUTQW W�\2�L^_W�W�N��M9MON}W�PRb9^_WQMf^��_^cpRt+Mfn T�\]b ^`qO\]V �CM:T�NQPR\]VDqgK�^_TQW5��K+PRqgK�^_W

PFW�N l M#^ � \]n 0 0 0 V+b K�^cN ^ qO\]VC�CMUT�NQP-\]V \]n 2 � + [ t+bfMUV+N ���D^_WQW�� JLK+PRNsqO\]V �CM:T�NQPR\]V� &

Page 88: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

Y T�P-V+v]NaW�K+M �c^cp-t+Ms\]nEbfPRV+P-b t+b �uP-NQP Y p-M���t9�8W�\�^ Y \]tuW � � � # # �5^_WQW�N�� J K+P-Nk�_^cpRt+M NQMUMObfNt+VuT�MO^cNQ\]V�^ Y p Z pR\��(�� W1qO\cTQTQMON�l@\]V+X+NjW�\�^ Y \]tuWj\]V+M l�K+\cW�\]V�MU�CMUT Z bfPRV tuW�M#� J K+P-N P-N V+\cWp-P � MOp Z � Y MOqO^ct+NQMyWQK+MjMON}W�PRb9^_WQMyP-NLnw\cT2^ p ^_T�v]Mk\ Y �}MOqUW Tg^_W�K+M:T�W�K�^cV�^ �}l \]PRVCW � p ^cNQMUT NQ\]tuTQqOM#�I bf\cT�MaT�M#^cp-PRN�W�P-qy�_^cpRt+Mynw\cT2b PRV+PRb t+b �{PRNQP Y pRM ��t9��NQK+\]t+pRX Y M1^ Y \]tuW � ��� ! � �5^_WQW�N��� � + � � � � � � � � ! � � �

JLK+M�V t+b Y MUTf\]nHl�K+\cW�\]V+N W�K�^_W MOVCW�MUTfW�K+M�M Z M�l MUTfNQMUqO\]V+X q#^cV Y M�X+MUW�MUT�b PRV+MOXnw\cT�b W�K+Ms� ��� ! � �D^_WQWQN W�K�^_WLW�K+MjM Z M qO^cV�NQMOM��

� # � �� � 2 �,2 � 2 � � � � X � � � � � + ��� � � � � � �

- - � � � � � � � - �10{��� ��� � � !� �

� � � ! � � �� � � ! ��

� �

� ��� ! �

- �,0{��� ��� � � !��� �]� l�K+\cW�\]V+N � NQMUqO\]V+X

T � � ��Q"* ���� �#�'��* �P��� � �P� Q �O��� ��� �E����@�8*���� � �F��������� � � � �ON����'*

JLK+M bfPRV+P-b t+b �c^cp-t+M nw\cT U W X[Z W�K�^_WaWQK+MsN Z N�W�MOb qO^cV bfMO^cNQtuT�M PRNknw\]t+V+X Y Z NQt Y 0N�WQP-W�tuW�P-V+v WQK+M bfP-V+PRb t+b&�uP-NQP Y p-M ��t9��PRVCW�\ W�K+MjMUz{t�^_W�P-\]V Y MUpR\�� ^cV+X�NQ\]p-�{PRV+v��

� � + � � � � � � � � �]� + � � � X � � U W X[Z� � � � # 0 �,2&3 � � � # X � U W X[Z� � � � #��K+MUT�M

� � + � � � � � � � � + � � � �� ��������

� � � � � � � ��� ! �

� 2 � � � � � � � � � � � � ��� � � � ! X � �

�2l \]V NQ\]p-�{PRV+v2PFW �L^cNenw\]t+V+X W�K�^_W!W�K+M�NQb9^cp-pRMON}W!�_^cpRt+M�\]nuW�K+PFT�X \cT�X+MUT�N�t+NQqOMUl+W�P Y PRp-P-W ZW�K�^_W�q#^cV Y M X+M:W�MOqUW�MUX �HPFW�K`^cV�M Z M ^cN W�K+MyN Z N�WQMObM/ N X+MUW�MUqUW�\cT�PRN

U W X[Z� � ! � � � � � � � ! � � � � ��� � � � � # � � #

� # �[ PRN}W�MOX PRV Wg^ Y pRM � ^_T�M�W�K+M�W�K+PFT�X \cT�X+MUTENQt+NQqOM:l+W�P Y P-pRP-WQPRMON�\]n�NQMU�CMUT�^cp+b9^_W�MUT�PR^cpRN"nw\]t+V+X

P-V�^�pRP-WQMUTg^_W�tuT�M NQMO^_T�qgK.� J K+MON�Ms�_^cpRt+MONyq#^cV�N�MUTQ�CMs^cNj^ lm^_TQW�PR^cp"qO\]b lm^_T�P-NQ\]V8W�\�MUN�W�PRbf^_W�M��K�^_W�WQK+Mj�_^cpRt+MON NQK+\]t+pRX Y M nw\cT W�K+MyW�MON�W x Y MUTQN��

� \cT�nwt+NQMOX`NQP-pRP-q#^u�m^cNH^cV�M���^cb l�p-Mc�� � + � � � � � � � � �]� + � � � X � �F� � � # # � #�

� � � ��� � � � � � � � � � � � � � � � � ���(

Page 89: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

D ��> NF� 4

� ��� � ��� � � � � � � � � �� � �� � � ����� � � � � � � � � �

� P Y MUT2J Z l@M U WYX[Z PRV`MUNQt U WYX[Z PRV � #� #

rL\cTQV+PRV+v v]pR^cNQNHr�~ + 0 2 ��

� ������

� ��� ! �~{qgK+\cWQW2v]pR^cNQN2��� 0�+ �

�� ��� �

�� ��� ! �

� t+N�MOX8~{PRp-PRq#^�

� � � ! �

� � � # #

� � � � � ��� �- �10 � � � � !� I2 �.-&+ � � � � l�K+\cWQ\]V+N � N�MOq �

�atuTax Y M:T�Ny^_T�M qO\]b l \]NQMOX8\]nenwt+NQMOX NQPRp-PRq#^ �2IaX+X+PFW�PR\]V�^cp�X+\clm^cV WQNk^_T�M ^cX+X+MOX.�a�5MY MOpRP-MU�CMaW�K�^_W�W�K+MkK+PRv]K�X+\clm^cV W qO\]V+qUMOV W�Tg^_W�PR\]V�PRV W�K+Max Y M:T�N�K+\]t+pRX�MUV+K�^cV+qOMyWQK+Mk�_^cpRt+Mk\]nU?W X[Z �`�5M M��ul MOqUW W�K�^_W1WQK+PRN1�_^cpRt+M9NQK+\]t+p-X Y M9K+PRv]K+MUT W�K�^cV5W�K+Mf�_^cpRt+M9nw\cT ^cVDt+V+X+\cl@MUX� l�pR^cPRV nwt+NQMOXDNQPRp-PRq#^ �2x Y M:T�� J K t+N��MsM��ul MOqUW \]tuT1X�^_T � ^cX�^_l+W�MOX M Z M W�\�N�MOMfbf\cT�M W�K�^cV� � � l�K+\cW�\]V+NLl@MUTHNQMOqO\]V+X�\]tuW�\]n�W�K+Myx Y MUT��

�#

Page 90: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� "

Page 91: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� � � ����� ����� *�����5���5���H��. � �!���"�� �#%

S �8����� ���?��@� �E�'���

JLK+M`x�V�^cp2N�WQMUl nw\cT9WQK+M`T�MONQM#^_TQq6K l+T�\��}MOqUW �L^cNfWQ\ W�MON�W \]tuT9l+T�MUX+PRqUW�P-\]V+N PRV W�K+MpR^ Y \cTg^_W�\cT Z �HJLK+M MOz{t+PFl�bfMOVCW �L^cNa\ Y Wg^cP-V+MOX8^cV+X�W�K+M bfM#^cN�tuT�MObfMOVCWaN Z N�W�MOb �L^cN2NQMUWktul^_W [ PRV+qU\]pRV [ ^ Y \cTg^_W�\cT Z �!o4�CMUT Z x Y MUT�t+N�MOXsP-V W�K+M�p ^ Y �L^cNeqOp-M#^#�CMOX��HPFW�K ^ /\cT � l+T�MOqOP-NQPR\]Vx Y MUTHqUpRM#^#�CMUTLW�\ ^cNQNQtuT�My\cl+W�P-b t+b qO\]tul�pRP-V+vsM � qOPRMUV+q Z \]n�W�K+MkpR^cNQMUT Y M#^cbdP-V W�\ W�K+Max Y MUT��JLK+M�x Y MUT�Nft+NQMUX PRV W�K+M�M��ul MUT�P-bfMOVCW7��MUTQM#( Z W�W�MUT Y P-t+b10 MUT Y PRt+b x Y MUTQNO�LMUT Y PRt+b x Y M:T�NO�^cV+X�^ rL\cTQV+PRV+vsx Y MUT/��P-WQK�W�K+M Y Tg^cV+X+V�^cbfM J PFWg^cV.�EJ K+M Z WQW�M:T Y PRt+b10 MUT Y P-t+bdx Y MUT�N ��MUT�MqOp-M#^#�CMOX5n T�\]b Y \cW�K NQP-X+MON1\]nL^�N�PRV+v]pRM N�l@\B\]p'��K+PRqgK �L^cN 2`bfPRqUTQ\]V+N � qU\cT�MfX+P ^cb MUW�MUT �k^_W\]V+MsMOV+X5^cV+X6+�bfPRqUTQ\]V+N ^_WyW�K+M \cWQK+MUT��sJ K+MsqO\cT�M N�PRhOM �c^_T�P-MOX Y MOq#^ct+NQMs\]n/W�K+M XuT�^���PRV+vl+T�\BqOMONQNLl@M:T�nw\cT�bfMOX�\]V�W�K+Max Y MUT�l+TQMOnw\cT�b2�Eo�^cqgK�p-MOV+vcW�K�qOpRMO^��CMOX�K�^cX�W�\ Y MyqgK+MOq � MOX�nw\cT^cPFT Y t Y+Y p-MON �HK+P-q6K ��\]t+pRXDl+T�MU�CMOVCWsbf\{X+M9l+T�\clm^cvC^_W�P-\]V.� JLK+M�WQK+MO\cT�MUW�P-q#^cp�nw\cT�b t+p ^8nw\cTW�K+PFT�X�K�^_T�bf\]V+P-qjl \���M:T+�L^cN2X+MUl MOV+X+MOVCWj\]V`WQK+M x Y MUTkqU\cT�M1NQP-hOM ^cV+X8pRMOV+vcWQK.�HJ!\ qO\]V W�T�\]p�_^_T�P ^ Y p-MON bf\]N�WLx Y MUTQN���MUTQM qOp-M#^��CMUX�W�\sWQK+M N�^cbfMkp-MOV+vcW�K.� � 09�10 qOMOVCW�PRbfM:W�MUT�N��

JLK+M NQ^cbfM l+TQ\{qOMOX+tuTQM7�L^cN t+N�MOX5nw\cT ^cp-p"x Y MUT�N t+V+X+MUT1W�MON}W��fJLK+Msx Y MUT�L^cNjK+MOpRXP-V�l�pR^cqOM�^_W Y \cW�K MOV+X+N Y Z x Y MUTsq6K t+q � N���JLK+MONQM�q6K t+q � N"��MUT�M�PRV+NQMUT�W�MOX P-V WQ\ � tuT�p-MOPRv]Kx Y MUT�l@\]NQPFW�PR\]V+P-V+v1N�Wg^cv]MUN��EJ K+MaN�W�^cv]MON6��MUTQMk^cpRPRv]V+MUX&�HPFW�KfW�K+M2pR^cNQMUT Y M#^cb&^cV+X nw\{qUt+NQNQPRV+v\cl+W�P-qON�� JLK+M8p ^cNQMUT K�^cX W�\5T�t+V ��P-W�K PFW�N � � N �HPFW�qgK+MUT�\]V�^_W9^cpRpHW�P-bfMON�� � MUq#^ct+NQM�W�K+M� � N ��P-W�qgK+MUT �L^cN ^cV�^cqO\]t+N�W�\�0 \cl+W�PRq bf\BX+t+p ^_W�\cTO�"PRn�W�K+M bf\BX+t+p ^_W�\cT �L^cN W�tuT�V+MOX�\# W�K+M^cp-PRv]V+bfMOVCW'��\]t+pRXfqgK�^cV+v]M#�4JLK+M Y M#^cb �L^cNEx+T�N�W�NQMUV W�WQKuT�\]t+v]K ^cV9^_WQW�MUVBt�^_W�\cT/qO\]b l+T�P-NQMOX\]na^ l@\]p ^_TQPRhOMUTf^cV+X ^�K�^cpRn 0 �L^#�CM�l�p ^_W�M�� J K+M`^_WQW�MOV t�^_W�PR\]V �L^cNfK+MOp-X K+PRv]K X+tuT�P-V+v W�K+Ml \]NQP-W�P-\]V+PRV+v�� J K+M�^_WQW�MUVBt�^_W�MUX Y M#^cb �L^cN X+P-T�MOq:W�MOX P-V WQ\8WQK+M�x Y MUT�� JLK+M x Y MUTs\]tuWQl�tuWY M#^cb �L^cNkNQMOVCW P-V WQ\�^ �aiyJ v]MUT�b9^cV+P-t+b X+MUW�MUqUW�\cT�� JLK+PRNkX+MUWQMOqUW�\cT��L^cNyq#^cpRP Y Tg^_W�MOX nw\cTW�K+Msp ^cNQM:T �L^#�CMOp-MOV+vcW�K5^cV+X5qO\]t+p-X5^cqOqOtuT�^_W�MOp Z X+MUWQMOqUW1M:�CMOV V�^cV+\��L^_WQW�Nj\]n/l@\���MUT�� Ian W�MUTv]\B\{X8qO\]tul�pRP-V+v �L^cNy^cq6K+P-MU�CMOX W�K+M1x Y MUT��L^cNaX+PFT�MOqUW�MUX�PRVCW�\�^fW�K+MUT�b \cl�PRpRM1l \���MUTybfMUW�MUT��JLK+M ^_WQW�MOV t�^_W�P-\]V ��^cN N�pR\��Hp Z X+MOqUTQM#^cNQMOX YBZ TQ\cWg^_W�PRV+v`WQK+M�K�^cp-n 0 �L^#�CMfl�p ^_WQM9qUT Z N}Wg^cp �2� W�L^cN�nw\]t+V+X W�K�^_W�PRn�W�K+M ^_WQW�MOV t�^_W�P-\]V ��^cNEX+MUqUT�M#^cNQMUX W�\{\aTg^_l�P-X+p Z WQK+MLx Y MUT�W�P-l"��\]t+p-X Y tuT�V\cT/n Tg^cqUW�tuT�M�� � n@PFW/n T�^cqUW�tuT�MOXfWQK+M2\]tuWQl�tuW/l \���MUT�n T�\]b W�K+M x Y MUT ��\]t+pRXfXuT�\cl9�CM:T Z Tg^_l�PRX+p Z �� W PRN Y MUpRPRM:�CMOX W�K�^_W n Tg^cq:W�tuT�PRV+v PRN q#^ct+NQMUX Y Z N�MOqO\]V+X�^_T Z M� MOqUW�N��5IdTg^_l�P-X PRV+q:T�M#^cNQM�PRVl \���M:THX+MOV+N�P-W Z ��PRp-p>pRM#^cX�W�\s^sp ^_TQv]MkWQK+MUT�b9^cp>vcTg^cX+P-MOVCW2^cqUTQ\]NQN�W�K+Mkx Y M:T2qO\cT�M��/JLK+MjpR^_T�v]MW�K+M:T�b9^cp+vcTg^cX+P-MOV W4q#^cV+V+\cW Y M�X+PRNQNQPFlm^_W�MOX Y Z W�K+M qO\cT�MHzBt+PRq � MOV+\]t+v]K.�4J K+M n Tg^cqUWQtuT�MON/\]V+p Z\BqOqOtuTQT�MUX`PRV�W�K+MjW�PFl�N�\]n�W�K+Myx Y MUT/��K+MUT�MyW�K+M P-Vul�tuWHl \���M:T/�L^cN�^_WHPFW�N K+PRv]K+MON�W��

� �

Page 92: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

JLK+M�^_WQW�MOV t�^_W�P-\]V �L^cN W�tuTQV+MOX ^cp-p6�L^ Z X+\���V N�\ W�K�^_W bf^ �+PRb t+b l@\���MUT"��\]t+pRXY M qU\]tul�pRMOX PRVCW�\ W�K+M x Y MUT�� J K+M Z WQW�MUT Y P-t+b10 M:T Y PRt+b x Y MUT��L^cNaW�K+M PRV+PFW�P ^cp�x Y MUTyW�MON�WQMOX.�� W �L^cNH^cN�NQt+bfMOX�W�K�^_W�WQK+MjK+P-v]K�X+\clm^cVCW2qO\]V+qOMUV WQT�^_W�PR\]V3��\]t+pRX`qO^ct+NQM ^ K+PRv]K�W�K+P-T�X�\cT�X+MUTNQt+N�qOMUl+W�P Y PRpRPFW Z ^cV+X�WQK+MUT�MOnw\cT�M W�K+P-N5��\]t+pRX Y M9W�K+M M#^cNQP-MON�W x Y M:TsP-V �HK+P-q6KDW�\�x�V+X WQK+P-T�XK�^_T�b \]V+PRq#� JLK+ML2`bfP-qUT�\]V�qU\cT�MfNQP-hOM&�L^cN t+N�MOX5W�\`M#^cNQM9qU\]tul�pRPRV+v�M � qOP-MOV+q Z ��rL\]tul�p-PRV+vM � qOPRMUV+q Z �L^cN MON�W�P-b9^_W�MOX�^_W ^ Y \]tuW 0 ��� P-V�WQK+M�N Z N�W�MUb2� [ \]NQNQMUNs\BqOqOtuTQT�MUX PRVDW�K+M nw\�0qOt+N�NQPRV+v�^cV+X8qO\]pRp-PRb9^_W�P-V+v b t+p-WQPRNQtuT�n ^cqUM \ Y �}MOq:W�P-�CM p-MOV+NQMONy^cV+X8n T�\]b W�K+M1x Y MUTyP-W�N�MOpRn �aIaVP-V+n Tg^_T�MOX��uP-NQPR\]V�NQqO\cl@M N�K+\���MUX8WQK�^_Wk^ pR\cWH\]n"W�K+M1Tg^cX+PR^_W�PR\]V ��^cN Y MOP-V+v9NQq#^_WQWQMUT�MOX8\]tuWa\]nW�K+Mkx Y M:T��/Ian W�M:T2b t+qgK�WQT�PR^cp�^cV+X`MUTQTQ\cT#��v]\{\{X�qO\]tul�pRP-V+v1�L^cN T�MOv]t+pR^_T�p Z ^cqgK+PRM:�CMOX.�

ILW W�K+M9\]tuWQl�tuW \]n�W�K+M9x Y M:T ^�K+M#^_W ^ Y N�\cT Y PRV+v8x�p-W�M:T � ~{qgK+\cWQW7�yp ^cN�N���� + � MOn 0nwMOq:W�P-�CMOp Z Y pR\{q � MOX ^cpRpk\]njW�K+M nwt+V+X�^cbfMOVCWg^cp Y M#^cb2� JLK+M WQTg^cV+N�bfP-WQW�^cV+qOM8\]n W�K+M WQK+P-T�XK�^_T�b \]V+PRqknw\cTHW�K+P-N x�pFW�MUT�PRN�^_l+l+T�\��+PRbf^_W�MOp Z � ���3�EJ K+MjNQMOqO\]V+X�K�^_T�bf\]V+PRqkWQTg^cV+N�bfP-WQW�^cV+qOMP-N�^cpRb \]N�W 0 ��� ��J K+MHnwt+V+X�^cbfMOVCWg^cp ��^��CMOp-MOV+vcW�K9K�^cN/^jWQTg^cV+NQb P-WQWg^cV+qUMH\]n@\��CMUT/x+�CMH\cT�X+MUT�N\]n�b9^cv]V+PFW�t+X+M pR\���MUT��yJLK+M PRV+n Tg^_T�MUX Y MO^cb ^ Y NQ\cT Y MOX P-NaT�MUTg^cX+PR^_W�MOX8PRV+qO\]K+M:T�MOVCW�p Z ^cNkn ^_TP-V+n Tg^_T�MOX Tg^cX+P ^_W�P-\]V�PRVCW�\ - � N�WQMUTg^cX+P ^cV+N��1JLK+M N�MOqO\]V+X�K�^_TQbf\]V+PRq5�L^cNax�pFW�MUT�MOX \]tuWkt+NQPRV+vW�K+Mybf\]V+\Bq6KuTQ\]b9^_W�\cT��

JLK+M9W�K+P-TQX�K�^_TQbf\]V+PRq&�L^cN X+M:W�MOqUW�MUX �uP-NQt�^cpRp Z�Y Z pR\B\ � P-V+v`W�KuT�\]t+v]K5W�K+M vcTg^_W�P-V+v���aV+qOM�WQK+M��uP-\]pRMUWEp-PRv]KCW%�L^cN�x�V�^cpRp Z X+MUW�MOqUWQMOXfP-W4NQMOMUbfMOX �CMUT Z P-V WQMOV+NQM#�$� W%��^cN/V+\cW4X+P � qUt+p-WW�\ NQMOMHW�K+M��uPR\]p-MUW Y M#^cb2��JLK+M2vcTg^_W�P-V+v qO\]Vux+TQbfMOXfW�K�^_W�WQK+M Y MO^cb �L^cN�^_W4W�K+M2pR^cNQMUT Y M#^cbW�K+PFT�X*K�^_T�bf\]V+PRq � - - �DV�^cV+\]bfMUWQMUT�N ����J K+M vcTg^_W�P-V+v qO\]Vux+TQbfMOX N�MOqO\]V+X K�^_T�b \]V+PRq)�L^cNl+T�MUNQMOVCWL^cpRNQ\ � 2 2 �jV�^cV+\]b MUW�MUT�N ���eo4�CMOVCW�t�^cp-p Z W�K+MHvcT�^_W�PRV+v��L^cN4T�MUbf\ �CMUX n T�\]b W�K+MHN�MUW�tul �I X+P-T�MUqUW p-PRV+M \]n/NQP-v]K WyM Z M M��+^cbfPRV�^_W�P-\]V8\]n4W�K+M Y M#^cb W�KuTQ\]t+v]K W�K+M x�p-W�M:TyTQMU�CM#^cpRMUX�W�K+MW�K+PFT�X�K�^_TQbf\]V+PRq Y MO^cb MUV+qOP-T�qUpRMOX YBZ W�K+MyNQMOqO\]V+X�K�^_T�bf\]V+PRq Y M#^cb2�EJ K+MyW�K+P-TQX�K�^_T�bf\]V+P-qNQMUMObfMOX Y T�PRv]KCW�MUTkW�K�^cV8W�K+M NQMOqU\]V+X K�^_T�bf\]V+P-q#�yJ K+M PRVul�tuWkl@MO^ � l@\���MUT��L^cNy^ Y \]tuW � � ��L^_W�W�N��EJ K+MyK+PRv]K �uP-NQP Y P-pRPFW Z \]n�W�K+M Y M#^cb NQt+v]v]MON�WQMOX�W�K�^_W�W�K+MkW�K+PFT�X�\cTQX+MUTHN�t+NQqOMUl+W�P Y PRp-P-W Z�L^cNaN}WQT�\]V+v��2IaN2W�K+M P-Vul�tuWknwt+V+X�^cbfMOVCWg^cp Y M#^cb �L^cNk^_WQWQMOVBt�^_WQMOX WQK+M K�^_T�bf\]V+PRqUN2n ^cX+MOX.�JLK+PRN qO\]Vux+T�bfMUX�W�K�^_W W�K+MjK�^_TQbf\]V+PRqON ��MUTQM1^snwt+V+q:W�PR\]V`\]n�W�K+M nwt+V+X�^cbfMUV Wg^cp�P-Vul�tuW��

Ian WQMUT�W�K+M2zBt�^cpRPFWg^_W�P-�CM bfM#^cN�tuT�MObfMOVCW �L^cN/b9^cX+M2^1zBt�^cV W�PFWg^_W�PF�CMH\]V+M/�L^cN/V+MOMOX+MOX.�IdNQt+PFWg^ Y pRMfW�t Y M&�L^cN nw\]t+V+X ^_W W�K+M9N�^cbfM9pR^ Y �8J K+P-N1W�t Y M&�L^cN ^cVDo | � ��~ �]� �`W�t Y M� b \{X+MOp�VBt+b Y MUTk� 2&0�2#� � ��� JLK+PRNHWQt Y M5�L^cN2MUN�l@MOqUP ^cpRp Z t+NQMUnwt+p Y MOqO^ct+NQM P-W ��^cNH�CMUT Z NQMOV90NQPFW�P-�CM PRV W�K+Ms�{PR\]pRM:WjT�MUv]PR\]V.�"zBt�^cV W�t+b M � qOPRMOV+q Z �L^cNj\ �CMUT ��0��3� J K+M W�t Y MfV+MUMOX+MOX W�\Y M q#^cpRP Y Tg^_W�MOX�x+T�N�W��2I q#^cpRP Y Tg^_W�PR\]V�M��ul@M:T�PRbfMUV W ��^cNaNQMUWktul ^cV+X ^ N�q6K+MUb9^_W�PRq PRNaNQK+\��HVP-V�x�v]tuT�M � -��

I r Z \]V+P-qONO� � V+q#�-� � � � 0 � �5^_WQW#��r�� I2T�v]\]V pR^cNQMUT �L^cN t+NQMUX ^cNyW�K+Mfp-PRv]KCW NQ\]tuTQqOM#�JLK+PRN�^cP-T�qO\B\]pRMOX*p ^cN�MUT�K�^cX ^cV ^cX �}t+N}Wg^ Y pRM8l@\���MUT � V+\ Y � JLK+PRN p ^cN�MUT�MObfP-W�W�MOX*N�WQT�\]V+v

� �

Page 93: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � � � � � ��� � � � ��� � � � � ����� � ��� �� � � ��� � � � � � ��

N�l MOqUWQT�^cp�pRP-V+MON PRV5W�K+M9�uP-NQP Y p-M Tg^cV+v]MON \]n vcT�MOMOV ^cV+X Y pRt+M#�8�5M#^ � MUT p-PRV+MON���M:T�M MObfP-W�W�MOX^cp-NQ\kPRV W�K+M��uPR\]p-MUW"T�MUv]PR\]V.� � V W�K+MLq#^cpRP Y Tg^_W�PR\]V M��{l@MUTQPRbfMOVCWeW�K+M��_^_T�PR\]t+N$�L^#�CMOpRMUV+vcW�K+N$��MUT�MNQM:lm^_Tg^_W�MOX YBZ ^ l+T�PRNQb �EI Y M#^cb Y p-\{q � �L^cN�l�pR^cqOMOX PRV n T�\]VCWL\]n!^cp-pmWQK+MyN�MUlm^_Tg^_W�MOX9�{PRNQP Y pRMp-PRV+MON M��uqOMUl+W nw\cT W�K+M9�uP-\]pRMUW���J K+P-N Y M#^cb ��^cN X+PFT�MOqUWQMOX�WQK+\]t+v]K ^�qgK+\cl+l@M:T1��K+MOMOp�^cV+XW�K+MUV�X+P-�CM:T�v]MOX Y Z ^ pRMOV+N PRVCW�\ W�K+Mal�K+\cW�\]b t+p-W�PFl�pRPRM:T�W�t Y M#� � V�\cT�X+M:T�W�\ l+T�\cWQMOqUW W�K+MaW�t Y Mn T�\]b W�\B\jb t+qgKfpRP-v]K WEW�K+M l�K+\cW�\{q#^_WQK+\{X+M���^cN/qO\��CMUT�MOX1�HPFW�KfV+MOtuWQT�^cpX+MOV+N�P-W Z x�pFW�MUT�N���J K+MV+MOtuW�Tg^cp4X+MUV+NQP-W Z ^_WQW�MOV t�^_W�PR\]V �L^cN � �������9JLK+MfqgK+\cl+l@MUT ^cpRpR\���MOX W�K+M \]V5^cV+X�\# NQP-v]V�^cp\]naW�K+M Y M#^cb W�\ Y M`�uP-M���MOX \]V W�K+M�\]NQqOP-pRp-\]NQqO\cl@M�� J K+M�\# NQPRv]V�^cp���\]t+pRX qO\cTQTQMON�l@\]V+XW�\�W�K+M X�^_T � 0 qOtuT�T�MOVCW NQP-v]V�^cp ��J K+M vcTg^_W�P-V+v)�L^cN t+NQMOX WQ\ x�V+X�W�K+M M���^cqUW N}l@MOqUW�Tg^cp�pRP-V+Mc�bfMO^cNQtuT�MOX�WQ\ Y MJ-70#��V�^cV+\]bfM:W�MUT�N�� ILW W�K+P-N��L^#�CMOp-MOV+vcW�K zBt�^cV W�t+b M � qOPRMOV+q Z �L^cNs�2��� WQK+PRN��c^cp-t+M'�L^cN�PRVCW�MUTQl \]p ^_W�MUX n T�\]b W�K+M�W�t Y M�/ N!X�^_Wg^ NQK+MOMUW!PRVyW�K+M/pR^cN�W"^_l+l MOV+X+P � ����~{MU�CM:Tg^cpbfMO^cNQtuT�MObfMUV W&��MUT�M8b9^cX+M�^_Wf�_^_T�P-\]t+Nfl@\���MUT NQMUW�W�PRV+v]NO� ��P-W�K �_^_T�PR\]t+N9V+MUtuWQTg^cpHX+MUV+NQP-W Zx�pFW�MUT�P-V+v��"M#^cqgK l@\���MUT pRMU�CMOp$�L^cNyT�M#^cX P-V \��CMUT1b9^cV Z8Y P ^cNk�C\]p-Wg^cv]MUN��fJLK+M qOtuT�T�MOVCW vC^cPRV

� �

Page 94: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � � � � � � � � ��� � � � ��� � ������

lm^_Tg^cb MUW�MUT�N���MUT�M bfM#^cN�tuT�MOX ^cV+X8qO\]b lm^_T�MOX�W�\ qOtuT��CM1x+W�N��kJLK+M TQMONQt+p-WQNaq#^cV Y M �uP-M���MOXP-V�x�v]tuT�M � 0 \cTH^cp-W�MUTQV�^_W�MOp Z P-V�x�v]tuT�M � 2 �

rL^cpRP Y Tg^_W�P-\]V5qOtuTQ�CMONs^cV+X W�K+M p-PRV+M9x+W�N nw\cT W�K+M9W ��\ K+P-v]K+MON�W l@\���MUTsNQMUWQWQPRV+v]N ^_T�MNQK+\���V.� [ \���MUTyl@\���MUTyNQMUW�W�PRV+v]N���MUT�M t+V�^ Y pRM W�\ Y Ms^cqOqOtuT�^_W�MOp Z b M#^cNQtuT�MOX Y Z WQK+M WQK+MUT 0bf\cl�P-pRM l@\���MUT bfMUW�M:T�� J K+M K+PRv]K+MON}W l@\���MUT PRVul�tuW�N���MUTQM \]V+p Z NQM:�CMUTg^cp�bfPRp-pRP �L^_WQW�N��1J K+MV+MOtuW�Tg^cp�X+MOV+NQP-W Z x�pFW�MUT�Ny\]V+p Z ^cp-pR\���MOX n Tg^cqUW�P-\]V+Nj\]n4V�^cV+\��L^_W�W�NyWQ\�MOVCW�MUTyW�K+M l�K+\cW�\{qO^_W�K90\BX+M#�/JLK+MyqOtuTQT�MOVCWavC^cP-V�lm^_Tg^cb MUW�MUT�N � ^cV+X �^_T�MkT�MOpR^_W�MOX�WQ\sW�K+MyPRVul�tuW l@\���MUT2^cV+X�W�K+MNQP-v]V�^cp�^cV+X Y P ^cN �C\]p-Wg^cv]MUN Y Z W�K+Mjnw\]p-pR\��HP-V+v nw\cT�b t+pR^ �

� ����� � ���� � � � ! � ���K+MUT�M

� � � ������� �

Page 95: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

����������� � � � � � � � � ��� � � � ��� � ������

P-N W�K+MjqOtuTQT�MUV WHvC^cPRV`^cV+X � I2 �,2 � 2 � � � ��X � ���,2 � � � � � � !�

� �� + ��� � �

-70#� � � � � I2 �10 0 ��� � ! $ &� �2��

� � � � � � �

JLK+M p-\C^cX T�MUNQPRN�W�^cV+qOMf\]n/W�K+M l�K+\cW�\]b t+p-W�PFl�pRP-MUTkW�t Y M"�L^cN1^cNQN�t+bfMOX5K+PRv]K�^cV+X W�K+MNQqU\cl@MHP-Vul�tuW6�L^cN4qO\]b lm^_Tg^_WQP-�CMOp Z pR\���MUT/NQ\ ��K+MOVfl�p ^cqUMOXfPRV lm^_Tg^cpRp-MOp+W�\ vcTQ\]t+V+X W�K+MHN�qO\cl@MP-Vul�tuW`T�MONQP-N�Wg^cV+qOM �L^cN�t+NQMUX.� JLK+M q#^cp-P Y Tg^_WQPR\]V qUtuTQ�CMON�X+MUW�M:T�bfPRV+MUX W�K+M qOtuT�T�MOVCW�vC^cPRVlm^_Tg^cb MUW�MUT�N \]n�WQK+MjW�t Y MyW�\ Y M � - �,2 � ��� ��� #�!H^cV+X � �,+u� �

���

Page 96: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

�aN�PRV+v9W�K+PRNaNQ^cbfM nw\cT�b t+p ^fW�K+M1W�K+PFT�X K�^_T�bf\]V+PRqjl@\���MUTyqUT�M#^_WQMOX P-V WQK+M x Y MUT��L^cNq#^cp-qOt+p ^_WQMOX.� � \cT1W�K+MONQM9b M#^cNQtuT�MOb MOV WQN W�K+M&�L^#�CMOpRMUV+vcW�K �L^cN - - �`V�^cV+\]bfMUWQMUT�N ^cV+X5W�K+Ml�K+\cW�\]b t+pFW�P-l�p-PRMUT1WQt Y M9K�^cX ^cV�P-b l+T�\��CMOX5z{t�^cVCW�t+b M � qOPRMUV+q Z \]ny�����3�`Iap-NQ\�W�K+M9pR\C^cXT�MUNQPRN�W�^cV+qOMfqgK�^cV+v]MOX.�fI 0 ��\]K+b N�qO\cl@MsPRVul�tuW��^cN t+NQMOX.�9I NQb9^cp-pRMUTjPRVul�tuW PRb l MOX�^cV+qOM�L^cNLT�MOzBt+P-T�MUX`PRV�\cT�X+MUTHWQ\ pR\B\ � ^_WLW�K+M n ^cN�W � 0 N ��P-W�qgK+MOX`l�t+p-NQMON��

I pR^_T�v]M Y ^_TQTQPRMUT��L^cN qU\]V+N�WQT�t+qUWQMOX ^_TQ\]t+V+X�W�K+M9MUV W�PFT�M9M��{l@MUT�P-bfMOVCW1W�\ � MOMUl ^cV ZN�W�Tg^ Z pRP-v]K W�n T�\]b T�MO^cq6K+P-V+v1W�K+M2l�K+\cW�\Bq#^_W�K+\{X+M��/�aV+p Z pRP-v]K W/NQMOVCWLPRV9n T�\]b W�K+MHx Y M:T ��\]t+pRXT�MO^cq6K`WQK+M1X+MUW�MOq:W�\cT�� � W/�L^cN2X+MUqOPRX+MOX�W�K�^_W�W�K+M vcT�^_W�PRV+v7��\]t+pRX�V+\cW Y M1t+NQMOX�P-V`W�K+M1bfMO^ 0NQtuTQMObfMOVCW�N��L~{M:�CMUTg^cp�TQM#^cNQ\]V+N Y ^cq � MOX`WQK+PRNHX+MUqOPRNQP-\]V.� � P-TQN�W#��W�K+M NQMUqO\]V+X�K�^_T�bf\]V+P-qjNQP-v]V�^cp�L^cNj�uPRN�t�^cpRp Z V+\cW ^cN Y T�PRv]KCW ^cN WQK+M W�K+P-TQX5K�^_T�bf\]V+PRq���~{\]bfM x Y M:T�N1X+PRX5V+\cW1MU�CMOV5NQK+\��NQP-v]V+Nj\]n/NQMOqO\]V+X K�^_TQbf\]V+PRq v]MOV+MUT�^_W�PR\]V.�"*HMON�M#^_T�qgK5PRV W�K+M NQt Y �}MOq:W1\]n/N�MOqO\]V+X5K�^_T�bf\]V+P-qv]MOV+M:Tg^_W�PR\]V>��^cNsqOPFW�MOX l+TQMU�uP-\]t+NQp Z �4N�Wg^_W�MOX W�K+M�MU�CMUV W�t�^cp Y t+PRp-X tul \]n2N�MOqO\]V+X K�^_T�bf\]V+P-qp-PRv]KCW�� � MUq#^ct+NQMkW�K+PRNLl+T�\{qUMONQN PRN�^ vcTg^cX+t�^cp>\]V+My\]V+p Z W�K+MyWQK+P-T�X�K�^_T�bf\]V+PRq ��PRp-p Y My\]tuWQl�tuWY Z WQK+Mjx Y M:T#�@^_WHpRM#^cN�WH^_WHx+TQN�W�� � V�W�K+Mjp ^ Y PFWHW�\B\ � K+\]tuT�N Y MUnw\cT�M T�MOX�p-PRv]KCW���^cN2V+\cW�PRqUMOX.�JLK+PRN4PRNE\]V+M�T�M#^cN�\]V W�K+M vcTg^_W�PRV+v��L^cN/X+MUMObfMOXst+V+V+MOqOMONQNQ^_T Z �4I�NQMOqO\]V+XfTQM#^cNQ\]VfP-NEW�K�^_W4W�K+MvcTg^_WQPRV+v qUtuWaX+\���V`W�K+M ^cb \]t+V WH\]n"pRP-v]K W2^��_^cPRpR^ Y pRM nw\cT2bfM#^cNQtuT�MUbfMOVCW�� � Wa^cpRN�\ l+T�MONQMUV W�MUXNQ\]b Ma^cpRP-v]V+bfMOVCW�l+T�\ Y pRMUbfN��EJ K+M2W�Tg^cV+NQbfPFWQWg^cV+qOM2nw\cT�WQK+M2T�MOX �L^cN�pRMON�N�W�K�^cV9W�K�^_W�nw\cTLW�K+M�{PR\]pRM:W YBZ ^ Y \]tuWV+ ���3� � P-V�^cpRp Z W�K+M z{t�^cVCW�t+b M � qOPRMOV+q Z \]n�W�K+M X+MUW�MUqUW�\cT��L^cNk\ �CMUTkW ��\\cT�X+M:T�N2\]neb9^cv]V+PFW�t+X+M p-\���M:Tanw\cT2W�K+M TQMOX�pRP-v]K W�� JLKBt+Nk^sbfM#^cNQtuT�MUbfMOVCWHWg^ � MOV2��\]t+pRX�V+\cWV+MOMUX�W�K+M vcT�^_W�PRV+v PRV`n TQ\]V W�\]n!W�K+Mkl�K+\cW�\{qO^_W�K+\{X+M#�

JLK+M W�K+P-T�X K�^_T�bf\]V+P-q p-PRv]KCW MUbfMUT�v]P-V+v�n T�\]b W�K+M x Y M:T �L^cNjqO\]pRp-PRb9^_WQMOX YBZ ^ pRMOV+N^cV+X N�MOV W1PRVCW�\�W�K+M Y ^_T�Msl�K+\cWQ\{q#^_W�K+\BX+M#� oE�CMOV�W�K+\]t+v]K W�K+M NQP-v]V�^cp'��^cNy�{PRNQt�^cp-p Z8Y T�PRv]KCWPFW �L^cNLV+\cWLbfPRp-pRP ��^_WQW�N/\]n�l@\���MUT�NQ\ W�K+MkV+MOtuWQT�^cp>X+MOV+NQP-W Z x�pFW�MUT�N ��MUTQMyV+\cWLT�MUz{t+P-TQMOX.�/J ��\NQP-v]V�^cpRN ��MUT�M NQMOVCW/WQ\yW�K+M�\]NQqOP-pRpR\]N�qO\cl@M#�E�aV+MHN�PRv]V�^cp �L^cN4^yWQTQPRv]v]MUTEn T�\]b W�K+M nwt+V+X�^cbfMOVCWg^cpY M#^cb2�2I v]MUTQb9^cV+PRt+b l�K+\cW�\{X+P-\{X+M5�L^cNaM��{l@\]NQMUX W�\fWQK+M � � N ��P-WQq6K+MUX NQP-v]V�^cp"\]tuWa\]n�W�K+MY ^cq � ^_l@M:TQW�tuT�M8\]naW�K+M8p ^cNQM:T�qO^��{P-W Z � J K+M8\cW�K+M:T�N�PRv]V�^cp/�L^cNfWQK+M8WQK+P-T�X*K�^_T�bf\]V+P-q � �N ��P-WQq6K+MUX5NQPRv]V�^cpEv]MOV+MUTg^_WQMOX YBZ W�K+M x Y MUT�� JLK+PRN��^cN X+MUW�MUqUW�MOX Y Z W�K+M l�K+\cW�\]b t+p-W�PFl�pRP-MUTW�t Y M#�8S/K+\cW�\]vcT�^_l�K+N5��MUT�MfWg^ � MUV�\]n NQqO\cl MfT�M#^cX+P-V+v]N n TQ\]b W�K+Mf�_^_T�PR\]t+N1x Y MUT�N����kV+M \]nW�K+MUNQM�l�K+\cW�\]vcTg^_l�K+N9PRN9N�K+\���V PRV x�v]tuT�M � 39� � \cT M#^cqgK x Y MUT W�K+M Y PR^cNf�C\]p-Wg^cv]Mc��N�qO\cl@MNQP-v]V�^cp'�/x Y MUTf\]tuW�l�tuW9^#�CMUTg^cv]M�l \���MUT9^cV+X x Y MUT9P-Vul�tuW9^#�CMUTg^cv]M�l \���MUT7��M:T�M�T�MOqU\cT�X+MOX.�JLK+M � � N ��P-WQq6K+MUX�l�t+pRNQMUN�\]n�W�K+MkW�K+P-T�X�K�^_T�bf\]V+P-qk^_T�MkqOMOVCW�MUT�MUX�^_WLW�K+Mal@M#^ � \]n�W�K+MkPRVul�tuWl�t+p-NQMON�� JLK+PRNkb9^ � MONkNQMUV+NQM Y MOq#^ct+NQMsP-WkNQK+\���NyW�K�^_Wynw\cT ^9p ^_T�v]MUTkl M#^ � PRVul�tuWyl@\���MUTyW�K+MqO\]VC�CMUT�N�PR\]V�WQ\ W�K+PFT�X�K�^_T�bf\]V+PRqal \���M:THP-N pR^_T�v]MUT���Iap-NQ\ WQK+Mjn ^cqUWLW�K�^_W � � N ��P-W�qgK+MOX�l�t+p-NQMONqO\]t+p-X Y M M#^cNQP-p Z N�MOMOV NQK+\���NaW�K�^_Wkb9^cV Z l�K+\cW�\]V+N+��M:T�M l+T�MONQMOVCW��HK+P-qgK bfMO^cV+N2W�K�^_WaW�K+MW�K+PFT�X�\cT�X+MUT2NQt+NQqOMUl+WQP Y PRp-P-W Z ��^cN2p ^_T�v]M���Iap-p�nw\]tuTax Y MUT�N ��M:T�M W�MON}W�MOX.� [ ^_W�MUT2NQ\]bfM p-\]V+v]MUT

� �

Page 97: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

p-MOV+vcW�K+Nk\]n/^ nwM�� \]n�W�K+MON�M x Y MUT�N+��MUT�Ms^cpRN�\ WQMON�W�MOX.� J K+M ^cX+X+PFW�PR\]V�^cp"p-MOV+vcW�K \]nEWQK+M pR^cN�Wx Y MUT/�L^cN�^cpRN�\sT�MU�CMO^cpRMOX Y Z W�K+MjWQPRbfMkNQK+P-n WHP-V�W�K+MkW�K+P-T�X�K�^_T�bf\]V+PRqal�t+p-NQM#�

����������� � � � � �� � � � � � � � � � + � ���� � � �

� &

Page 98: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

S �F4 � � ��* ��NF��*

JLK+M2l�K+\cW�\]vcTg^_l�K+N%��MUT�Mk^cV�^cp Z hOMOX�^cV+XfW�K+MaP-Vul�tuW ^cV+X9\]tuWQl�tuW�l@\���MUTQN ��MUT�M2l�p-\cW 0W�MUX.� � P-v]tuT�M � ��N�K+\���N1\]V+MfNQt+qgK5l�pR\cW \]n�\]tuWQl�tuW WQK+P-T�X5K�^_T�b \]V+PRqsl \���MUT1�CMUT�N�t+N1PRVul�tuWnwt+V+X�^cbfMUV Wg^cp�l \���M:T��5JLK+M�pR^ Y MOp-MOX P-Vul�tuW l \���MUTf^cq:W�t�^cpRp Z T�MOnwMUTQNsW�\8W�K+M nwt+V+X�^cbfMOVCWg^cp\]tuWQl�tuW l@\���MUT n T�\]b WQK+M�x Y MUT�� J K+M�nwt+V+X�^cbfMOVCWg^cpHl@\���MUT9TQMOb9^cPRV+NsMONQNQMUV W�PR^cpRp Z t+V+X+M�0l�p-MUW�MOX � qU\]V+N�Wg^cVCW ����P-W�K�TQMON�l@MUqUW W�\�W�K+M K�^_T�bf\]V+PRqUN�( J K�^_W1^cV+X W�K+M9n ^cqUWjW�K�^_W1W�K+Mfp-\]NQN\��CMUT ^�nwM�� qOMOVCW�PRbfM:W�MUT�N1P-N1NQb9^cp-p/^cp-pR\��HNjW�K+M9\]tuWQl�tuW nwt+V+X�^cbfMOVCWg^cpEl@\���MUT W�\ Y M9t+NQMOX.��/^_T�P ^_WQPR\]V+N P-V5qO\]tul�pRP-V+v�M � qUPRMOV+q Z pRMOX W�\�P-V+qO\]V+NQP-N�Wg^cVCW T�MONQt+pFW�N5�HK+MUVDWQK+M T�MOqO\cTQX+MOX P-V90l�tuWyl@\���MUT �L^cNjt+N�MOX.� JLK+M \]tuWQl�tuWjl \���MUT T�MO^cX+PRV+v�P-V+qOpRt+X+MUX�W�K+M pR\]NQNj^cNQNQ\BqOP ^_W�MUX ��P-W�Kx Y MUT2qO\]tul�p-PRV+v+��NQ\sP-W l+T�\ �CMUX�W�\ Y Mjb t+qgK`bf\cTQMj^cqUqOtuTg^_W�M#� �kPRNQt�^cp�^cV+X�bf\]V+\{qgKuT�\]b9^_WQ\cTP-V+N�l@MOq:W�PR\]V�l+TQ\ �CMOX�W�K+Mjp-PRv]KCW���^cN�W�K+PFT�X�K�^_T�b \]V+PRq#��IaqOqO\cTQX+PRV+v W�\ \]tuTHl+TQMOX+PRqUWQPR\]V+N�(

� � + � � � � X � � � %NQ\`WQK+M9pR\]v�\]n�W�K+M9NQp-\cl@Mf\]nL\]tuWQl�tuW WQK+P-T�X5K�^_T�b \]V+PRq W�\�P-Vul�tuW nwt+V+X�^cbfMOVCWg^cp/N�K+\]t+pRX Y MW�KuTQMOM#�EJ K+P-N�NQpR\cl M2\]n@W�KuT�MUM2q#^cV Y M2N�MOMOV PRVfW�K+M�T�MOnwMUT�MUV+qOMkpRPRV+MUN6�HK+P-qgK�K�^#�CM Y MOMOV�^cX+X+MOX.�iy^_Wg^ l@\]PRVCW�N ��MUT�MyWg^ � MOV�^_WHNQM:�CMUTg^cp�PRVul�tuW�l@\���MUT2p-MU�CMOp-N��

ILW x+TQN�W W�K+Msp ^cNQM:T5�L^cN \cl MUTg^_W�MUX5^_W ^�l�t+p-NQM T�M:l@MUW�PFW�PR\]V�n T�MOz{t+MUV+q Z \]n + �,0-��,ah#�JLK+MONQM�l�t+p-NQMON&��M:T�M�^ Y \]tuWC2 � � V�^cV+\]NQMUqO\]V+X+N pR\]V+v5^_Wsnwt+pRp �HP-XuW�K ^cV+X K�^cpRnHb9^ �+P-b t+bK+MOP-v]K W����2l W�\5K t+V+XuT�MOX+N \]n �L^_W�W�Nf\]n2l@MO^ � l@\���MUT7��MUT�M�P-Vul�tuW PRVCW�\�W�K+M`x Y MUT���J K+M\]tuWQl�tuWkP-NaT�MUl+T�MON�MOV WQMOX Y Z W�K+M X�^_Wg^9PRV8W�K+M p-\���M:Tjp-MOn WkK�^cV+X qO\cT�V+MUT�Nk\]n�W�K+M1l�pR\cWQN��yJ K+Mtul+l MUTaT�PRv]KCWaK�^cV+X8X�^_Wg^1��^cN2\ Y Wg^cPRV+MUX P-V�\cT�X+MUT2WQ\9PRV+qUT�MO^cNQM1W�K+M1X Z V�^cbfPRqyTg^cV+v]M1\]neW�K+Ml�p-\cW�N WQ\ T�MO^cpRp Z N�K+\��dW�K+M�NQpR\cl M�\]n�W�KuT�MOM#� JLK+PRN X�^_Wg^�L^cN \ Y Wg^cP-V+MOX Y Z pR\���MUT�P-V+v�W�K+M� � N ��P-W�qgK Tg^_WQM W�\ � �10+��,ah#��I WEW�K+PRNEn T�MOzBt+MOV+q Z W�K+M�l M#^ � l@\���MUT4T�M#^cqgK+MOX9P-V W�\ � P-pR\��L^_WQW�N��

JLK+M�N�l+T�M#^cX P-V W�K+M�X�^_Wg^8l@\]PRVCW�N qO\cTQT�MUN�l@\]V+X+N W�\ ^8N Z N}W�MOb9^_W�P-q9l+T�\ Y pRMOb �DJ K+MqOp-\]NQMON�W Y t+V+qgK+MON2\]n!l \]PRVCW�NH^_TQM pR\Bq#^_W�MOX�V+M#^_T�W�K+M bfMUX+P ^cV+N�^cV+X�W�K+MyNQPRV+v]p-Mjl@\]P-V WQNH^_T�Mj^_WMOPFW�K+MUT MOV+X.� � I2l+l@MUV+X+P � I qO\]VCWg^cPRV+N�X�^_Wg^ l�pR\cWQN�nw\cT�MO^cq6K x Y M:T ��K+MUT�MaW�K+MkX�^_Wg^ bfMUX+P ^cV+N��M:T�M1x+WaW�\LU?WYX[Z�qOtuT��CMON ���yJLK+M K+PRv]K8X�^_Wg^ l@\]P-V WQNaqO\]t+pRX Y M ^_W�WQT�P Y tuWQMOX�W�\&��\cT � PRV+v9PRV ^V+\]V+p-PRV+M#^_T�TQMON�l@\]V+N�M2T�MOv]PR\]V9\]n@WQK+M2l�K+\cW�\]b t+p-W�PFl�pRPRM:T4W�t Y M#�4J K+M2p-\��*l@\]P-V WQN�^_T�MHl+T�\ Y ^ Y p Zq#^ct+N�MOX Y Z W�K+M�p-PRbfPFW�MOXD^cqOqUtuTg^cq Z l+T�\��uPRX+MUX Y Z W�K+M�N�qO\cl@M#�DJLK+M�NQPRv]V�^cp��C\]pFWg^cv]M9pRMU�CMUpRN��M:T�M`Wg^ � MOV*^cN W�K+M�b M#^cV \]naW�K+M2�HP-XuW�K \]naW�K+M`l�t+pRN�M`WQTg^cqOMON�� J K+M`l�t+p-NQMON ��MUTQM8^cpRNQ\\]NQqUPRpRpR^_W�PRV+v�tulD^cV+X X+\���V nw\]pRp-\���PRV+v W�K+Msp ^cNQMUT � � N �HPFW�qgK.� JLK+M P-V+N�Wg^ Y P-pRP-W Z \]nEW�K+M pR^cNQMUTl�t+p-NQM2^cV+Xf\]tuW�l�tuW4l \���M:T�q#^cV Y M2^_W�WQT�P Y tuWQMOXsW�\jNQ\]bfM \]nW�K+M PRV�^cqUqOtuTg^cq Z � ^jnwM���X � n T�\]bW�K+Mkl�pR\cWQN ���

��(

Page 99: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

������������ � � � � ��� � � � � � ��� � � � � � � � ��� � � � � � ��� � �

� T�\]b&W�K+MaW�K+PFT�X�K�^_TQbf\]V+PRqaX�^_Wg^u�uWQK+MjbfMO^cNQtuT�MOX��c^cp-t+MONLnw\cT U?W X[Z ��MUTQMjMU�_^cpRt�^_WQMOX.�[ PRV+M2x+W�N ��MUT�Mab9^cX+M2t+N�PRV+v1�_^_T�PR\]t+N U W X[Z �_^cpRt+MUN�� � \cTL^1N�PRV+v]pRM2W Z l@MHx Y MUT �HPFW�K ^ N�l@MUqOP-x�qqO\cTQMyN�PRhOMk^cV+X�pRMOV+vcWQK>�+pRPRV+MUN�\]n�NQp-\cl@M2W�KuTQMOMal+T�\cl@\cTQWQPR\]V�^cp W�\ U?W X[Z�qO\]t+p-X Y Mal�pR\cWQWQMOX.�EJ K+MX�^_Wg^ bfMO^cNQtuT�MOX�K+MUT�M+�L^cN�x+WLW�\ W�K+MONQMypRP-V+MON��ES/pR\cWQNL^_T�MkNQK+\���V-��P-WQK �_^cpRt+MUNLWQK�^_W Y MON�WLx+WW�K+MyX�^_Wg^ �4J K+Myx�V�^cp>�c^cp-t+MONHnw\cT W�K+M nw\]tuT�x Y MUTQN2^_T�MypRP-N�W�MOX.�

Iap-p@x Y MUTQN � 09�10 qOMOVCW�PRb MUW�MUT�N PRV�pRMOV+vcWQK.�

� \cT1W�K+M pR\]V+v]MUT p-MOV+vcW�KD\]n�MUT Y P-t+b x Y M:T � U W X[Z �L^cN1q#^cp-qOt+p ^_WQMOX�^cNf� � � #�! �`JLK+PRNp-\���M:Ta�c^cp-t+M nw\cTaW�K+M N�^cbfM x Y MUTyq#^cV8bf\]N�WHpRP � MUp Z�Y M ^_WQWQT�P Y tuW�MOX�W�\ ^ Y NQ\cT�l+W�PR\]V.�aILWaW�K+Mn T�\]VCW4MOV+X \]n�W�K+MLx Y MUTEW�K+MLPRVul�tuWEl@\���MUT4PRN�vcT�M#^_WQMON�W�( | \]N�WE\]nmW�K+M�W�K+P-T�XsK�^_T�bf\]V+P-q�PRNel+T�\�0X+t+qOMUXfK+MUT�M#��IaNeW�K+MLW�K+P-TQX K�^_T�bf\]V+P-q�l+T�\clm^cvC^_W�MONEX+\���VsWQK+M x Y MUT/PFWEb9^ Z Y MLT�M#^ Y NQ\cT Y MOX.�JLK+M1MUT Y P-t+b WQT�^cV+NQbfPRN�NQPR\]V�N�l@MOq:WQT�t+b NQK+\���MOX8NQ\]b M ^ Y NQ\cT�l+W�PR\]V8^_W�W�K+PRN �L^��CMUpRMOV+vcW�K.�LI

�#

Page 100: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

D ��> NF� A

� � � ��� � � � �� � �� � � ����� � � � � � � � � � �

� P Y MUT r�\cT�MyikP ^cbfMUWQMUT � @b � U W X[Z PRV � #� #

Y 0 oET 2 - �L� ��� # # Y 0 oET + � �.- �L� � � # #o4T � � �10 - �L� � � !�JLP-Wg^cV �9�10 � �,+ �L� � � !�

v]\B\{X �L^ Z W�\ W�MON�W W�K+P-N ��\]t+p-X Y MyW�\st+NQM1^cV�I2T�v]\]V�pR^cNQMUT �HPFW�K W�K+Mjx Y MUT2^cV+X�X+MUW�MUT�b PRV+MK+\�� b t+qgK \]nLW�K+M Y M#^cb qO\]tul�p-MOX P-V W�\8W�K+M x Y MUT"�L^cN ^_WQW�MUVBt�^_W�MUX.� IaV+\cW�K+MUT l@\]NQN�P Y PRp 0PFW Z ^_T�PRNQMUNyn TQ\]b W�K+M x Y MUTyqO\cT�M X+P ^cb MUW�MUT��kILWkW�K+M nwt+V+X�^cbfMOVCWg^cp �L^#�CMOpRMOV+vcWQK PFWkb9^ Z�Y MNQP-V+v]pRM�0 bf\{X+M Y tuW ^_W W�K+M W�K+P-TQX K�^_T�b \]V+PRq9P-W ��PRp-p Y M b t+p-W�P 0 bf\BX+M#� rL\]tul�p-PRV+v8W�\ pRM#^ �BZbf\BX+MON qO\]t+pRX�\{qOqOtuT2^cV+X�^_WQW�MUVBt�^_W�MkW�K+MjNQPRv]V�^cp �

S � A � � � ���7N���* �F� ��*

�2�CMUTg^cp-pW�K+M2TQMONQt+p-WQNL^_T�M2v]\{\BX.�eIapRpmx Y MUT�N�M��+K+P Y PFW�MOX bfM#^cN�tuTg^ Y pRMHWQK+P-T�X K�^_T�bf\]V+P-qv]MOV+M:Tg^_W�PR\]V.��IapRp�W�K+M x Y M:T�NkK�^��CM �_^cpRt+MUNa\]nEN�t+NQqOMUl+W�P Y PRp-P-W Z W�K�^_Wa^_T�M ^_W2p-M#^cN�Wk^cNapR^_T�v]M ^cNW�K�^_Wjnw\cTjnwt+NQMOXDNQPRp-PRq#^ v]p ^cN�NO�4� ��� # # �sJ K+P-N K+MOpFl�N NQtul+l \cTQW WQK+Ms�_^cpRPRX+PFW Z \]n/W�K+M VBt+b Y M:T�N��JLK+M Y MUWQW�M:T TQMONQt+p-W P-NLWQK�^_W WQK+Mkx Y MUT�N K�^cX��_^cpRt+MONL\]n:U W X[Z W�K�^_W ��MUT�MkW ��\ WQ\ WQKuT�MOMy\cT�X+MUT�N\]n@bf^cv]V+P-W�t+X+M K+PRv]K+MUT��4JLK+MONQM2^_T�MHV+\cW4Tg^cX+PRq#^cp��_^cpRt+MON Y MOq#^ct+N�M2\cW�K+MUT/X+\cl@MOX9v]pR^cNQNQMON4K�^��CMY MOMOV`bfMO^cNQtuT�MOX�^_WL�_^cpRt+MON�K+PRv]K+MUT2^cV+X`pR\���MUT��

� W4PRN/^ Y P-W4\]n>^ N�tuTQl+T�PRN�M�W�K�^_W4W�K+M Z WQW�MUT Y P-t+b10 M:T Y PRt+b X+\cl@MUX x Y MUT�K�^cX W�K+MHp-\���MON�WV+\]V+p-PRV+M#^_TeN�t+NQqOMUl+W�P Y PRp-P-W Z � � W �L^cN Y MOp-PRMU�CMUX1W�K�^_W!W�K+M/K+PRv]K1qO\]V+qUMOV W�Tg^_W�PR\]V \]nuP-\]V+N ��\]t+p-X Y M^ q#^_Wg^cp Z N�W�nw\cTLK+PRv]K+MUTLW�K+PFT�X K�^_T�bf\]V+PRq2l \���MUT��/~{PRV+qOMaW�K+M2l�pR^cPRV MUT Y P-t+b K�^cX�W�K+MaK+P-v]K+MON�W�_^cpRt+Mc��W�K+MsqO\{X+\cl�P-V+v�qO\]t+p-X Y M W�K+MsTQM#^cNQ\]V�nw\cT NQb9^cp-pRMUTyNQt+NQqUMUl+W�P Y P-pRPFW Z � JLK+M Z WQW�MUT Y P-t+bP-\]V+NjvcT�MO^_W�p Z \]tuWQVBt+b Y M:TjW�K+M MUT Y P-t+b PR\]V+N�� JLK+MOP-Tkl�tuTQl \]NQM P-NyW�\�NQMOV+N�P-W�P-hOM WQK+MsMUT Y PRt+bP-\]V+N��2I�WQTg^cV+N�nwMUTy\]nEMUV+MUT�v Z�Y MUW ��MOMOV8W�K+M1W ��\ PR\]V+NH\{qOqOtuTQN��aI Y ^cq � WQTg^cV+NQnwM:Tj\]n�MOV+M:T�v Zq#^cV ^cpRNQ\y\{qUqOtuT��EJ K+M Y ^cq � WQTg^cV+NQnwMUT/\]n MOV+M:T�v Z qO\]t+pRXfK�^#�CM q#^ct+NQMOX9^kT�MOX+t+qOMUX l@\cl�t+pR^_W�PR\]V

� "

Page 101: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

P-V W�K+M M��+qUP-W�MOX N�Wg^_WQMON�� J K+P-N Y ^cq � ^cV+X�nw\cT�W�K�MOV+M:T�v Z WQTg^cV+NQnwMUTjl+T�\{qUMONQNj^cbf\]V+v�WQK+M W ��\P-\]V+N�N�WQPRpRp>V+MUMOX+NHW�\ Y M N}W�t+X+PRMOX.�

JLK+MaT�MONQt+pFW nw\cT WQK+MjJLP-W�^cV�x Y MUT �L^cN ^cpRNQ\ t+V+M��ul MOqUW�MUX.�%� W �L^cN�W�K+\]t+v]KCW WQK�^_W WQK+PRN�L^cN�\cT�X+PRV�^_T Z qO\]bfb t+V+PRq#^_WQPR\]V+NLx Y MUT��'� n!X+\clm^cVCW�N2M��uPRN�W W�K+M Z b9^ Z K�^��CMjqO\]VCWQT�P Y tuWQMOX�W�\^cV8MOV+K�^cV+qOMUX U?WYX[Z � � V+nw\cT�b9^_WQPR\]V2�L^cNaV+\cWk\ Y Wg^cP-V+MOX8\]V WQK+M X+\clm^cV W�Nk\]neW�K+P-N2lm^_TQW�PRqUt+p ^_Tx Y MUT��%� W�b9^ Z V+\cWHK�^#�CM Y MOMOV�^ v]\{\BX�qgK+\]PRqOMjnw\cTa^ T�MOnwMUT�MUV+qOM x Y M:T��

JLK+M9l�p ^cP-V MUT Y PRt+b x Y MUTsb9^ Z K�^#�CM Y MOMOV X+\cl MOX ��P-WQK ^8K+PRv]K+MUT qO\]V+qUMOV W�Tg^_W�PR\]VW�K�^cV�W�K+\]t+v]KCW��/JLK+M M:T Y PRt+b qO\]V+qOMOVCWQTg^_WQPR\]V+NH\]n�W�K+MyMUT Y PRt+b X+\cl@MUX�^cV+X�W�K+M Z WQWQMUT Y PRt+b"0MUT Y PRt+b X+\cl@MUX8x Y MUT�N+��MUTQM qU\]b lm^_T�MOX Y Z qO\]b lm^_T�P-V+v ^_WQW�MOV t�^_W�P-\]V X�^_W�^ �kJ K+M X�^_Wg^9nw\cTW�K+M l�p ^cP-V�X+\cl@MUX MUT Y P-t+b x Y MUT1b9^ Z V+\cW K�^#�CM Y MOMOV5^cqUqOtuTg^_W�M#� J K+MsX�^_Wg^�^cp-NQ\�N�K+\���MUXW�K�^_W W�K+Mfx Y MUT ��P-W�K5pR^_T�v]MON�W1qO\cT�M9X+P ^cb MUW�MUT K�^cXDW�K+M9K+P-v]K+MON�W �_^cpRt+M9\]n U W X[Z ��JLK+M n ^cqUWW�K�^_W/W�K+MkMUT Y PRt+b X+\cl@MOX x Y MUT K�^cX9W�K+MkK+PRv]K+MUN�W�W�K+P-TQX�\cTQX+MUT NQt+NQqOMUl+WQP Y PRp-P-W Z NQtul+l \cTQW�NL\]tuTl+T�MUX+PRqUW�P-\]V+N�W�K�^_WH^sK+P-v]K+p Z X+\cl MOX`x Y MUT���\]t+pRX�PRV+qUTQM#^cNQM V+\]V+p-PRV+M#^_THM� @MUqUW�N��

JLK+MabfM#^cN�tuT�MObfMOVCWL\]n>W�K+P-TQX�\cTQX+MUTLNQt+NQqOM:l+W�P Y P-pRP-W Z P-N�\]V+Mk^cqOqO\]b l�p-PRNQK+b MOV W�\]n�WQK+PRNW�K+MUNQPRN�� JLK+PRN T�MON�M#^_T�qgK X�^_Wg^ �HP-pRp Y M�^ Y p-M W�\Dl+T�\��uP-X+M�^cV+N ��MUT�N�WQ\ ^_W�pRMO^cN�W�^�nwM�� \]nW�K+M zBt+MON�W�P-\]V+N2W�K�^_W+��PRpRp Y M MUV+qO\]t+V WQMUT�MOX PRV�W�K+M X+MU�CMOp-\cl�bfMOVCWk\]n�X+MU�uP-qOMONaW�K�^_W ��PRp-p!t+NQMNQzBt+MOMOhOMUX N�Wg^_WQMON�� IaV+\cW�K+MUT�^cqUqO\]b l�pRP-NQK+bfMOVCW9\]nkW�K+PRNfWQK+MONQPRN9P-NfW�K�^_W P-WfK�^cN�P-X+MOVCW�P-x�MOXNQ\]b M � M Z W�MUq6K+V+P-q#^cp+PRN�NQt+MON �HK+P-q6K T�MOzBt+P-T�M�nwtuT�W�K+MUTET�MONQM#^_TQq6K.�4~{\]bfM�P-V WQMUT�MON�WQPRV+vkz{t+MON}W�PR\]V+NK�^#�CM ^cpRNQ\ Y MOMUV Tg^cP-NQMOX.� � W��L^cNknw\]t+V+X WQK�^_W ^cV PRVCW�MOV+N�Ms\cl+W�P-q#^cp"l�t+b l�L^cNaT�MOzBt+P-T�MOX8W�\l+T�\BX+t+qOM�zBt�^cXuTg^_W�tuT�M�0'l�K�^cNQM�0 NQz{t+MOMUhOMOX N�Wg^_W�MON�\]nupRP-v]K W�� � V1\cT�X+MUT�W�\2^_l+l�p Z W�K+P-N�W�MUq6K+V+\]p-\]v ZW�\�X+MU�uP-qOMONjNQt+qgK5^cNjW�K+M x Y M:T1\cl+W�P-qsv Z T�\]NQqO\cl MsPFW b t+N�W Y M X+MUW�MUTQbfPRV+MOX�PRn4WQK+M PRV+q:T�M#^cNQMP-V t+V+qOM:TQWg^cPRVCW Z �/P-V WQTQ\{X+t+qOMOX n T�\]b ^cV P-V WQMOV+NQM�N�\]tuT�qOMc�4PRN \]tuW ��MOPRv]K+MUX Y Z WQK+M�X+MUqUT�M#^cNQMP-V t+V+qOMUTQWg^cP-V W Z ��^_WQWQT�P Y tuW�MOX W�\ WQK+M`l�K�^cNQM8NQz{t+MOMUhOPRV+v�� �2W�K+MUT W�MUq6K+V+P-q#^cpHT�MUz{t+P-TQMObfMOVCW�N\]V W�K+M9N�\]tuT�qOM9T�MOpR^_W�PRV+v�WQ\8^`qO\]b l�pRM:W�MfN Z N�W�MOb ��PRp-p4\ Y �uP-\]t+NQp Z K�^��CMfWQ\ Y M9qO\]V+N�PRX+MUT�MUX^cp-NQ\�� � t+b Y MUT 0 NQz{t+MUMOhOMOX NQ\]tuTQqOMONf^cV+X�W�K+MOPFT NQzBt+MOMOhOP-V+v pRP-bfP-W1NQK+\]t+pRX Y M�P-V �CMUN�W�PRvC^_WQMOX.�o �ul@M:T�PRbfMUV W�N�T�MOqUMOV WQp Z qO\]V+X+t+qUW�MOX K�^#�CMHNQK+\���VfW�K�^_W�qOpR^cNQNQP-q#^cp ^cN ��MOp-p ^cN4z{t�^cVCW�t+b V+\]PRNQMq#^cV Y M2NQz{t+MUMOhOMOX�PRV \cl+W�P-q#^cpmx Y MUT�N��4JLK+MONQMkM��ul MUT�P-bfMOVCW�N�MOb l�p-\ Z MUX9t+V+X+\cl@MOX�NQPRp-PRq#^1v]pR^cNQNx Y MUT�N���J K+M�b9^ �}\cT V+\]P-NQM`NQ\]tuT�qUM�PRV NQzBt+MOMOhOP-V+vDz{t�^cVCW�t+b V+\]P-NQM-�L^cN v]t+PRX+MOX*^cqO\]t+N�WQPRq�L^#�CM � T�P-pRpR\]t+P-V NQq#^_W�W�MUT�P-V+v�� | MUW�K+\BX+N \]n�T�MOX+t+qOP-V+v \cT1^��C\]P-X+PRV+v`W�K+P-N1V+\]PRN�MfNQ\]tuT�qOM ^cV+X\cW�K+M:T�Nkb t+N}W Y M X+MUW�MUTQbfPRV+MOX�W�\�^cp-pR\���vcT�M#^_WQMUTkNQz{t+MUMOhOPRV+v W�\ \{qUqOtuT�� � PRV�^cpRp Z �@V+\]V+pRP-V+M#^_TM� MOqUW�N PRV��_^_T�PR\]t+NyW Z l@MUN \]n/x Y MUT�N1b t+N�W Y M nwtuT�W�K+MUT N�WQt+X+PRMOX.�9I&qU\]V W�P-VBt+MUX5PRVCW�MUT�MON}W PRVV+\]V+p-PRV+M#^_T x Y MUTQN2qO\]t+pRX�pRM#^cX�W�\ ^cV�M � qOP-MOVCW2NQzBt+MOMOhOP-V+vfX+MU�uP-qOM P-V�W�K+MynwtuW�tuT�M��

� �

Page 102: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� )�) ���!A2����� � � ���{���f.$�e�C�

� �

Page 103: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� �

Page 104: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

��� 0������ ����� <

� \ Z X>��*H\ Y MUTQW�� �-� � � � ��� � ��� � � � �� ������� � ��� � � � � � � � ��� � � � � � ��� �>��� � + �

� \ Z X>��*H\ Y MUTQW�� �-� ����� � ��� � � � � � � � � �����]� � �rL^��CMUNO�mr ^_TQp-W�\]V | �R��� � t�^cVCW�t+b10 b MOqgK�^cV+PRq#^cp>V+\]P-NQMkPRV�^cV�P-V W�M:T�nwMUT�\]bfM:W�MUT#� � � � � ��� � � � � ��

�� � � � �/\]p � � +u� � \��%�u��I2l+T�P-p���0{�>��� �u� ��l+l ���2]� + 0���3 � � �

r�Tg^cPRv�0 * Z ^cV>�~ ��S$�R� � ������IaPRV+NQp-PRMc� � � � � � ��� � ����� ��� � � � ��� � � � � � ��� �� � � � � � � � �����]�u� �

o4hOM � P-MOp'�m~ �-��,�� ����I2T�X+PFWQW Z �+MOX.� ��� � � � � � � � � � � � � � � ��� � �� � ��� � ����� � � �

�k\]pRX+PRV>��o4X �HP-V>� �� � � � � ��� ����� �� � �� ��� � � ����� � ��� ��� � � � � ����� � � � � � � ����� � � �

,k^_T�X Z �+I��r+�R� � ��,���SeMUTQT�P-V>� � �� � ��� � � � ��� � � � � � � ��� ����� + � �

,k^ct+NO��,��+I��-���1� � MUT�v]b9^cV>� ��~{z{t+MOMOhUPRV+vfP-V�x Y M:T�N���P-W�K�\cl+W�P-q#^cp>l�t+pRNQMONU��� � � � � � � �� �� � � �� \��L�2u�����]�u�]�ul+l � 2 2 + 0 2 2&39�

,k^ct+NO� ,��>I��-�.�1� � MUT�v]b9^cV>� "� [ ^cP � � � P Y MUTyv Z T�\3��P-WQK NQzBt+MOMOhOMUX�Tg^cX+P-W�^_W�PR\]V>� ��� � � � � �� � ��� � � � � ���4\]p �'�u� � \��E�u� ~{M:l+W�MOb Y MUT ���]�u� �el+l �H���&0 � 0����&0 39�

[ MU�CMOV+NQ\]V>� | ^_T�q`i �-� � � M#^cN�P Y PRp-P-W Z \]n | M#^cNQtuT�P-V+v W�K+M � \]V+pRP-V+M#^_T7� V+X+M�� \]n+*HMOn T�^cqUW�PR\]VY Z J K+PFT�X90 �2T�X+MUT � T�MOzBt+MOV+q Z | P �+P-V+v+��� � � � � � ��� � � � � �� � � ������� � � ��� ���� � � � � �/\]p �� o'0Q� �u� � \�� � � � M Y T�t�^_T Z ���&3G-���l+l �R�]� � 0��]� -��

[ MU�CMOV+NQ\]V>� | �>i �R�.* � | ��~{K+MOp Y Z ��~ �.,��@SeMUT�p-b tuWQW�MUT#� ��~{z{t+MOMOhUPRV+v�\]n�qOpR^cNQNQP-q#^cpeV+\]PRNQM Y ZV+\]V+X+MOv]MUV+MUTg^_W�Msnw\]tuT 0 �L^#�CM b P �+P-V+v PRV ^cV�\cl+W�P-q#^cp"x Y MUTO��� � � � � ��� � �� ���� � � �/\]p �f� �u� � \��� �u�m�aqUW�\ Y MUT1��� �&09��l+l � 0{� -�0 0{�2 �

[ MU�CMOV+NQ\]V>� | �i"�-� * � | �>~{K+MOp YBZ �@I��IaN�l@MUqUW#� | � *�MOPRX>�@^cV+X i � � ��D^cp-pRNO� � �yMOV+MUT�^_W�PR\]V^cV+X X+MUW�MUqUW�PR\]V \]n�NQz{t+MUMOhOMOX N�Wg^_W�MUNe\]nmp-PRv]KCW YBZ V+\]V+X+MOv]MOV+MUTg^_WQM nw\]tuT 0 �L^#�CMLbfP �uPRV+v+��� � � � � �� � � ���

�� � � ���4\]p �?+ � � � \��?+u� ~{M:l+W�MOb Y MUT ��� �&09�el+l �H��0 0 � 0���0�2 � �

| ^cMOX�^u� | ^_T�P"� �R�>SET�MOb �yt+b9^_T#��^cV+X �]M� T�M Z ,���~{K�^_l�P-TQ\+� ��� Y NQM:TQ�c^_WQPR\]V�\]n�NQzBt+MOMOhOMUXV+\]P-NQMHl+T�\BX+t+qOMOX Y Z nw\cT �L^_TQX9nw\]tuT 0 �L^#�CM2bfP �+P-V+v PRV NQ\{X+P-t+b �_^_l@\cT#� � � � � � � � � �� � � � � �/\]p �� � � � \�� +u� | ^_TQq6K���� �&39��l+l ���2u��0��2 + �

| ^_T�qOt+N�Mc�ikP-MUWQT�P-q6K>� � ���� � � ��� � � �� � � ��� ��� � � ��� � ��� � � � ����� � � �� �

Page 105: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

| ^_TQW�M_� | �EI��R��i � � �E�5^cpRpRNU� ��o/V+K�^cV+qOMOX NQMUV+NQP-W�PF�uPFW Z \]n2x Y MUT 0 \cl+WQPRq�T�\cW�^_W�PR\]V N�MOV+NQ\cT�N��P-W�K NQz{t+MUMOhOMOX p-PRv]KCW#��� � � � � � � ��� � � � � ���4\]p � -+� � \��*�]�]� � \��CMOb Y M:T���� �&39�Dl+l �����-C� 0Q���&0�+ �

| PRp Y tuT�V>�/�"� ���-� | ��i � [ MU�CMUV+NQ\]V>��* � | ��~{K+MOp YBZ ��^cV+X i � � �4�5^cpRpRNU� ���2l+W�P-q#^cp 0'x Y MUTbfMUX+P ^�nw\cT NQz{t+MUMOhOMOX90 N�Wg^_W�M�v]MOV+MUTg^_W�P-\]V>��� � � � � � � � � � � � �� � � � � ��� � � � � �4\]p � -+� � \��� �u�m�aqUW�\ Y MUT1��� �&39��l+l ��� -73�2 0Q� - � � �

��aN�W�MUT Y MUT�v+����R��� � | ^_T�v]t+pRP-NO����i Z Mjp ^cNQMUTHl�t+b l@MOX Y Z � X.(! /I � p ^cNQM:THl�t+pRN�MONan T�MOzBt+MOV+q ZX+\]t Y p-MOX`PRV�^sv]pR^cNQNH\cl+W�P-q#^cp@x Y M:T#��� � � � � � � �� ���� � � � \�� �]�]����� � 2u�ul+l �,0{�2 0 0{��� �

��aN�W�MUT Y MUT�v+�m���R�+� � | ^_T�v]t+p-PRNO� ��o'�{l@MUT�P-bfMOVCWg^cp�~BW�t+X+P-MON2\]V`M� @MOqOP-MOVCWan T�MOzBt+MOV+q Z X+\]t Y p-PRV+vP-V�v]p ^cN�N�\cl+W�P-q#^cp>x Y MUTQNO��� � � � � � � �� ���� � � � \�� �]�]����� �&3{�ul+l �,0 3�0 0c�

��aN�W�MUT Y MUT�v+� � �kT�\���WQK5\]n�J K+PFT�X ,k^_T�bf\]V+P-qf~{P-v]V�^cp�PRV��2l+W�PRq#^cp6�ypR^cNQN � P Y MUTO��� � � ��� � ��� � �� �� ���� � � �/\]p � � 2u� � \�� � � �C^cVBt�^_T Z ���]� � �el+l �R� � + 0Q� ��-��~u^cpFW�PRMOp �c~ � | � � � �/^cVj�5\]VCW�MUTQv]K+MOb`�c^cV+X S$� | ��*HMOVCW�hOM:l�PRNO� �QJLK+M�JLK+P-T�X �aT�X+M:T � \]V+pRP-V+M#^_T~{t+NQqUMUl+W�P Y P-pRPFW Z \]n2~{MObfP-qO\]V+X+t+qUW�\cT ik\cl@MOX �ypR^cNQNQMONs^_W [ \�� Se\���MUTso'�uqOP-Wg^_WQPR\]V>��� � � � � �� ��� � � � � � � � � ��� � � �4\]p � 3 3{� � \��L�]� �Ct+V+Ms���]� � �el+l �10c� 0 2�-��

~{p-t+NQK+MUT#� * � o��R� [ � � ��,a\]pRp Y MUT�v+� � �� /tuT � Mc� ���_r�� | MUTQW�h_�]^cV+X ��� � � ��^cp-pRM Z � ��� Y NQMUTQ�_^_W�PR\]V\]n�NQz{t+MOMUhOMOX N�Wg^_WQMONsv]MUV+MUTg^_W�MOX YBZ nw\]tuT 0 ��^��CM�bfP �uPRV+v8PRV ^cV \cl+W�PRqO^cp�q#^��{P-W Z ��� ��������� � � ��

�� � � � �� � � ���4\]p � 0 0{� � \�� �]� � � \ �CMOb Y MUT � 0{�>��� �&09��l+l � � - �]� 0 � -+� � �

~{V+PFW�hOMUT#��o��R����� ~ �+S�^_W�MUV W � -+�-� � 2u� �&0 39�����&3#� �

~BW�\]p-MUT#�Ciy^��{PRX>� ��o/z{t+PF�c^cp-MOV+qOM r�p ^cNQN�MON4\]n | PRV+P-b t+b �aV+qUMUTQWg^cP-V W Z S�^cq � MUW�NO� � � � � ��� � � � � ���� � � � �/\]p ���]� � \���� � ���]t+V+M ���&3 � ��l+l � + � ��3�0 + � ��� �

�D^cp-pRNO�Ei � � �R� ��~{z{t+MOMUhOMOX N�W�^_W�MON \]nHp-PRv]KCW#��� � � � ��� ���/\]p �E+ � 2u� � \ �CMOb Y MUT���� � + ��l+l �� -+��0Q� -&2 �

�5t>� [ P-V+v�0 IaV>� ,�� ��� �yPRb Y pRMc�6��� [ � ,k^cpRp �/^cV+X ,at+PRn ^ � t>� � �yMOV+M:Tg^_W�PR\]V \]nHNQzBt+MOMOhOMUXN�W�^_W�MON Y Z lm^_Tg^cbfMUW�T�PRqjX+\���V qU\]V �CMUTQNQPR\]V>� � � � � ��� � � � �

�� � � �� �� � � � �/\]p � 0 3{� � \�� � �u�

� \��CMOb Y MUTj��3{�>��� � 2 �el+l � � 0 � � 0 � 0 � + � �^cb9^cbf\cW�\+� "�R�m~ � | ^cqgK+PRX�^u� � ���}b \cW�\+� | ���jPFWg^cvC^���^u��^cV+X��"� � � �\cT � � � �kMOV+MUTg^_WQPR\]V`\]nV t+b Y MUT 0'l�K�^cNQM bfP-V+PRb t+b10 t+V+qUMUTQWg^cP-V W Z N�Wg^_W�MUNa^cV+X�VBt+b Y MUTkN�Wg^_W�MUNO����� � � � � � � � � � � � �� ���4\]p � -+� � \�� � �u����� �&39�el+l �H�2�-70�0Q�2 2u� �

���

Page 106: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

/t+MOV>�.,a\cTg^cqOM S$�-� �kPRV+qOMUV Wk� ��~ ��rLK�^cV>� � � \]PRNQM P-V K+\]b \{X Z V+M ^cV+X K+MUW�M:T�\{X Z V+MsX+MUWQMOq�0W�P-\]V>��� � � � � � � � �� �� � � � �4\]p �'�u� � \�� +u� | ^_T�qgK5��� � + �el+l �H��3 3�0Q��3c� �

&�� �

Page 107: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

� � � � � � ( � � � ��� 0 ����� ����� <

� MOV90 I2T Z MOK>�� "� ^cV+X � ��,atuWQW�V+MUTO� ��~{z{t+MOMOhUMOXs~BWg^_W�MON"SET�\{X+t+qUMOX � Z S/K�^cNQM�rL\]V �}t+vC^_W�P-\]V>���� � � ��� � � � � �� � � � � �/\]p �L� -+�]� � \��6�u� �u� � \ �CMOb Y MUT ��� �]� �el+l � + 2&3�0 + 2]� �

rL^_T�bfP-q6K�^cMUp'� ��� ,��R��~{tuT�MOV+XuTg^D~{P-V+v]K>� *HMOM:Wg^ � Z ^cNO��^cV+X S$�'* �%*�PRqOM_� ��S/K+\cW�\BMOpRMUqUWQT�\]V�L^cPFW�PRV+vfWQPRbfMONk^cV+X ^_W�\]bfP-q N�W�^_W�M T�MOX+t+qUW�P-\]V P-V�T�MONQ\]V�^cV+qOM ��t+\cT�MON�qOMOV+qOMc� � ������� � � � � � ��

�� � � ���4\]p �?+]�u� � \��?+u� � M Y T�t�^_T Z �]����� �]� �el+l �H� � � � 0Q� � ��� �

rL^��CMUNO�+r+� | �-� � � [ �+~{qgK t+b9^ � MUT#� � � M��*nw\cT�b9^cpRP-NQb nw\cT�W ��\�0 l�K+\cWQ\]V9z{t�^cVCW�t+b \cl+W�P-qON��$���� t�^cXuTg^_W�tuT�M1l�K�^cN�MONk^cV+X�NQz{t+MUMOhOMOX N�Wg^_W�MUNO��� � � � ��� � � � �

�� � � � �/\]p �=+u�]� � \�� 0{� | ^ Z

��� �&09�el+l � + � 2 � 0 + �]� � �

ik\cT�NQqgK+V+MUTO�/J��"I��R�$,��!I�� ,k^ct+NO� | � ,a\]pRh_�4^cV+X ,���~BW�^_W�hc��� [ ^cN�MUT1� Z T�\ ^_W � t�^cVCW�t+b[ PRbfPFW#��� � � � � � ��� � � � � � � � � ����� � � � � ���� � ��� � �/\]p � � o'0Q�2u� � \�� � � ��ikMOqUMOb Y MUT��� � � �el+l �H�+&3�2 0Q�+&3c� �

�kp ^ct Y M:T#� *H\ Z ���R� ��rL\]K+MUTQMOV WE^cV+X P-V+qO\]K+MUT�MOVCW�N�Wg^_WQMON"\]n+W�K+M/Tg^cX+PR^_W�PR\]V1x�MUpRX>��� � � � ��� � ��

� �� � � � � �/\]p � �+u�]� � \�� 2u�m~{MUl+W�MUb Y MUT1��0{����� 2 + �el+l � � 3�2 2 0 � 3#� � �

,a\+�m~ �J��-� � �mr��+�5\]V+v+�^cV+X2��� ,��m~{K�^_l�P-T�\+����~{PRV+v]p-M�0 Y M#^cb N�z{t+MOMOhUMOX90 N�W�^_W�M1v]MOV+MUT�^_W�PR\]VP-V�NQ\BX+PRt+bd�c^_l \cT2^cV+X`PFW�NHN�MOpRn 0 nw\{qOt+NQP-V+v9pRP-bfP-Wg^_WQPR\]V+NO� � � � � � � � � �� ���� � � �/\]p � �2u� � \����]�]��]t+V+M ���]�u� �el+l �6��- � 0 ��- � �,a\]p-pRMOV+K+\cT�N}W#� � ^cb MON � �-� � � t�^cVCW�t+b pRPRb P-W�Na\]V T�MONQ\]V�^cVCW 0 bf^cNQN vcTg^#�uPFWg^_W�P-\]V�^cp 0 T�^cX+P ^_W�P-\]VX+MUWQMOqUW�\cT�NU��� � � � ��� �

�� � � �/\]p � ���u� � \�� 2u� | ^_T�qgK ��0{�����&3c� �el+l �H�2 2]� 0��2&3c� �

| ^cV+X+MOp � [ �R� � �� ��� � � �� � � � � � � ����� 2 + �

| PRp Y tuT�V>� � �%���-� � � t�^cVCW�t+b V+\]PRNQM�T�MOX+t+qUWQPR\]V Y Z l�K+\cW�\{X+MUWQMOqUW�P-\]V �HPFW�K nwMUMOX Y ^cq � ��� � �� � �� � � � � � � � ���4\]p �?+ �u� � \�� � �u�>���]�u� ��l+l �����&3�+ 0���� � � �| t>� yP2^cV+X�r�� | ��~u^��_^cv]Mc� ��S�^_Tg^cbfMUW�T�PRq�^cbsl�pRP-x�M:T�NfPRV l�K�^cN�M�0 V+\]P-NQM�0 p-PRbfPFW�MOX*\cl+W�PRqO^cpqO\]b b t+V+P-q#^_W�P-\]V+NO��� � � � � � � � � ��� � � � � ���/\]p �E�u� � \��L�]� �C^cVBt�^_T Z ���]� � ��l+l � 2&0�0 3 � ��at>� � �# "�R�{r�� � � ,a\]V+v+�B^cV+X [ � | ^cV+X+MOp � ��r�\]K+MUT�MOV+qUMHl+T�\cl@M:TQW�PRMUN�\]n@NQzBt+MOMOhOMOX9p-PRv]KCW�^cV+XW�K+M X+MUvcT�MOM \]n�NQz{t+MUMOhOPRV+v+� ��� � � � � � � � ��� � � � � � �4\]p �=-+� � \��j� �u�>�aqUW�\ Y M:Ts��� �&39� l+l ���0 3G-�0Q��0#�&39�

&���&

Page 108: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

Se\cWQWQ\]V>� * � ��� ��~{MOqO\]V+X K�^_T�bf\]V+PRq�v]MOV+M:Tg^_W�PR\]VjPRVj\cl+W�PRq#^cp]x Y MUT�N�(�b t+pFW�P-l�K+\cWQ\]V ^ Y NQ\cT�l+W�PR\]V^cV+X9WQTg^cV+N�p ^_W�P-\]V90 PRVC�CMUT�N�PR\]V N Z b bfMUWQT Z � � � � � � � � � � � � � � ���4\]p � + �u� � \��L� �u� ���]�u� �el+l ����&3c� 0Q��� �u� �

*�PRqOMc��S$� * �R� ,�� ����r ^_T�b PRqgK�^cMOp'� � � \]V+qOpR^cNQNQP-q#^cpeM� @MUqUW�NyPRV�\cl+WQPRq#^cp"N}l@MOqUW�Tg^u��� � � � � � � ���� � � � ���4\]p � 0{� � \��%�u��Iat+v]t+N�Wj��� � � �el+l �H�2 2u��0Q�2 2 � �

*�PRMOX>� | �]i �R�Ci � � �c�D^cpRp-NO� � �yMUV+MUTg^_W�P-\]Vs\]nmNQz{t+MUMOhOMOXsN�Wg^_W�MONe�{P ^aX+MOv]MOV+MUT�^_W�P-�CM nw\]tuT 0 ��^��CMbfP �+P-V+v+��� ��������� �

�� � � �4\]p �?+u�]� � \��.+u� | ^_TQq6K���� �&09��l+l ���2 �]� 0��2 +&09�

*�PRMOX>� | �i"�-�@i � � �m�D^cpRp-NO� � � t�^cV WQt+b ~BWg^_W�PRN�PRqONk�an�ikMOv]MOV+MUTg^_WQM � \]tuT 0'�D^#�CM | P �+P-V+v+���� � � � ����� ��� � � � � � � � � ��� � � �4\]p � 0 �u� � \��?2u� �]t+p Z ��� ��-��el+l � - � 2 0 - �]� �

~u^#�c^cv]M_� r�� | �]^cV+X i � � � �5^cpRpRNU� ��~{z{t+MOMOhUPRV+v YBZ lm^_T�^cbfMUWQT�P-q�\]NQqOP-pRpR^_W�PR\]V ^cV+X PRVCWQTg^cq#^#�uPFW Znw\]tuT 0 �L^#�CM bfP �uPRV+v+��� � � � � � � � � ��� � � � � ���4\]p � -+� � \��k� �u� �kq:W�\ Y MUT ��� �&39��l+l �y��0{� -�0��0{��� �

~{qgK t+b9^ � MUT#� � \]V+V Z [ �R� � � \]PRNQM P-V K+\]b \{X Z V+M X+M:W�MOqUW�P-\]V>��� � � � � � � � �� �� � � � �4\]p �j�u� � \��0{� | ^ Z ��� ��-��el+l �H���]� 0Q���u� �

~{qgK t+b9^ � MUT#� � � [ �R�er+� | �!rL^��CMONU� � � M�� nw\cT�b9^cp-PRNQb nw\cT1W ��\�0'l�K+\cW�\]V5z{t�^cVCW�t+b \cl+W�PRqUN��� ��� | ^_W�K+MUb9^_W�PRqO^cp!nw\]t+V+X�^_W�P-\]V�^cV+X qO\]b lm^cqUWkV+\cW�^_W�PR\]V>� � � � � ��� � � � �

�� � � � �/\]p �V+u�]�

� \�� 0{� | ^ Z ��� �&09�el+l � + �]� + 0 +u�]�]� �

~{qOt+p-p Z � | ^_T�pR^cVs� �-� ��I qO\cTQT�MOpR^_W�MOX90 MObfPRN�NQPR\]V p ^cN�MUTev Z TQ\]NQqO\cl@M_��� ��������� � � ��� �� � � � �/\]p �

+&0{� � \�� �]� � ^cV t�^_T Z �]����� �&39�el+l � -70 � 0 -70 09�

~{K+MOp YBZ � *� | �-� | ��i � [ M:�CMOV+NQ\]V>�e~ �.,��>SeM:T�pRb tuWQW�M:T#� *� �"�>ikM �4\{M_��^cV+X i � � ���5^cpRpRNU�� � T�\C^cX90 � ^cV+X�S�^_Tg^cbfMUWQTQPRqkikM#^cb l�pRPFx�q#^_W�P-\]V�\]n � t�^cV W�t+b � \]PRNQMjPRV�^cV��al+W�P-q#^cp � P Y M:T#���� � � ��� � � ���

�� � � � �� � � ���4\]p �?0 3{� � \��?2u��Iat+v]t+N�W1��� � 2 �el+l � 2]�u��0 2]��-��

~{K+PFTg^cN�^ � P � | �R� ,��@I��.,k^ct+NO� ��~{z{t+MUMOhOPRV+v�\]n4l�t+p-NQMONyPRV ^�V+\]V+p-PRV+M#^_TyP-V W�M:T�nwMUT�\]bfM:W�MUT#� ��� �� � � ��� � � ��� � � � � ���/\]p � 3{� � \��L�]� �C^cVBt�^_T Z ���]� � �el+l �,+ � 0 +�-��~{p-t+NQK+MUT#�$* �!o/��^cV+X � � /tuT � Mc� ��~{z{t+MOMOhUMOX [ P-v]K W nw\cT rL\]K+MUTQMOV Wsr�\]bfb t+V+PRqO^_W�PR\]V+NO� � � �� ��� � � � � �

� � � ����� � ��� ���/\]p �'�u� � \��?+u� | ^_T�qgK ���]� � ��l+l � -&2 2 0 -73 39�

~{V+PFW�hOMUT#�>o��R� * �>J!t+bfb PRV+MOp-pRP'� � � � ��# qOp ^cX�x Y MUT�N+�HPFW�K8NQMOp-MOqUW�PF�CMOp Z �C\]pR^_W�PRp-PRhOMUX`NQ\]n W 0 v]p ^cNQNqO\cTQMONO��� � � � � � � � �� �� � � � �4\]p �L� -+� � \���� -+���]t+p Z ��0{����� �]� �el+l � 3 0 3�0 3 0c� �

&��%(

Page 109: ece.northeastern.edu€¦ · !" # $ #%& ' (*) + -,/.102 34 5 6 879 ! : !; < =!>>?@>A < B C>D E D F;HG IJLK+MONQPRN S4T MUNQMOVCW MOX YBZ [MU\]V ^_T X`IaX ^cbdSe\]bfMUTg^cV+h

~BW�\]p-MUT#�Ciy^��{PRX>� ��o4z{t+P-�_^cpRMUV+qOM�rLpR^cNQNQMONE\]n | PRV+P-b t+b10 �aV+qOM:TQWg^cPRVCW Z S�^cq � MUW�N�� � �:� � ��������� � � �� �� � � � �4\]p � -+� � \��?2u�~{MUl+W�MOb Y M:T1���&3{� �el+l �H��� � 0�0Q��� � 2 �

J!t+b bfPRV+MOp-pRP ��*��S$�R� � � r�� | q�r�\]pRpRt+b��_^cV+X1o�� ~{V+P-W�hUMUT#� � � ^ Y T�PRqO^_W�PR\]Vy\]n9,aP-v]K r�\]V+qOMOVCWQTg^ 0W�P-\]V�*2^_T�M�0 o�^_TQWQK ik\cl@MUX �2l+W�PRqO^cp � P Y MUT�Nk�aNQPRV+v�r�K+MOp ^_W�MUNO����� � � � � ��� � � �

� � � ����� � ��� ��4\]p �'�u� � \�� �]�]� � \ �CMOb Y MUT ���]� � �el+l ���2 � � 0��2 � + � /t+MOV>� ,��mS$�R� �QJ ��\�0'l�K+\cW�\]V�qO\]K+MUTQMOV WyN�W�^_W�MON2\]neW�K+M1Tg^cX+PR^_W�PR\]V�x�MOpRX>� � � � � ��� � � ���

�� �

� ���4\]p �L�+u� � \��?2u� �]t+V+Ms���&3�2 �El+l � �]�]� 2 0 �]� -&+ �

&�� #