8C120 - 2010
Inleiding Metenen Modellen – 8C120
Prof.dr.ir. Bart ter Haar Romeny
Dr. Andrea FusterFaculteit Biomedische Technologie
Biomedische Beeld Analyse
www.bmia.bmt.tue.nl
8C120 - 2010
Chapter 3 - Webster
Operational Amplifiers and Signal Processing
8C120 - 2010
The three major operations done on biological signals using Op-Amps:
1)Amplifications and Attenuations2)DC offsetting: add or subtract a DC3)Filtering: Shape signal’s frequency content
Applications of Operational Amplifier
In Biological Signals and Systems
8C120 - 2010
Ideal Op-Amp
Figure 3.1 Op-amp equivalent circuit. The two inputs are 1 and 2. A differential voltage between them causes current flow through the differential resistance Rd. The differential voltage is multiplied by A, the gain of the op amp, to generate the output-voltage source. Any current flowing to the output terminal vo must pass through the output resistance Ro.
Most bioelectric signals are small and require amplifications
8C120 - 2010
20 transistors11 resistors1 capacitor
Inside the Op-Amp (IC-chip)
8C120 - 2010
Ideal Characteristics
1- A = (gain is infinity)2- Vo = 0, when v1 = v2 (no offset voltage)3- Rd = (input impedance is infinity)4- Ro = 0 (output impedance is zero)5- Bandwidth = (no frequency response limitations) and no phase shift
8C120 - 2010
Two Basic Rules
Rule 1When the op-amp output is in its linear range, the two input terminals are at the same voltage.
Rule 2No current flows into or out of either input terminal of the op amp.
8C120 - 2010
Inverting Amplifier
Figure 3.3 (a) An inverting amplified. Current flowing through the input resistor Ri also flows through the feedback resistor Rf . (b) The input-output plot shows a slope of -Rf / Ri in the central portion, but the output saturates at about ±13 V.
Rii
o
i
Rf
i
+
-
(a)
10 V
10 V
(b)
i
o
Slope = -Rf / Ri
-10 V
-10 V
i
f
i
oi
i
fo R
R
v
vGv
R
Rv
8C120 - 2010
Summing Amplifier
2
2
1
1
R
v
R
vRv fo
1
o
-
+
R2
R1Rf
2
8C120 - 2010
Example 3.1
i
vb
i
o
o
-
+
+15V
+10
0Time
i + b /2
-10
(a) (b)
5 kW
-15 V
Rb
20 kW
Ri
10 kW
Rf
100 kW
Volt
age,
V
The output of a biopotential preamplifier that measures the electro-oculogram is an undesired dc voltage of ±5 V due to electrode half-cell potentials, with a desired signal of ±1 V superimposed. Design a circuit that will balance the dc voltage to zero and provide a gain of -10 for the desired signal without saturating the op amp.
8C120 - 2010
Follower (buffer)
Used as a buffer, to prevent a high source resistance from being loaded down by a low-resistance load. In other words: it prevents drawing current from the source.
oi+
-
1 Gvv io
8C120 - 2010
Noninverting Amplifier
o
10 V
10 V
i
Slope = (Rf + Ri )/ Ri
-10 V
-10 V
Rf
oi
i
+
-
iRi
i
f
i
ifi
i
ifo R
R
R
RRGv
R
RRv 1
8C120 - 2010
Differential Amplifiers
)( 343
4 vvR
Rvo
3
4
34 R
R
vv
vG od
R4
R4
R3
R3v3
v4 vo
Differential Gain Gd
Common-mode rejection ratio CMMR
c
d
G
GCMRR
Common Mode Gain Gc
For ideal op amp if the inputs are equal then the output = 0, and the Gc =0. No differential amplifier perfectly rejects the common-mode voltage.
Typical values range from 100 to 10,000
Disadvantage of one-op-amp differential amplifier is its low input resistance
8C120 - 2010
InstrumentationAmplifiers
Advantages: High input impedance, High CMRR, Variable gain
Differential Mode Gain
123
4
1
122vv
R
R
R
RRvo
1
12
21
43
121
21243
2
)(
R
RR
vv
vvG
iRvv
RRRivv
d
8C120 - 2010
Comparator – No Hysteresis
uo
uiuref
10 V
-10 V
-10 V
v2
+15
-15
ui
uo
-
+
R1
R1
R2
uref
If (vi+vref) > 0 then vo = -13 V else vo = +13 VR1 will prevent overdriving the op-amp
v1 > v2, vo = -13 Vv1 < v2, vo = +13 V
8C120 - 2010
Comparator – With Hysteresis
ui
uo
-
+
R1
R1
R2
R3
uref
uo
ui- uref
10 V
-10 V
With hysteresis
-10 V 10 V
Width of the Hysteresis = 4VR3
Reduces multiple transitions due to mV noise levels by moving the threshold value after each transition.
8C120 - 2010
Rectifier 10 V
(b)
-10 V
o
i
-10 V 10 V
-
+
(a)
D3
R
R
o=
i
-
+
D2D1
D4
xR (1-x)R
i
x
Full-wave precision rectifier: a) For i > 0, D2 and D3 conduct, whereas D1 and D4 are reverse-biased.Noninverting amplifier at the top is active
(a)
D2
vo
i
-
+
xR (1-x)R
8C120 - 2010
Rectifier
10 V
(b)
-10 V
o
i
-10 V 10 V
-
+
(a)
D3
R
R
o=
i
-
+
D2D1
D4
xR (1-x)R
i
x
Full-wave precision rectifier: b) For i < 0, D1 and D4 conduct, whereas D2 and D3 are reverse-biased. Inverting amplifier at the bottom is active
(a)
D4
voi
-
+
xRi R
8C120 - 2010
Rectifier
One-op-amp full-wave rectifier. For i < 0, the circuit behaves like the inverting amplifier rectifier with a gain of +0.5. For i > 0, the op amp disconnects and the passive resistor chain yields a gain of +0.5.
(c)
D
vo
i
-
+
Ri = 2 kW Rf = 1 kW
RL = 3 kW
8C120 - 2010
Figure 3.8 (a) A logarithmic amplifier makes use of the fact that a transistor's VBE is related to the logarithm of its collector current. For range of Ic equal to 10-7 to 10-2 the range of vo is -.36 to -0.66 V.
(a)
Rf
IcRf /9
o
Rii
-
+
Logarithmic Amplifiers
1310log06.0
i
io R
vv
S
CBE I
IV log06.0
VBE
8C120 - 2010
Figure 3.8 (a) With the switch thrown in the alternate position, the circuit gain is increased by 10. (b) Input-output characteristics show that the logarithmic relation is obtained for only one polarity; 1 and 10 gains are indicated.
(a)
Rf
IcRf /9
o
Rii
-
+(b)
10 V
-10 V
vo
i
-10 V
1
10
10 V
Logarithmic Amplifiers
VBE
VBE
9VBE
8C120 - 2010
Logarithmic Amplifiers
Uses of Log Amplifier:
1.Multiply variable2.Divide variable3.Raise variable to a power4.Compress large dynamic range into small
ones5.Linearize the output of devices
8C120 - 2010
Integrators
CRRjR
R
jV
jV
ifi
f
i
o
ffc
i
f
i
o
CRf
R
R
v
v
2
1
for f < fc
i
f
i
o
t
icifi
o
Z
Z
jV
jV
vdtvCR
v
)(
)(
1 1
0
A large resistor Rf is used to prevent saturation
8C120 - 2010
Integrators
Figure 3.9 A three-mode integrator With S1 open and S2 closed, the dc circuit behaves as an inverting amplifier. Thus o = ic and o can be set to any desired initial conduction. With S1 closed and S2 open, the circuit integrates. With both switches open, the circuit holds o constant, making possible a leisurely readout.
8C120 - 2010
R
+ FET
Piezo-electricsensor
-
uo
C
is
isRisC
dqs/ dt = is = K dx/dt
Long cables may be used without changing sensor sensitivity or time constant.
Example 3.2The output of the piezoelectric sensor may be fed directly into the negative input of the integrator as shown below. Analyze the circuit of this charge amplifier and discuss its advantages.
isC = isR = 0vo = -vc
C
Kxdt
dt
Kdx
Cv
t
o 1
0
1
8C120 - 2010
Differentiators
Figure 3.11 A differentiator The dashed lines indicate that a small capacitor must usually be added across the feedback resistor to prevent oscillation.
RCjZ
Z
jV
jV
dt
dvRCv
i
f
i
o
io
)(
)(
8C120 - 2010
Active Filters- Low-Pass Filter
Active filters (a) A low-pass filter attenuates high frequencies
ffi
f
i
o
CRjR
R
jV
jV
1
1Gain = G =
|G|
freq fc = 1/2RiCf
Rf/Ri
0.707 Rf/Ri
+
-Ri
Rf
(a)
Cf
ui
uo
MMA
8C120 - 2010
Active Filters (High-Pass Filter) Ci
+
-Ri
uiuo
(b)
Rf
Active filters (b) A high-pass filter attenuates low frequencies and blocks dc.
ii
ii
i
f
i
o
CRj
CRj
R
R
jV
jV
1
Gain = G =
|G|
freq fc = 1/2RiCf
Rf/Ri
0.707 Rf/Ri MMA
8C120 - 2010
Active Filters (Band-Pass Filter)
+
-ui uo
(c)
RfCi Ri
Active filters (c) A bandpass filter attenuates both low and high frequencies.
iiff
if
i
o
CRjCRj
CRj
jV
jV
11
|G|
freq fcL = 1/2RiCi
Rf/Ri
0.707 Rf/Ri
fcH = 1/2RfCf
Cf
MMA
8C120 - 2010
Frequency Response of op-amp and Amplifier
Open-Loop GainCompensationClosed-Loop GainLoop GainGain Bandwidth ProductSlew RateOffset voltageBias currentNoise
8C120 - 2010
Input and Output Resistance
di
iai RA
i
vR )1(
+
-
RdiiRo
RL CL
ioAud
ud
uo
ui
+-
1
A
R
i
vR o
o
oao
Typical value of Rd = 2 to 20 M Typical value of Ro = 40
8C120 - 2010
Chapter 3 - Webster
Operational Amplifiers
and Signal Processing
Wikipedia:OperationalAmplifier
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