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