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Prof. Dr. Nizamettin AYDIN

naydin@yildiz.edu.trnaydin@ieee.org

http://www.yildiz.edu.tr/~naydin

Biomedical Instrumentation

Amplifiers and Signal Processing

Applications of Operational AmplifierIn Biological Signals and Systems

• The three major operations done on biological signals using Op-Amp:

– Amplifications and Attenuations– DC offsetting:

• add or subtract a DC– Filtering:

• Shape signal’s frequency content

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Ideal Op-Amp

• Most bioelectric signals are small and require amplificationsOp-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.

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Inside the Op-Amp (IC-chip)

20 transistors11 resistors1 capacitor

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Ideal Characteristics

• A = (gain is infinity)• Vo = 0, when v1 = v2 (no offset voltage)

• Rd = (input impedance is infinity)

• Ro = 0 (output impedance is zero)• Bandwidth = (no frequency response limitations) and no phase

shift

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Two Basic Rules

• Rule 1– When the op-amp output is in its linear range, the two input terminals are

at the same voltage.

• Rule 2– No current flows into or out of either input terminal of the op amp.

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Inverting Amplifier

(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.

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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

RvvGv

RR

v

Summing Amplifier

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2

2

1

1

Rv

RvRv fo

1

o

+

R2

R1Rf

2

Example 3.1

• 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.

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Answer 3.1

• We assume that vb, the balancing voltage at vi=5 V. For vo=0, the current through Rf is zero. Therefore the sum of the currents through Ri and Rb, is zero.

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i

vb

i

o

o

+

+15V

+10

0Time

i + b /2

-10

(a) (b)

5 k

-15 V

Rb

20 k

Ri

10 kRf

100 k

Vol

tage

, V

44

1025

)10(100i

bib

b

b

i

o

vvRR

Rv

Rv

Follower ( buffer)

• Used as a buffer, to prevent a high source resistance from being loaded down by a low-resistance load. In another word it prevents drawing current from the source.

12

oi +

1 Gvv io

Noninverting Amplifier

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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

RR

RRGv

RRR

v 1

Differential Amplifiers

• Differential Gain Gd

• 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.

• Common-mode rejection ratio CMMR– Typical values range from 100 to 10,000

• Disadvantage of one-op-amp differential amplifier is its low input resistance

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3

4

34 RR

vvvG o

d

v3

v4

)( 343

4 vvRRvo

c

d

GGCMRR

Instrumentation Amplifiers

Differential Mode Gain

Advantages: High input impedance, High CMRR, Variable gain

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1

12

21

43

121

21243

2

)(

RRR

vvvvG

iRvvRRRivv

d

Comparator – No Hysteresis

o

iref

10 V

-10 V

-10 V

v2

+15

-15

i

o

+

R1

R1

R2

ref

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

Comparator – With Hysteresis

• Reduces multiple transitions due to mV noise levels by moving the threshold value after each transition.

Width of the Hysteresis = 4VR3

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i

o

+

R1

R1

R2

R3

ref

o

i- ref

10 V

-10 V

With hysteresis

-10 V 10 V

Rectifier

• Full-wave precision rectifier: – For i > 0, D2 and D3 conduct, whereas

D1 and D4 are reverse-biased.Noninverting amplifier at the top is active

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10 V

(b)

-10 V

o

i

-10 V 10 V

(a)

D2

vo

i

+

xR (1-x)R

+

(a)

D3

R

R

i

+

D2D1

D4

xR (1-x)R

xvv i

o

Rectifier

• Full-wave precision rectifier: – For i < 0,

D1 and D4 conduct, whereas D2 and D3 are reverse-biased. Inverting amplifier at the bottom is active

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10 V

(b)

-10 V

o

i

-10 V 10 V

+

(a)

D3

R

R

i

+

D2D1

D4

xR (1-x)R

xvv i

o

(b)

D4

voi

+

xRi R

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.

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(c)

D

vo

i

+

Ri = 2 k Rf = 1 k

RL = 3 k

Logarithmic Amplifiers• Uses of Log Amplifier

– Multiply and divide variables– Raise variable to a power– Compress large dynamic range into small ones– Linearize the output of devices

(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 10-7 to 10-2 and the range of vo is -.36 to -0.66 V.

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(a)

Rf

Ic

Rf /9

o

Rii

+

1310log06.0

i

io R

vv

S

CBE I

IV log06.0

Logarithmic Amplifiers

(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.

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(b)

10 V

-10 V

vo

i

-10 V

1

10

10 V

(a)

Rf

Ic

Rf /9

o

Rii

+

VBE

VBE

9VBE

Integrators

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ffc

i

f

i

o

CRf

RR

vv

21

for f < fc

CRj

RRjV

jV

CRRjRR

jVjV

ZZ

jVjV

vdtvCR

v

if

ii

o

ifi

f

i

o

i

f

i

o

t

icifi

o

1

)()(

1 1

0

A large resistor Rf is used to prevent saturation

• 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.

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Differentiators

• A differentiator – The dashed lines indicate that a small capacitor must

usually be added across the feedback resistor to prevent oscillation.

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RCjjVjV

ZZ

jVjV

dtdvRCv

i

o

i

f

i

o

io

)()()()(

Active Filters- Low-Pass Filter

• A low-pass filter attenuates high frequencies

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ffi

f

i

o

CRjRR

jVjV

1

1 G Gain

|G|

freq fc = 1/2RiCf

Rf/Ri

0.707 Rf/Ri

+

Ri

Rf

(a)

i

o

Active Filters (High-Pass Filter)

• A high-pass filter attenuates low frequencies and blocks dc.

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Ci

+

Rii

o

(b)

Rf ii

ii

i

f

i

o

CRjCRj

RR

jVjV

1

G Gain

|G|

freq fc = 1/2RiCf

Rf/Ri

0.707 Rf/Ri

Active Filters (Band-Pass Filter)

• A bandpass filter attenuates both low and high frequencies.

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iiff

if

i

o

CRjCRjCRj

jVjV

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|G|

freq fcL = 1/2RiCi

Rf/Ri0.707 Rf/Ri

fcH = 1/2RfCf

+

i o

(c)

RfCi Ri

Cf

Frequency Response of op-amp and Amplifier

• Open-Loop Gain• Compensation• Closed-Loop Gain• Loop Gain• Gain Bandwidth Product• Slew Rate

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Input and Output Resistance

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di

iai RA

ivR )1(

+

Rdii

Ro

RL CL

ioAd

d

o

i

+

1

AR

ivR o

o

oao

Typical value of Rd = 2 to 20 M Typical value of Ro = 40

Phase Modulator for Linear variable differential transformer LVDT

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+

-

+

-

Phase Modulator for Linear variable differential transformer LVDT

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+

-

+

-

Phase-Sensitive Demodulator

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Used in many medical instruments for signal detection, averaging, and Noise rejection

The Ring Demodulator• If vc is positive then D1 and D2 are forward-biased and vA = vB. So vo = vDB

• If vc is negative then D3 and D4 are forward-biased and vA = vc. So vo = vDC

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