BmE_05

8/4/2019 BmE_05

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1

Prof. Dr. Nizamettin AYDIN

[email protected] [email protected]

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

Biomedical Instrumentation

mailto:[email protected]

mailto:naydin@i

mailto:naydin@i

mailto:naydin@i

mailto:naydin@i





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Amplifiers and Signal Processing

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Applications of Operational Amplifier

In Biological Signals and Systems

• The three major operations done on biologicalsignals 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 amplifications

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.4

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Inside the Op-Amp (IC-chip)

20 transistors

11 resistors

1 capacitor

5

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Ideal Characteristics

• A = (gain is infinity)

• V o = 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 terminalsare at the same voltage.

• Rule 2

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

7

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Inverting Amplifier

(a) An inverting amplified. Current flowing through the inputresistor 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.

8

Ri i

o

i

Rf

i

+

-

(a)

10 V

10 V

(b)

i

o

Slope = - Rf / Ri

-10 V

-10 V

i

f

i

oi

i

f

o R

R

v

vGv

R

Rv --

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Summing Amplifier

9

-

2

2

1

1

R

v

R

v Rv f o

1

o

-

+

R2

R1 Rf

2

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Example 3.1

• The output of a biopotential preamplifier thatmeasures 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.

10

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Answer 3.1

• We assume that vb, the balancing voltage at vi=5 V. For vo=0,

the current through R f is zero. Therefore the sum of the currents

through Ri and Rb, is zero.

11

i

v b

i

o

o

-

+

+15V

+10

0 Time

i + b /2

-10

(a) (b)

5 k W

-15 V

Rb

20 k W

Ri

10 k W

Rf

100 k W

V o l t a g e , V

W--

-

44

1025

)10(100

i

bi

bb

b

i

o

v

v R R

R

v

R

v

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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

o i +

-

1 Gvv io

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Noninverting Amplifier

13

o

10 V

10 V

i

Slope = ( Rf + Ri )/ Ri

-10 V

-10 V

Rf

o i

i

+

-

i

Ri

i

f

i

i f

i

i

i f

o R

R

R

R RGv

R

R Rv 1

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Differential Amplifiers

• Differential Gain G d

• Common Mode Gain G c – 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

14

3

4

34 R

R

vv

vG o

d -

v3

v4

)( 34

3

4 vv R

Rvo -

c

d

GGCMRR

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Instrumentation Amplifiers

Differential Mode Gain

Advantages: High input impedance, High CMRR, Variable gain

15

1

12

21

43

121

21243

2

)(

R

R R

vv

vvG

iRvv

R R Rivv

d

-

-

-

-

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Comparator – No Hysteresis

o

i ref

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 V

R1 will prevent overdriving the op-amp

v1 > v 2, v o = -13 V

v1 < v 2, v o = +13 V

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Comparator – With Hysteresis

• Reduces multiple transitions due to mV noise levels

by moving the threshold value after each transition.

Width of the Hysteresis = 4VR3

17

i

o

-

+

R1

R1

R2

R3

ref

o

i- ref

10 V

-10 V

With hysteresis

-10 V 10 V

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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

18

10 V

(b)

-10 V

o

i

-10 V 10 V

(a)

D2

v o

i

-

+

xR (1-x)R

-

+

(a)

D3

R

R

i

-

+

D2 D1

D4

xR (1- x) R

x

vv io

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Rectifier

• Full-wave precision rectifier:

– For i < 0,

D1 and D4 conduct, whereas D2 and D3 arereverse-biased.

Inverting amplifier at the bottom is active

19

10 V

(b)

-10 V

o

i

-10 V 10 V -

+

(a)

D3

R

R

i

-

+

D2 D1

D4

xR (1- x) R

x

vv io

(b)

D4

v o i

-

+

xRi R

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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, theop amp disconnects and the passive resistor chain

yields a gain of +0.5.

20

(c)

D

v o

i

-

+

Ri = 2 k W Rf = 1 k W

RL = 3 k W

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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 V BE 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.

21

(a)

Rf

I c R f /9

o

Ri i

-

+

-13

10

log06.0

i

io

R

vv

S

C BE

I I V log06.0

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Logarithmic Amplifiers

(a) With the switch thrown in the alternate position, the

circuit gain is increased by 10. (b) Input-outputcharacteristics show that the logarithmic relation is

obtained for only one polarity; 1 and 10 gains are

indicated.

22

(b)

10 V

-10 V

v o

i

-10 V

1

10

10 V

(a)

Rf

I c R f /9

o

Ri i

-

+

VBE

VBE

9VBE

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Integrators

23

f f

c

i

f

i

o

C R f

R

R

v

v

2

1

-

for f < f c

C R j R R jV

jV

C R R j R

R

jV

jV

Z

Z

jV

jV

vdt vC Rv

i

f

ii

o

i f i

f

i

o

i

f

i

o

t

ici f i

o

-

-

-

-

1

)(

)(

1 1

0

A large resistor Rf is used to prevent saturation

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• 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.

24

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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.

25

RC j jV

jV Z

Z

jV

jV

dt

dv RC v

i

o

i

f

i

o

io

-

-

-

)(

)()(

)(

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Active Filters- Low-Pass Filter

• A low-pass filter attenuates high frequencies

26

f f i

f

i

o

C R j R

R

jV

jV

-

1

1 GGain

|G|

freq f c = 1/2RiCf

Rf /Ri

0.707 Rf /Ri

+

- Ri

Rf

(a)

i

o

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Active Filters (High-Pass Filter)

• A high-pass filter attenuates low frequencies

and blocks dc.

27

C i

+

- Ri

i o

(b)

Rf ii

ii

i

f

i

o

C R j

C R j

R

R

jV

jV

-

1 GGain

|G|

freq f c = 1/2RiCf

Rf /Ri

0.707 Rf /Ri

A i i ( i )

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Active Filters (Band-Pass Filter)

• A bandpass filter attenuates both low and high

frequencies.

28

ii f f

i f

i

o

C R jC R j

C R j

jV

jV

-

11

|G|

freq f

cL= 1/2R

iC

i

Rf /Ri

0.707 Rf /Ri

f cH

= 1/2Rf C

f

+

- i

o

(c)

Rf C i Ri

C f

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Frequency Response of op-amp and Amplifier

• Open-Loop Gain

• Compensation

• Closed-Loop Gain

• Loop Gain

• Gain Bandwidth Product• Slew Rate

29

I d O R i

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Input and Output Resistance

30

d

i

iai R A

i

v R )1(

+

-

Rdii

Ro

RL C L

io A d

d o

i

+

-

1

A

R

i

v R o

o

oao

Typical value of Rd = 2 to 20 MW Typical value of Ro = 40 W

Phase Modulator for Linear variable differential

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Phase Modulator for Linear variable differentialtransformer LVDT

31

+

-

+

-

Phase Modulator for Linear variable differential

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Phase Modulator for Linear variable differentialtransformer LVDT

32

+

-

+

-

Ph S iti D d l t

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Phase-Sensitive Demodulator

33

Used in many medicalinstruments for signal detection,

averaging, and Noise rejection

Th Ri D d l t

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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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