KonkukKonkuk UniversityUniversity

Principles & Applications ofElectrical Engineering

Ch. 8 Operational amplifier

Rizzoni, 5th Ed.

2

ContentsContents Learning objectives

Understand the properties of ideal amplifiers and the concepts of gain, input impedance and output impedance Sections 8.1.

Understand the difference between open-loop and closed loop op-amp configurations; and compute the gain of (or complete the design of) simple inverting, non-inverting, summing, and differential amplifiers using ideal op-amp analysis. Analyze more advanced op-amp circuits, using ideal

op-amp and circuit analysis; and identify important performance parameters in op-amp data sheets

Sections 8.2.

3

ContentsContentsAnalyze and design simple active filters; analyze and

design ideal integrator and differentiator circuitsSection 8.3. 8.4

Understand the structure and behavior of analog computers; design analog computer circuits to solve simple differential equationsSection 8.5

Understand the principal physical limitations of an op-amp Section 8.6

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8.1 Ideal amplifier8.1 Ideal amplifier Ideal amplifier characteristics

Convert small signal from e.g., cassette tape player, CD player, or radio receiver into large level to drive loading components e.g., tallboy speakers

Passive circuit only (passive elements only without any active source) cannot provide sufficient gain required (as is smaller than the input signal)

5

A voltage amplifier Ideal relationship

Can be seen as equivalent load from source and equivalent source from load

Simple voltage amplifier modelis obtained using internal input/output resistance

( ) ( )L Sv t Av t

inin S

S in

LL in

out L

Rv vR R

Rv A vR R

6

Then by substituting amplifier voltage,

Note that If input resistance and output resistance of the

amplifier is very large and small respectively, the amplifier acts as an ideal one as depicted the black box in the figure.

In other words, a good amplifier shows very large input impedance and very small output impedance

in LL S

S in out L

R Rv A vR R R R

L Sv Av

7

8.2 The operational amplifier8.2 The operational amplifier Operational amplifier (Op-Amp)

An integrated circuit, and found in most measurement, instrumentation, and control applications

Serving as extremely versatile building blocks for any application that requires the electrical signal conditioning and processing

Behaves as ideal difference amplifier The open-loop model

, ( )out V OL inv A v v v

8

Simplified circuit symbolTwo input modeone output node

Assumed to have large input resistance and open loop gain

IC op-amp diagram chip

9

Operational amplifier in closed-loop modeSee the practical assumption Inverting amplifier case

0

s F in

s outin

s F

i i i

v v v v iR R

, ,

,

( )out V OL V OL

out

V OL

v A v v A vvvA

, ,

, ,

, ,

1( )

S out out out

S V OL S F V OL F

S out out out

S V OL S F V OL F

S SS out

V OL F V OL F

thereforev v v vR A R R A R

v v v vR A R R A R

R Rv vA R A R

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Since the open loop gain of op-amp is large enoughUsually 100k ~ 10M

Therefore, the inverting gain of closed loop amplifier is

Practical assumptionThe effect of the feedback connection from output to

inverting input is to force the voltage at the inverting input to be equal to that at the non-inverting input

Two useful assumptions for op-amp application with feedback connect

out F

S S

v Rv R

1. 0

2. ini

v v

11

Summing amplifier (or weighted adder)One of useful application using op-amp

1 2 3

1

...

,

N F

sn outn F

sn F

NF

out snn sn

i i i i iv vi iR R

Rv vR

Derive!!

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Non-inverting amplifier Input voltage is applied into non-inverting node of op-

amp

? , ?S in F S

F S

i i i iwhere i i

1out F

S S

v Rv R

Derive!!

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Differential amplifierA combination of inverting and non-inverting amplifierAmplify the difference of two input signals

22 1

1

( )outRv v vR

Derive!!

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Practical illustrationElectrocardiogram (EKG) measurementUsually, the EKG waveform is interfered with 60Hz

noise signal from power (due to various kinds of couplings)

15

Reduction of common noise components by differential amplifier strategy

1 1 1 1 1 1

2 2 2 1 2 2

( ) ( ) ( ) ( ) cos(2 )( ) ( ) ( ) ( ) cos(2 )

n n n

n n n

v t v t v t v t V ftv t v t v t v t V ft

16

Instrumentation amplifierCommon mode signal (e.g., bias, common noise) is

rejected (cancelled) and only differential mode signal is to be amplified

Bring CMRR as figure of merit

2

1

2(1 )FV

R RAR R

Derive!!

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Level shiftAdjust bias offset voltage of output decided by Vref

(1 )F Fout sensor ref

S S

R Rv v vR R

Derive using principle of superposition!!

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8.3 Active filter8.3 Active filter Active filter

Shapes the frequency response characteristics using op-amp and complex impedance using dynamic elements

For instanceTransfer function given by

( )

( ) 1

out F

S S

out F

S S

V ZjV ZV ZjV Z

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Active low pass filter p.437 Transfer function (or gain)? ( )

/1

FLP

S

F S

F F

ZA jZ

R Rj C R

1)Passive filter: ( )1LPcf H j

j CR

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Frequency response3-dB frequency (Used in frequency response

analysis)

Amplitude response of LPF

0

0

( ) ?

?LP dB

A j

/( )

1F S

LPF F

R RA jj C R

/ 10, 1F S F FR R R C

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Active high pass filter p.438 Transfer function ( gain )? Zero and infinite frequency gain?

( )

1

lim ( )

FHP

S

S F

S S

FHP

S

ZA jZ

j C Rj C R

RA jR

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Frequency response of HPFAmplitude response

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Active bandpass filter p.439 Transfer function or gain? Zero and infinite frequency gain?

??

( )

(1 )(1 )lim ( ) 0

F

S

FBP

S

S F

F F S S

HP

ZZ

ZA jZ

j C Rj C R j C R

A j

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Normalized amplitude response of active BPF

11 :

1 13 : ,

F S

LP HPF F S S

unit gain frequencyR C

dB frequencyR C R C

1. : 1, 10, 1000LP HPEx

25

Example 8.6Second-order LPFDerive transfer function!!

( ) ?LPA j

26

Second-order filter dynamicsSteeper gain attenuation than 1st order filter

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Summary of 8.3Summary of 8.3 Active Filter

Consist of Op-amp and dynamic elements (R,L,C)Arbitrary design of gain and frequency response

characteristicsNormally, inverting amplifier form

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8.4 Integrator and Differentiator8.4 Integrator and Differentiator Op-amp based circuit can generate ideal linear

circuit element IntegratorDifferentiator

Ideal integrator, p443

( ) ...1 ( ') '

out

t

S

v t

v t dtRC

,Derive output voltage

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Example 8.7 Integrator

( )Sv t ( )outv t

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Example 8.8P-I control with op-amp for thermal systemControl objective is to maintain constant temperature

P control only cannot remove error

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Physical implementation using op-amp circuit

,??

e

o

Derive output voltagevv

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Output response Thermal system voltage response under disturbancePower amp output current response

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Ideal differentiator, p449Not used practically, since noise can be amplifiedPhase shift and gain can be used as an alternative

implementation of ideal differentiator

,( ) ?out

Derive output voltagev t

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8.5 Analog computer8.5 Analog computer Analog computer

Analog computing circuit using Op-ampUsed to calculate solution of differential equation and

simulation of complex dynamic systems before digital computer was invented

Still widely used to simulate real dynamic systemswhich is hard to implement in physical world using other methods

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Elements of analog computer IntegratorDifferentiatorGainSummerPossibly, multiplier

36

Analog computer example For automotive suspension

2

2

, ( ) sin

...?

R

M

Assume x t X t

d xdt

37

Final simulation model for the mechanical suspension system

2

2 cos( ) sin( )M MM

d x dxB K B Kx X t X tdt M dt M M M

38

Example 8.10Differential equation from analog computer circuit

2

2

???

400 1000

xzy

d x x fdt

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8.5 Physical limitation of Op8.5 Physical limitation of Op--ampamp Voltage supply limits Frequency response limits

Finite BW limitationProduct of gain and BW is constant

Input offset voltage and bias currents Slew rate limit Short circuit output current limits CMRR (common mode rejection ratio)

All is considered to select the op-amp with the appropriate application field

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SummarySummary Summary

Understand the properties of ideal amplifiers and the concepts of gain, input impedance and output impedance Sections 8.1.

Understand the difference between open-loop and closed loop op-amp configurations; and compute the gain of (or complete the design of) simple inverting, non-inverting, summing, and differential amplifiers using ideal op-amp analysis. Analyze more advanced op-amp circuits, using ideal op-amp analysis; and identify important performance parameters in op-amp data sheetsSections 8.2.

41

SummarySummaryAnalyze and design simple active filters; analyze and

design ideal integrator and differentiator circuitsSection 8.3. 8.4

Understand the structure and behavior of analog computers; design analog computer circuits to solve simple differential equationsSection 8.5

Understand the principal physical limitations of an op-amp Section 8.6