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EMT 212

Analog Electronic IIChapter 1- Operational Amplifier

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1.0 Operational Amplifier

1.1 Introduction1.2 Ideal Op-Amp

1.3 Op-amp input modes

1.4 Op-amp Parameters

1.5 Operation

Single-mode

Differential-mode

Common-mode operation

1.6 Op-Amps basics

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1.1 Introduction

Uses of Op-Amp To provide voltage amplitude changes

(amplitude and polarity)

Comparators

Oscillators

Filter circuits

Instrumentation circuits

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1.1 Introduction

Definition: The operational amplifier or op-amp is an

integrated circuit that amplifies the differencebetween two input voltages and produces a

single output. A typical op-amp is powered by two dc voltages

and has an inverting(-) and a non-inverting input

(+) and an output. Op-amps were used to model the basic

mathematical operations; addition, subtraction,integration, differentiation, etc, in electronic

analog computers.

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1.1 Introduction

Stages of an Op-ampINPUTSTAGE OUTPUT

STAGE

GAINSTAGE

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1.1 Introduction

Two Power Supply Inverting input

Non-inverting input

One Output Terminal

Two Input Terminal

+V : Positive PS

-V : Negative PS

Op-amp schematicsymbol

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1.2 Ideal Op-Amp

Practical Op-Amp

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1.2 Ideal Op-Amp

Ideal Op-Amp

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1.2 Ideal Op-Amp

Infinite input impedance

Zero output impedance Infinite open-loop gain

Infinite bandwidth

Zero noise contribution

Zero DC output offset Both differential inputs stick

together

Ideal Op-AmpPractical Op-Amp

input impedance 500k-2M

output impedance 20-100 open-loop gain (20k to 200k)

Bandwidth limited (a few kHz)

noise contribution

Non-zero DC output offset

Properties

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1.2 Ideal Op-Amp

Infinite Input Impedance Input impedance is measured across the input

terminals

It is the Thevenin resistance of the internalconnection between the two input terminals.

Input impedance is the ratio of input voltage toinput current

in

in

in

I

VZ

Iin

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1.2 Ideal Op-Amp

Infinite Input Impedance When Zi is infinite, the input current is zero.

the op amp will neither supply current to acircuit nor will it accept current from any

external circuit.

In real, the resistance is 500k to 2M

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1.2 Ideal Op-Amp

Zero Output Impedance Looking back into the output terminal, we see

voltage sourcewith an internal resistance

Iin

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1.2 Ideal Op-Amp

Zero Output Impedance The internal resistance of the op-amp is op-amp

output impedance, Zout.

This internal resistance is in series with the load,

reducing the output voltage available to the load Real op-amps have output impedance in the range

20-100 .

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1.2 Ideal Op-Amp

Infinite Open-Loop Gain

Open-Loop Gain, A is the gain of the op-amp without

feedback In the ideal op-amp, A is infinite

In real op-amp is (20k to 200k)

invout VAV

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1.2 Ideal Op-Amp

Infinite Bandwidth The ideal op-amp will amplify all signals from DC to

the highest AC frequencies

In real op-amps, the bandwidth is rather limited

This limitation is specified by the Gain-Bandwidthproduct, which is equal to the frequency where theamplifier gain becomes unity

Some op-amps, such as 741 family, have very limited

bandwidth up to a few kHz

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1.2 Ideal Op-Amp

Zero Noise Contribution in an ideal op amp, all noise voltages produced are

external to the op amp. Thus any noise in the outputsignal must have been in the input signal as well

the ideal op amp contributes nothing extra to theoutput noise

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1.2 Ideal Op-Amp

Zero Output Offset The output offset voltage of any amplifier is the

output voltage that exists when it should be zero

The voltage amplifier sees zero input voltage when

both inputs are grounded. This connection shouldproduce a zero output voltage

If the output is not zero then there is said to be anoutput voltage present

In the ideal op amp this offset voltage is zero volts,but in practical op amps the output offset voltage isnonzero

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1.2 Ideal Op-Amp

Both Differential Inputs Stick Together this means that a voltage applied to one inverting

inputs also appears at the other non-inverting inputs

If we apply a voltage to the inverting input and then

connect a voltmeter between the non-inverting inputand the power supply common, then the voltmeterwill read the same potential on non-inverting as onthe inverting input

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1.3 Op-Amp input Modes

Single-Ended input mode input signal is connected to one input and the other

input is grounded.

1. Inverting () terminal is grounded and input

signal is applied to the non-inverting (+)terminal

In this configuration, the resultant output signal is inphase with the input signal

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2. The non-inverting (+) terminal is grounded andinput signal is applied to the inverting ()terminal

In this configuration, the resultant output signal is in

anti-phase with the input signal

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Differential mode input two out-of-phase signals are applied with the

difference of the two amplified and produced at theoutput

21 inind

ddout

VVV

VAV

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Common mode input two signals of same phase, frequency, and amplitude

are applied to the inputs which results in no output(signals cancel).

Practically, a small output signal will result. This iscalled common-mode rejection. This type of modeis used for removal of unwanted noise signals

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1.4 Op-Amp Parameters

Common-Mode Rejection Ratio (CMRR) The ability of amplifier to reject the common-mode

signals.

Ratio of open-loop gain to common-mode gain.

The higher the CMRR, the better

open-loop gain is high and common-mode gain is low.

cm

ol

A

ACMRR

dBlog20

cm

ol

A

ACMRR

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ExampleA certain op-amp has an open-loop differentialvoltage gain of 100, 000 and a common-modegain of 0.2.

Determine the CMRR and express it in decibels.

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Common-Mode Input Voltage The range of input voltages which, when

applied to both inputs, will not cause clipping orother output distortion.

Input Offset Voltage

The differential dc voltage required between

the inputs to force the output to zero volts. Range between 2 mV.

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Input Bias Current The dc current required by the inputs of the amplifier

to properly operate the first stage.

Is the average of both input currents.

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Input Impedance Is the total resistance between the inverting and

non-inverting inputs.

1. Differential input impedance is measured by the

changes of differential input voltage over changes ofbias current:

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2. Common-mode input impedance is measured bythe changes of common-mode input voltage overchanges of bias current

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Input Offset Current The difference in the input bias currents:

21 IIIos

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Input Offset Current The difference in the input bias currents

offset voltage:

inininos RIIRIRIV 2121

inosos RIV

inosverrorout RIAV )(

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Output Impedance The resistance viewed from the output terminal of the

op-amp.

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Slew Rate The maximum rate of change of the output voltage in

response to a step input voltage.

Test circuit

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Slew Rate

t

VSlewRate out

)( maxmax VVVout

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Example:

Determine the slew rate:

t

VSlewRate out

sVs

VVSlewRate

/181

)9(9

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Example:When a pulse is applied to an op-amp, the outputvoltage goes from -8 V to +7 V in 0.75 s.

What is the slew rate?

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1.5 Operation - Differential Amplifier Circuit

Basic differential amplifier circuit

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1.5 Operation

If an input signal isapplied to either inputwith the other input isconnected to ground,the operation isreferred to as single-ended.

The input signal is applied to input 1

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1.5 Operation

If an input signal isapplied to either inputwith the other input isconnected to ground,the operation is referredto as single-ended.

The input signal is applied to input 2

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1.5 Operation

If two opposite-polarity input signals are applied, theoperation is referred to as double-ended:

Vi1 and Vi2 are

in oppositepolarity

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1.5 Operation

If the same input isapplied to both inputs,the operation is calledcommon-mode.

Viis sometimes

known as Vcm

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The differential amplifier

is a circuit that has twoseparate inputs andproduces two separateoutputs where theemitters are connectedtogether.

It amplifies the differencevoltage between the twoinput (Vdiff).

There are threeoperations can be done ina differential amplifiercircuit; dc bias, acoperationand common

mode operation.

Figure: The basic differential amplifier.

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DC bias of differentialamplifier circuit.

DC Analysis:

0 EEEEBE VRIV

E

BEEEE

R

VVI

221

Ecc

III

cE

cccccccc RI

VRIVVV221

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Example

Calculate the dc voltagesand currents:

Solution

mA5.2k3.3

V7.0V9

E

BEEE

E

R

VVI

mA25.1

2

m5.2

221

EccI

II

ccccc RIVV

V1.4

)k9.3)(m25.1(9

VVc

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AC Analysis:

For ac analysis, VCCand VEEmay beconsidered as ground.

AC connection of differentialamplifier

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AC Analysis

AC equivalent of differential amplifiercircuit

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AC Analysis

Single-Ended ACVoltage Gain

Single-ended ac

voltage gain iscalculated byconnecting one ofvoltage sources to oneinput and the otherconnected to ground.

1

1

1

i

o

v

V

VA

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AC Analysis Single-Ended AC Voltage Gain

AC equivalentcircuit

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AC Analysis


i

i

bcr

VII

2

1

01

ibibi rIrIVbbb III 21

iii rrr 21

21

i

i

br

VI

2

1

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AC Analysis


where

1

1

2

2

1

i

e

c

c

i

i

cco

Vr

R

Rr

V

RIV

e

c

i

ov

r

R

V

VA

21

1 E

eI

mVr

26

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Example:

Calculate the single-ended output voltageVo1.

Given that;

75

k20

21

21

ii rr

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Solution

A193k43

V7.0V9

7.0

E

EE

E

R

VVI

V5.4

k47A5.969

ccccc RIVV

1.88)267(2

k47

2

e

cv

r

RA

V176.0

)mV2)(1.88(

ivo VAV

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AC Analysis - Double ended

A similar analysis can be used to show that for thecondition of signals applied to both inputs, thedifferential voltage gain magnitude is:

where:

i

c

d

o

d

r

R

V

VA2

21 iid VVV

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AC Analysis - Common-

mode To operate a differential

amplifier in a common-mode connection, thesame ac voltage sourceis applied to both inputs.

In most ac operation, adifferential amplifierprovides largeamplification, but in thisoperation it providessmall amplification.

Common-mode connection

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AC Analysis - Common-mode

Ei

ib

Rr

VI

)1(2

i

Ebib

r

RIVI

)1(2

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AC Analysis - Common-mode

Ei

c

i

ov

Rr

R

V

VA

)1(2

Ei

ci

cbccoRr

RVRIRIV

)1(2

1

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1.6 Op-Amp Basics

High input impedance

Low output impedance

Made using difference amplifiers having 2 inputsand at least 1 output

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1.6 Op-Amp Basics

AC equivalent circuit

Input impedance, Riis typically very high

Output voltage, Vois amplifier gain times input signaltaken through output impedance, Rowhich is typicallylow.

Ideal op-amp would have infinite input impedance, zerooutput impedance and infinite voltage gain.

IdealPractical

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1.6 Op-Amp Basics - constant-gain multiplier

Basic circuit connection

The input voltageV1 is applied to theinverting terminalthrough R1.

The output voltageVo is fed back to theinverting terminalthrough Rf.

The output voltage Vo is inantiphase with the input voltageVi

The non-invertingterminal isgrounded

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Practical op-amp

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Ideal op-amp Redrawn

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Using superposition theorem

i) V1 only (setAvVi= 0)

ii)AvVionly (set V1 = 0)

1

1

1 VRR

R

Vf

f

i

ivf

i VARR

RV

1

12

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Solving for Vi, gives us;

21 iii VVV

ivff

fVA

RR

RV

RR

R

1

11

1

f

ivf

RR

VARVR

1

11

1

1)1(V

RAR

RV

vf

f

i

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Usually and

Then1

1

VRA

RV

v

f

i

1vA fv RRA 1

11

1

1

RR

VV

VRA

RAVAV

fo

v

fvivo

The ratio Vo/V1 is dependent onthe external components RfandR1 only.

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1.6 Op-Amp Basics

Basic Op-amp unity gain

If Rf= R1;

Shown that the output voltage equal to input voltagewith 180 phase inversion.

1

1

V

Vo

11 R

R

V

V fo

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1.6 Op-Amp Basics

Basic Op-amp constant magnitude gain

If Rf= 10R1;

Shown that the output voltage is equal to 10X theinput voltage with 180 phase inversion.

10

1

V

Vo

11 R

R

V

V fo

ch 1 - op-amp

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