third analogue electronics

8/12/2019 Third Analogue Electronics

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Operational Amplifiers (Op Amps)


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What is an op amp?

An inexpensive, versatile, integrated

circuit that is anotherbasic buildingblock to electronics (made of resistorsand transistors)

Amplifier that hasLarge open loop gain (intrinsic)

Differential input stage, inverting input (-)and non-inverting input (+)

One output

Uses components in the feedback networkto control the relationship between theinput and output


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What does an Op-Amp do?

Performs operations on an input

signal

Amplification

Buffering

Integration/Differentiation

Addition/Subtraction


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Open Loop/Closed Loop and

Feedback

Open loop

Very high gain (intrinsic gain)

Poor stability

Open loop gain assumed to be infinite for ideal op amps

Closed loop

Uses feedback to add stability

Reduces gain of the amplifier

Output is applied back into the inverting (-) input Most amplifiers are used in this configuration

Open loop

gain

Feedback

VinVout

-

+


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Golden Rules of Op-Amp Analysis

Rule 1: VA = VB The output attempts to do whatever is necessary to

make the voltage difference between the inputs zero.

The op-amp looksat its input terminals and swings

its output terminal around so that the externalfeedback network brings the input differential to zero.

Rule 2: IA= IB= 0

The inputs draw no current

The inputs are connected to what is essentially an

open circuit


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1) Remove the op-amp from the circuit and

draw two circuits (one for the + and one for

theinput terminals of the op amp).

2) Write equations for the two circuits.

3) Simplify the equations using the rules for opamp analysis and solve for Vout/Vin

Steps in Analyzing Op-Amp Circuits

Why can the op-amp be removed from the circuit?

There is no input current, so the connections at the

inputs are open circuits.

The output acts like a new source. We can replace it

by a source with a voltage equal to Vout.


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Ideal Op Amp

Non-inverting Amplifier

Unity-Gain Buffer

Inverting Amplifier

Differential Amplifier Current-to-Voltage Converter

Non-ideal Op Amp


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Ideal Op Amp

1) 0 vv A v v

The open-loop gain,Av

, is very large, approaching infinity.

2) 0i i

The current into the inputs are zero.

+

-

i

ov

v

vi

DDV

SSV

0SS DDV v V


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Ideal Op Amp with Negative Feedback

+

- ov

v

v

Network

Golden Rules of Op Amps:

1. The output attempts to do whatever is necessary to

make the voltage difference between the inputs zero.

2. The inputs draw no current.


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Ideal Op Amp


Unity-Gain Buffer

Inverting Amplifier


Non-ideal Op Amp


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+

-

1R

2R

ivov

v

v oF

i

vA

v

2

1

1oF

i

v RA

v R

1

1 2

i oRv v v vR R

Closed-loop voltage gain


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Ideal Op Amp


Unity-Gain Buffer

Inverting Amplifier


Non-ideal Op Amp


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Unity-Gain Buffer

+

- ov

v

viv

oF

i

vA

v

1oFi

vA

v

i ov v v v

Closed-loop voltage gain

Used as a "line driver" that transforms a high input impedance

(resistance) to a low output impedance. Can provide substantial

current gain.


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Ideal Op Amp


Unity-Gain Buffer

Inverting Amplifier


Non-ideal Op Amp


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Inverting Amplifier

0v v

1 1

0i ii v viR R

Current into op amp is zero

+

-

1R

2R

iv

ovv

vii i

i

0 0

2 2

0i

v vi

R R

2

1

oF

i

v RA

v R

0

1 2

iv v

R R


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Ideal Op Amp


Unity-Gain Buffer

Inverting Amplifier


Non-ideal Op Amp


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Differential Amplifier

v v

11

1

v viR

Current into op amp is zero

01

2

v vi

R

+

-1R

2R

1v

ov

v

v1i

1

i

2v

1R

2R

22

1 2

Rv v

R R

01

1 2

v vv v

R R

2 21 2 2 0

1 2 1 2

1 2

R Rv v v v

R R R R

R R


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+

-1R

2R

1v

ov

v

v1i

1

i

2v

1R

2R

2 21 2 2 0

1 2 1 2

1 2

R Rv v v vR R R R

R R

2

2 2 20 1 2 2

1 1 2 1 1 2

R R Rv v v vR R R R R R

2 2 20 1 2

1 1 2 1

1R R R

v v v

R R R R

20 2 1

1

Rv v v

R


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Ideal Op Amp


Unity-Gain Buffer

Inverting Amplifier


Current-to-Voltage Converter

Non-ideal Op Amp


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i fi i

0v v

00 f Fv i R

0 i Fv i R

0Transresistance

i Fv i R

+

- o

vv

v

ii

FR fi


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Photodiode Circuit

25 A per milliwatt of incident radiationii

650 25 10 1.25mAii

Assume 3.2kF

R

3 3

0 1.25 10 3.2 10 4Vi Fv i R

+

- ov

v

v

ii

FR fi

h At 50 mW


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Ideal Op Amp


Unity-Gain Buffer

Inverting Amplifier



Non-ideal Op Amp


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Non-ideal Op Amp

Output voltage is limited by supply voltage(s) Finite gain (~105)

Limited frequency response

Finite input resistance (not infinite)

Finite output resistance (not zero)

Finite slew rate

Input bias currents

Input bias current offset Input offset voltage

Finite common mode rejection ratio (CMRR)

0slew rate ( )

MAXdv t dt


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Ref:080114HKN Operational Amplifier 24

Non-ideal case (Inverting Amplifier)

+

~

Rf

Ra

VinVo

3 categories are considering

Close-Loop Voltage Gain

Input impedanceOutput impedance

Equivalent CircuitRf

Ra

Vin Vo+

+

R RV

-AV

+

AVinVin Vout

Zout

~

Zin

Practical op-amp


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Close-Loop GainRf

RaVin

Vo+

+

R R

-AV

Ra Rf

R

V

V

Vin Vo

Applied KCL at Vterminal,

0

f

o

a

in

R

VV

R

V

R

VV

By using the open loop gain,

AVVo

0f

o

f

oo

a

o

a

in

AR

V

R

V

AR

V

AR

V

R

V

fa

aafaf

o

a

in

RRAR

RARRRRRRRV

R

V

The Close-Loop Gain,Av

RARRRRRRR

RAR

V

VA

aafaf

f

in

ov


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Close-Loop Gain

When the open loop gain is very large, the above equation become,

a

f

vR

RA

~

Note : The close-loop gain now reduce to the same formas an ideal case


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Closed-Loop Gain

2 1

1

1 1

1 2

1

2

1

0

0

1

o

I I

Io I I

o

I

vv v

A

v vi R R

vv v i R v R

R

v R

v R


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Input ImpedanceRf

Ra

VinVo

+

+

R

-AV

R'

RV

Rf

+

R

-AV

if

V

Input Impedance can be regarded as,

RRRR ain //

whereRis the equivalent impedance

of the red box circuit, that is

fi

VR

However, with the below circuit,

A

RR

i

VR

RRiAVV

of

f

off

1

)()(


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Input ImpedanceFinally, we find the input impedance as,

1

11

of

ainRR

A

RRR

RARR

RRRRR

of

of

ain)1(

)(

Since,

RARR of )1( , Rinbecome,

)1(

)(~

A

RRRR

of

ain

Again with )1( ARR of

ain RR ~

Note: The op-amp can provide an impedance isolated from

input to output


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Output ImpedanceOnly source-free output impedance would be considered,

i.e. Viis assumed to be 0 Rf

Ra

Vo+

R

-AV

RV

io

VV

Rf

Ra R+

R

-AV

V

i2 i1

(a)(b)

Firstly, with figure (a),

o

fafa

ao

af

a VRRRRRR

RRVV

RRR

RRV

//

//

By using KCL,io

= i1

+ i2

o

o

faf

oo

R

AVV

RRR

Vi

)(

//

By substitute the equation from Fig. (a),

RRARRRRRRRRRRRRRR

iV

R

afafao

fafao

o

o

out

)1())(1()(

isimpedance,outputThe

RandAcomparably large,

a

fao

outAR

RRRR

)(~

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