Basic Block Diagram of Op-AmpAn Op-Amp can be conveniently divided in to four main blocks1. An Input Stage or Input Diff. Amp.2. The Gain Stage3. The Level Translator4. An Out put Stage Note: It can be used to perform various mathematical operations such

as Addition, Subtraction, Integration, Differentiation, log etc.

Input Stage(Diff. Amp.)

Gain Stage (C E Amp.)

Level Shifter

Out put Stage (Buffer)

V1

V2

VO

Op-Amp IC

I/P

An IDEAL OP AMP

An ideal op amp has the following characteristics:1. Infinite open-loop voltage gain, AV ≈ ∞.

2. Infinite input resistance, Ri ≈ ∞.

3. Zero output resistance, Ro ≈ 0.

4. Infinite CMRR, ρ =∞

5. The output voltage Vo=0; when Vd = V2-V1 = 0

6. Change of output with respect to input, slew rate = ∞

7. Change in out put voltage with Temp., ∂Vo/∂Vi=0

An Electrical Representation of Op Amp.

• i(+), i(-) : Currents into the amplifier on the inverting and non-inverting lines respectively

• vid : The input voltage from inverting to non-inverting inputs• +VS , -VS : DC source voltages, usually +15V and –15V• Ri : The input resistance, ideally infinity• A : The gain of the amplifier. Ideally very high, in the 1x1010 range.• RO: The output resistance, ideally zero• vO: The output voltage; vO = AOLvid where AOL is the open-loop voltage gain

The Operational Amplifier+VS

-VS

vid

Inverting

Noninverting

Output

+

_i(-)

i(+)

vO = AdVid

RO

ARi

• An operational amplifier circuit is designed so that

1) Vout = Av (V1-V2) (Av is a very large gain)

2) Input resistance (Rin) is very large

3) Output resistance (Rout) is very low

Operational Amplifier Model

V1

V2

VoutRin

+-

Rout

Av(V1- V2)

Practical Op-Amp Circuits

These Op-amp circuits are commonly used:– Inverting Amplifier– Noninverting Amplifier– Unity Follower– Summing Amplifier– Integrator– Differentiator

Slide 7

Inverting Op-Amp

V1R1

RfVo

Notice the output formula is similar to Inverting Amplifier, but they are not the same.

Noninverting Amplifier

V1)R1

Rf1(Vo

Summing Amplifier

Because the op-amp has a high input impedance the multiple inputs are treated as separate inputs.

3

3

f2

2

f1

1

fV

R

RV

R

RV

R

RVo

Summing Amplifier

Inverting Amplifier: Input and Output Resistances

Rinvsis

R1 since v 0

11i

22iov RR

But i1=i2)

12(

1iv RRo

Since v- = 0, i1=0. Therefore vo

= 0 irrespective of the value of io

. 0 outR

Rout is found by applying a test current (or voltage) source to the amplifier output and determining the voltage (or current) after turning off all independent sources. Hence, vs = 0

Differential Amplifier Using Op Amp

v v

11

1

v vi

R

I/P Current to op amp is zero

01

2

v vi

R

+

-1R

2R

1vovv

v1i

1i

2v1R

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

Differential Amplifier Using Op Amp

+

-1R

2R

1vovv

v1i

1i

2v1R

2R

2 21 2 2 0

1 2 1 2

1 2

R Rv v v v

R R R R

R R

2

2 2 20 1 2 2

1 1 2 1 1 2

R R Rv v v v

R R R R R R

2 2 20 1 2

1 1 2 1

1R R R

v v vR R R R

20 2 1

1

Rv v v

R

The Unity-Gain Amplifier or “Buffer”

• This is a special case of the non-inverting amplifier, which is also called a voltage follower, with infinite R1 and zero R2.

Hence Av = 1.• It provides an excellent electrical isolation while maintaining the signal voltage

level.• The “ideal” buffer requires no input current and can drive any desired load

resistance without loss of signal voltage.• Such a buffer is used in many sensor and data acquisition system applications.

1oF

i

vA

v

i ov v v v

+

-ov

v

viv

oF

i

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.

Unity-Gain Buffer

Op-Amp Integrator

Since the inverting input is at virtual ground

dt

dvCi o

2

R

vi in1

Applying KCL at the inverting input

i1+i2 = 0

0R

v

dt

dvC ino

)initial(vdtvRC

1v oino

Op-Amp Integrator Cont…

Op-Amp Differentiator Circuit

dt

dvCi in

1

R

vi o

2

i1+i2 = 0

0R

v

dt

dvC oin

dt

dvRCv in

o

Since the inverting input is at virtual ground

Applying KCL at the inverting input

Differentiators are avoided in practice as they amplify noise

Op-Amp Differentiator Cont…

Instrumentation Amplifier

Combines 2 non-inverting amplifiers with the difference amplifier to provide higher gain and higher input resistance. Gain can be varied by varying single resistor R1

)b

va(v

3

4v R

Ro

bv

2i)

1i(2

2iav RRR

12

2v

1v

iR

)2

v1

(v

1

21

3

4v

R

R

R

Ro

NOTE

Ideal input resistance is infinite because input current to both op amps is zero. The CMRR is determined only by Op Amp 3.

Finite Open-loop Gain and Gain Error

21

1

ovov

21

11

v

RR

R

RR

R

is called the feedback factor.

AA

vA

AAA

1svov

)ovsv()1

vsv(id

vov

Av1

1R

2R1

This is the “ideal” voltage gain of the amplifier. If Ab is not >>1, there will be “Gain Error”.

• Gain Error is given by

GE = (ideal gain) - (actual gain)

For the non-inverting amplifier,

• Gain error is also expressed as a fractional or percentage error.

)1(1

11

AAAGE

FGE

1

A1A1

11A

1A

PGE 1A

100%

io 5V500

10mA

)21

(

ov

12

ovovF

iL

ioi

RRLR

EQR

EQRRR

LR

For the inverting amplifier,

2RLREQ

R

Practical op amps have limited output voltage and current ranges.

Voltage: Usually limited to a few volts less than power supply span.

Current: Limited by additional circuits (to limit power dissipation or protect against accidental short circuits).

The current limit is frequently specified in terms of the minimum load resistance that the amplifier can drive with a given output voltage swing. Eg:

Output Voltage and Current Limits

Bistable