The operational amplifier

Difference amplifier

V1 V2

Ri

+

_

Ro

+

_A(V1-V2)

Vo

ModelFor an ideal op ampRi→∞Ro→0A→∞

Vcc+

+

_

V1V2

Vo

Vcc-

Vcc+

Vcc-

Vsat+

Vsat-

1 7

814

LM324

+_ + _

+_ + _

Vcc+

Vcc-

Example of packagingFor an actual op-amp:A = 105 Rin= 2 MΩRo = 75 ΩVsat+= 13.5V Vsat-= -13.5VIn the open loop mode it operates as a comparator

Vcc+

+

_

V1V2

Vo

Vcc-

Vcc+

Vcc-

Vsat+

Vsat-

t

V2

V1V1+0.135mVV1-0.135mV

Digital to Analogue Converter (D/A Converter)

+

_

Vo

bo

b1

b2

b3

Rf

Ri

2Ri

4Ri

8Ri

b3b2b1bo is a 4-bit binary number

Vo= - [ Rf/Ri b3 + Rf/(2Ri) b2 + Rf/(4Ri) b1+ Rf/(8Ri) bo ]

Vo= - Rf/Ri [ b3+ b2/ 2 + b1/4 + bo/8 ]

Vo= - Rf / (8Ri) [ 8 b3 + 4 b2 + 2 b1 + bo ]

Vo= - Rf / (8Ri) [ 23 b3 + 22 b2 + 21 b1 + 2o bo ]

Analogue to Digital Converter (A/D converter)

Single Slope Dual Slope

Single Slope A/D Converter

+ Comparator_

Vi

rampgenerator

Clock

And Counter

ramp o/p

Vi

t

t

Comparatoro/p

t

Input tocounter

A single slope A/D converter has a ramp generator with a slope of 1 V/ms and a clock frequency of 100 kHz. If the analogue input voltage is 2 volts, what is the count at the end of the conversion cycle?

The time taken by the ramp to reach 2 V

(2V) / (1V/ms) = 2 ms

The counter counts for 2 ms at a frequency of 100 kHz

During 2 ms the number counted by the counter is

( 100 × 103 × 2 ×10-3 = 20010 clock pulse or 110010002

Ramp Generator

Vin Vo - V2

- V2sC + = 0sR3 R4

V2[ sC + 1/R4] =Vin/(sR3) + Vo/R4 V2[R4sC + 1 ] = R4 Vin/(sR3)+ Vo

Vo R1

V1 = R1+R2

+

_

R1R2

R3R4

1 SC

Vin

S

Vo

V1

V2≈ V1 Vin

SR3

R3

V2

1SC

R4

Vo

R4 Vin /s Vo R1 V2 = + = Vo R3 [ 1 + R4Cs ] [ 1 + R4Cs ] [ R1+R2]

R4 Vin /s Vo R1 V2 = + = Vo

R3 [ 1 + R4Cs ] [ 1 + R4Cs ] [ R1+R2]

R4 Vin/s R1 1 = ( - ) Vo R3 [ 1+R4Cs ] [R1+R2] [ 1+ R4Cs]

[ 1+R4Cs ] R1

R4/R3 Vin/s = ( - 1 ) Vo [R1+R2]

R1+R1R4Cs – R1 – R2 R4/R3 Vin/s = Vo [R1+R2]

R1R4Cs – R2 R4/R3 Vin/s = Vo [R1+R2]

Dual Slope A/D Converter

Vin

- Vref

+

_

R1R2

R3R4

C

+

_

ramp generator

comparator

AND gate

clock

counter

electronic switch

MSB