Chapter 3: Applications of Resistive Circuits

Chapter 3: Outline

Details in Chap. 7

Amplifier Models

Types of Amplifiers

l VCVS à Voltage amplifierl CCCS à Current amplifierl (VCCS, CCVS),…

Voltage Amplifier

: overall voltage amplification

)()( tsvvAtoutv =

vA

Voltage Amplifier

.

: input resistance iR

: open-circuit output voltage invcv µ=: output resistanceoR

in

ini i

vR ≡

Voltage Amplifier

.

oL

L

is

i

c

out

in

c

s

in

s

out

RRR

RRR

vv

vv

vv

vv

+××

+=××= µ

l A good voltage amplifier hasso that

. sRiR >> LRoR <<

µ≈vA

Current Amplifier

l Current amplifier with short-circuit output current:

inici β=

inici β=

l A good current amplifier hasso that

. sRiR >> LRoR <<

µ≈vA

Example 3.4:Cascade Voltage Amplifier

515

)10(241

1)10(

2488

+−

+−

+=vA

Operational Amplifiers(Op-Amps)

Amplifiers with very nice characteristics

Op-Amps

l Op-amps provide high-gain amplifications of the difference between two input voltages : nvpvdv −=

Op-Amps

Op-Amps

Op-Amps: Linear Region

0== nipi

)( nvpvAdAvoutv −==

maxmaxwhen vdvv <<−

PSVoutvPSV <<− and

APSVv /max ≈

∞→≈ Av for 0max

Op-Amps: Saturation Region

max if vdvPSVoutv >≈

max if vdvPSVoutv −<−≈

What is the equivalent circuit of an op-amp in the saturation region?

Op-Amps: Feedback Connection

l A stable op-amp requires negative feedback connection.

Various Op-Amp Circuits

l Non-inverting voltage amplifierl Voltage follower (buffer)l Inverting voltage amplifierl Inverting summing amplifierl Difference amplifierl many more…

Non-inverting Voltage Amplifier

Feedback factor B, loop gain AB, closed-loop gain A/(1+AB).

outoutf

n vBvRR

Rv ⋅=⋅

+=

1

1

dinoutind ABvvBvvv −=−=

ind vAB

v+

=1

1inout v

ABA

v+

=1

Non-inverting Voltage Amplifier

indinout vvvB

vAB <<≈>> ,1

, 1

Non-inverting Voltage Amplifier

With a load and a real source

BRRR

Av

v Fv

s

out 1

1

1 =+

== à No loading effects

Voltage Follower (Buffer)

No loading effects, Input resistance à∞, Output resistance=0

Ideal Op-Amps

l Aà∞ (infinite gain)l Vd=0 (virtual short)l ip=in=0 (no input current)l Still in the linear region

Vd

Vout

+VPS

-VPS

linear

+saturation

-saturation

Example 3.6: A Non-inverting Current Amplifier

Vd=0ip=in=0

sL

s

L

outoutnn

Foutssnp i

RkR

Rv

ikvvR

RRvRivv ===

+=== , ,

1

1

Inverting Voltage Amplifier

1RR

vRiRiv FinFinFFout −=−== invertergain unity 1 ⇒= RRF

Inverting Voltage Amplifier

With source internal resistance Rss

iin

11

1 ,RR

Rv

vA

RRR

vvs

F

s

outv

ssin +

−==+

=

To minimize loading effects, R1>>Rs, or add a voltage follower

- Non-inverting voltage amplifier: loading effects- Inverting voltage amplifier: loading effects

Inverting Summing Amplifier

KCL

21211

22

11

1

1

2

2

if )()( RRvvRR

vRR

vRR

v

Rv

Rv

Rv

FFFout

F

out

=+−=+−=

−=+

Example 3.7Want to have: )(40)(200)( tvtvtv baout −≈

)(40))5((40 21 vvvvv baout +−=+−−≈

PSout VVv <=11max

Inverting amplifier Inverting summing amplifier

Example 3.8: Difference Amplifier

32

32 RR

RvvP +

=32

2

1

3

1

11 RR

vRR

Rv

iiF ++−=−=

11

232

1

1 /1/1

vRR

vRRRR

RR

iRvv FFFFFnout −

++

=+=

)( if 121

1

3

2 vvRR

vRR

RR F

outF

−=⇒=

Chapter 3: Problem Set

l 14, 16, 20, 23, 25, 27, 29, 32, 36, 37, 39, 40, 45, 48