OP-AMP: OPERATIONAL AMPLIFIERS

The linear (first order) models for Op-Amps include DEPENDENT SOURCES and resistors

Op-amp IC: interconnection of transistors, resistors

PIN OUT FOR LM324 DIMENSIONAL DIAGRAM LM324

LM 324: General purpose Quad (four in a pack) op-amp

Amplifier 1: PIN 3 (IN 1+) and PIN 2 (IN 1-) are input pins : The output PIN is at PIN 1

IN 1+ : Non-inverting Input IN 1- : Inverting Input

PIN 4 : dc source VCC PIN 11: dc source VEE Amplification requires power

CIRCUIT SYMBOL FOR AN OP-AMP SHOWING POWER SUPPLIES

Relationship Between OUTPUT and INPUT VOLTAGES:

V0 = A0 (IN+ - IN-)

A0 = gain of the op-amp (10,000 -1,000,000) IN+ increases, V0 increases :non-inverting IN- increases, V0 decreases :inverting

VCC = positive dc voltage with respect to ground VEE = negative dc voltage Or ground itself

LINEAR MODEL

5 12

5 70

: 10 10: 1 50

: 10 10

i

O

RRA

Ω − Ω

Ω − Ω

−

TYPICAL VALUES

Op-amps are good voltage amplifiers: easy to create an Accurate first order (linear) model

Relationship Between OUTPUT and INPUT VOLTAGES:

V0 = A0 (IN+ - IN-) = A0 Vin

Condition 1: Input and Output currents are proportional to Input and Output voltages. Design: Find the input and output resistances using Ohm’s law

Voltage controlled voltage source: V0 = A0 Vin

CIRCUIT WITH OPERATIONAL AMPLIFIER

DRIVING CIRCUIT

LOAD

OP-AMP

Find the voltage gain V0/Vs

Choose Op-amp parameters that maximizes the gain.

Effect of supply voltages: VCC and VEE

-minimum and maximum supply voltage ranges over which Op-amp is guaranteed to function

- For proper function in the linear range, input and output voltages are limited to no more than the supply voltages

TRANSFER PLOTS FOR SOME COMERCIAL OP-AMPS

SATURATION REGION LINEAR

REGION

IDENTIFY SATURATION REGIONS OP-AMP IN SATURATION

CIRCUIT AND MODEL FOR UNITY GAIN BUFFER

0=+++− inOOis VAIRIRV :KVL

0=++ inOO VAIRoutV- :KVL

IRV iin = : VARIABLEGCONTROLLIN

iOO

is

out

RARRV

V

++

=1

1SOLVING

1→⇒∞→S

outO V

VA

WHY UNIT GAIN BUFFER?

BUFFER GAIN

PERFORMANCE OF REAL OP-AMPS

Op-Amp BUFFER GAINLM324 0.99999LMC6492 0.9998MAX4240 0.99995

⇒∞=A

)(0 −+ −=⇒= vvAvR OO

THE IDEAL OP-AMP

⇒∞=iR

∞=∞==⇒ ARR iO ,,0IDEAL

+i

−i

THE UNITY GAIN BUFFER – IDEAL OP-AMP ASSUMPTION

svv =+

+− = vv

OUTv v−

=

OUT Sv v=

OUTv+

−

1OUT

S

vv

⇒ =

USING LINEAR (NON-IDEAL) OP-AMP MODEL WE OBTAINED

1

1

out

is

O O i

VRV

R A R

=+

+

PERFORMANCE OF REAL OP-AMPS

Op-Amp BUFFER GAINLM324 0.99999LMC6492 0.9998MAX4240 0.99995

IDEAL OP-AMP ASSUMPTION YIELDS EXCELLENT APPROXIMATION!

WHY USE THE VOLTAGE FOLLOWER OR UNITY GAIN BUFFER?

svv =+

+− = vv

−= vvO

SO vv =

SO vv =

THE VOLTAGE FOLLOWER ACTS AS BUFFER AMPLIFIER

THE SOURCE SUPPLIES POWER

THE SOURCE SUPPLIES NO POWER

THE VOLTAGE FOLLOWER ISOLATES ONE CIRCUIT FROM ANOTHER ESPECIALLY USEFUL IF THE SOURCE HAS VERY LITTLE POWER

CONNECTION WITHOUT BUFFER CONNECTION WITH BUFFER

LEARNING EXAMPLE

s

out

VVG = GAIN THE DETERMINE

0=+v

0=∴=⇒∞= −−+ vvvAo

0=−v

0==⇒∞= +− iiRi

00021

=−

+−

RV

RV outs

- v@KCL APPLY

0=−i1

2

RR

VVGs

out −==

FOR COMPARISON, NEXT WE EXAMINE THE SAME CIRCUIT WITHOUT THE ASSUMPTION OF IDEAL OP-AMP

REPLACING OP-AMPS BY THEIR LINEAR MODEL

WE USE THIS EXAMPLE TO DEVELOP A PROCEDURE TO DETERMINE OP-AMP CIRCUITS USING THE LINEAR MODELS

1.  Identify Op Amp nodes

v−

v+

ov

2. Redraw the circuit cutting out the Op Amp

v−

v+

ov

3. Draw components of linear OpAmp (on circuit of step 2)

v−

v+

oviR

OR

+

−( )A v v+ −−

4. Redraw as needed

2R

v−

v+

INVERTING AMPLIFIER: ANALYSIS OF NON IDEAL CASE

NODE ANALYSIS

CONTROLLING VARIABLE IN TERMS OF NODE VOLTAGES

USE LINEAR ALGEBRA

Ω=Ω=

=

10,10

,108

5

Oi RR

A :AMP-OPTYPICAL 9996994.45,1 21 −=⇒Ω=Ω=

S

O

vvkRkR 000.5−=⇒∞=

S

O

vvA

0=−i

0==⇒∞= +− iiRi

−+ =⇒∞= vvA

0=+v

0=−v

KCL @ INVERTING TERMINAL

000

21=

−+

−Rv

Rv OS

1

2

RR

vvs

O −=⇒

THE IDEAL OP-AMP ASSUMPTION PROVIDES EXCELLENT APPROXIMATION. (UNLESS FORCED OTHERWISE WE WILL ALWAYS USE IT!)

GAIN FOR NON-IDEAL CASE

SUMMARY COMPARISON: IDEAL OP-AMP AND NON-IDEAL CASE

NON-IDEAL CASE

REPLACE OP-AMP BY LINEAR MODEL SOLVE THE RESULTING CIRCUIT WITH DEPENDENT SOURCES