EENG 2610: Circuits AnalysisClass 6: Operational Amplifiers (Op-Amp), 1/2

Oluwayomi AdamoDepartment of Electrical EngineeringCollege of Engineering, University of North Texas

Operational Amplifier (Op-Amp) Op-amp is the single most important integrated circuit (IC) for analog circuit

design; it has been extensively used in circuit design at all levels. Op-amp is consisted of individual transistors and resistors interconnected

on a printed circuit board (PCB) Op-amp was originally designed to perform mathematical operations such

as addition, subtraction, differentiation, and integration. We have learned tools to analyze practical circuits using op-amps !

Op-Amp Models Op-amp is just a really good voltage amplifier! Example: LM324 from National Semiconductor

General purpose quad (four in a pack) op-amp.

unit: inch

Dual Inline Pack (DIP) style packageFour identical op-amps in the package IN +: noninverting input IN -: inverting inputOUT : output VCC: positive voltage VEE: negative voltage or ground

)(00 ININAV

Typically, A0 is between 10,000 and 1,000,000 !

In-Out Voltage Relation:

Op-amp is modeled using a dependent voltage source and resistors

Power Supply and Ground

A simple model of op-amp

gain amp-op :

resistoroutput :

resistorinput :

A

R

R

o

i

)( vvAvo

In-Out Voltage Relation:

voltage source

Effects of Power Supply Each op-amp has minimum and maximum supply ranges over

which the op-amp is guaranteed to function For proper operation, the input and output voltages are limited to no

more than the supply voltages (VCC, VEE). Inputs and output are called rail-to-rail, if the inputs and output can

reach within a few dozen millivolts of the supplies. An op-amp is said to be in saturation,

If an increase in the input voltage may not yield a corresponding increase in the output voltage

Saturation and Rail-to-Rail

)( vvAvo

In-Out Voltage Relation:

Rail-to-rail output voltage

PA03

Unity Gain Buffer Circuit

iin

inOOout

inOOis

IRv

vAIRv

vAIRIRV

0

0

iOO

is

out

RAR

RV

v

1

1

1S

outO V

VA

That’s why it’s called Unity Gain Buffer,or Voltage Follower.PERFORMANCE OF REAL OP-AMPS

Op-Amp BUFFER GAINLM324 0.99999LMC6492 0.9998MAX4240 0.99995

VoltageGain:

?,, ooi ARRWhat should be the values for

Lo

Lo

Thi

i

S

o

RR

RA

RR

R

V

v

1

Voltage Gain:

To achieve large overall gain independent of ideally 0,, oio RRA

LTh RR ,1

(Commercial op-amps do have this tendency !)

Equivalent resistance of voltage source Equivalent load

resistance

Op-amp Model

Ideal Op-Amp Model

ARR iO ,,0 : Model Ideal

vv

ii 0

i

i

iR

)(

vvAv

A

o

0 vv

Analyze unity gain buffer using ideal model

ARR iO ,,0 : Model Ideal

vv

ii 0

v

v

0i

0i

1i

LR

CCV Where does the current come from?1i

v

v

so vvvv

Why use unity gain buffer? Unity gain buffer is buffer amplifier

Unity gain buffer isolates driving circuits from load circuits, which is called buffering

The load current (or energy) comes from op-amp power supply, which have plenty of current (or energy) output capacity, rather than the driving circuit.

CONNECTION WITHOUT BUFFER CONNECTION WITH BUFFER

Sv

consume source energySR does not consume source energySR

driving circuitdriving circuit

load load0 0 CCV

iRvv sso so vv

Op-Amp Circuit Analysis General rule for op-amp circuit analysis

Use the ideal op-amp model conditions Write nodal equations at the op-amp input terminals

ARR iO ,,0 : Model Ideal

vv

ii 0

Example 4.2: Basic inverting op-amp configurationDetermine gain using both non-ideal model and ideal model

Note: the ground can all be connected to a single node.

Equivalent

1. Identify op-amp nodes

2. Redraw the circuit cutting out the op-amp

v

v

ov

4. Redraw as needed

2R

v

v

v

v

ov

3.Draw components of linear op-amp

v

v

oviR

OR

( )A v v

Using non-ideal op-amp model:

)1

()1

()11

)(111

(1

)1

)(1

()11

)(111

(

))(1

(

22221

1

2

22221

12

ooi

S

o

ooi

S

oo

RA

RRRRRRR

RR

v

v

RA

RRRRRRR

R

v

RA

Rv

51

2lim

R

R

v

v

S

o

A

Typical values:

kRkR

RRA i

5,1

,10,10,10

21

085

59996994.4 S

o

v

v2v

3v

v

v

ov

Using ideal op-amp model:

vv

ii 0Ideal op-amp model:

000

0

21

R

v

R

v

vv

oS1

2 R

R

v

v

s

o

From now on, unless otherwise stated, we will use the ideal op-amp model to analyze circuits containing op-amp.

General rule for op-amp circuit analysis Use the ideal op-amp model conditions Write nodal equations at the op-amp input terminals