Chapter 4The Operational Amplifier

Ckts W/ Operational Amplifiers• Why Study OpAmps

At This Point?1. OpAmps Are Very

Useful Electronic Components

2. We Have Already Developed The Tools To Analyze Practical OpAmps Circuits

3. The Linear Models for OpAmps Include Dependent Sources

• A PRACTICAL Application of Dependent Srcs

OpAmp Symbol & Model• The Circuit Symbol

Is a Version of the Amplifier TRIANGLE

The Linear Model

OUTPUT RESISTANCE

INPUT RESISTANCE

GAIN

75

125

1010:

501:

1010:

A

R

R

O

i

• Typical Values

• -Vcc, when A(Vp-Vn)<-Vcc

• A(Vp-Vn),

when -Vcc< A(Vp-Vn)< +Vcc

• +Vcc, when A(Vp-Vn) >+Vcc

Vo =

2 Ways of Using Op-Amps

• “Open Loop”: very high gain amplifier– Useful for comparing 2 voltages– Fixed gain, always at MAX OUTPUT!!

• “Closed Loop” with negative feedback– Useful for amplifying, adding, subtracting,

differentiation and integration (using capacitors)– Variable gain, controlled by resistor selection

“Open-Loop” examples• Ideal Comparator and Transfer Characteristic

“Zero-Cross” Detector → Heart of Solid State Relay Cnrtl

““Closed Loop” Example: Unity Gain Buffer Closed Loop” Example: Unity Gain Buffer

Controlling Variable = IRV iin

Solve For Buffer Gain

O

iOO

is

out A

RARRV

Vrecall

1

1 Thus The Amplification

1S

outO V

VA

0 inOOis VAIRIRV :KVL

0 inOO VAIRoutV- :KVL

Op-Amp BUFFER GAINLM324 0.99999LMC6492 0.9998MAX4240 0.99995

Consequences for Vp-Vn• Normally, A is 10,000 or more, so to avoid

saturation, abs(Vp-Vn) must be < Vcc/10000, or, if Vcc = 20V, about 2 mV which is negligible for most circuits

• With an Ideal Op-amp, A = infinity, so Vp = Vn to avoid saturation

• Negative Feedback resistors “force” Vp = Vn i.e. if Vp-Vn gets large, A(Vp-Vn) pulls back toward zero (more on this later)

But…always remember Vcc/-Vcc limits…if Vo saturates Vp does not = Vn !!!

Terminal Characteristics for an ideal op amp in it’s Linear Range:

• Ip = In = 0 (very high input resistance=1MOhm)

• Io can be very large (coming from Vcc/-Vcc)

Inverting Amplifier

Vo = -RfVs Rs

When in linear

region

Inverting Amplifier with Feedback Path broken

• Vo= -AVs

Saturation

(unless Vs<2mv)

Summing Amplifier

Vo = - Rf (Va + Vb + Vc) (in linear region)

Rs

Non-Inverting Amplifier

Vo=(Rs+Rf) Vg

Rs

In linear region

Difference Amplifier

Vo= Rb (Vb – Va) in linear region AND

Ra IFF Ra/Rb = Rc/Rd

Common Mode Rejection Ratio

IF Ra/Rb =(1-e) Rc/Rc (e=very small)CMMR = abs(1 + Rb/Ra)

e

Comparator, used in digital circuits

Application, the Flash Converter

• Comparators quantize

Encoder converts to binary