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MICROELECTRONICS ELCT 703 (W19)LECTURE 6 : OP-AMP LINEAR/NONLINEAR

APPLICATIONS

Dr. Eman Azab

Assistant Professor

Office: C3.315

E-mail:

[email protected]. EMAN AZAB

ELECTRONICS DEPT., FACULTY OF IET

THE GERMAN UNIVERSITY IN CAIRO

1

EXAMPLE

Find the input resistance of the inverting amplifier shown in Figure taking into account the input resistance Rin and finite gain A of the op-amp

DR. EMAN AZAB



2

R2

R1Vin

Vout

_

+

RinVid

+

-

A Vid

Rin

Fig.2(a)

iin

𝑹𝒊𝒏 =𝑽𝒊𝒏

𝒊𝒊𝒏= 𝑹1 + 𝑹𝒊𝒏 /

𝑹2

1 + 𝑨

NON-IDEALITIES EFFECT ON OP-AMP APPLICATIONS Linear and Non-linear

Applications

DR. EMAN AZAB



3

VOLTAGE AMPLIFIER

DR. EMAN AZAB



4

Inverting and Non-Inverting Amplifiers

𝑣𝑂𝑣𝐼

= −𝑅2𝑅1

𝑣𝑂𝑣𝐼

= 1 +𝑅2𝑅1

Figure from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.

VOLTAGE BUFFER

DR. EMAN AZAB



5

Voltage Buffer

The voltage at the input is derived at the output node without drawing any current fromthe input source

𝑣𝑂𝑣𝐼

= 1


VOLTAGE DIFFERENCE AMPLIFIER

DR. EMAN AZAB



6

The circuit subtracts two voltage signals

By Applying Superposition principle between 𝑣𝐼1 and 𝑣𝐼2

By Choosing:

𝑣𝑂 = −𝑣𝐼1𝑅2𝑅1

+ 𝑣𝐼2𝑅4

𝑅4 + 𝑅31 +

𝑅2𝑅1


𝑅2𝑅1

=𝑅4𝑅3

𝑣𝑂 =𝑅2𝑅1

𝑣𝐼2 − 𝑣𝐼1

VOLTAGE INTEGRATOR

DR. EMAN AZAB



7

Inverting configuration with General Impedances

Lossless inverting Integrator


𝑉𝑂𝑉𝑖

= −𝑍2𝑍1

VOLTAGE INTEGRATOR

DR. EMAN AZAB



8

Lossy Integrator

DC Gain is defined by:


𝑣𝑂𝑣𝑖

= −

𝑅𝐹𝑅

1 + 𝑠𝐶𝑅𝐹

𝑣𝑂𝑣𝑖

(0) = −𝑅𝐹𝑅

VOLTAGE DIFFERENTIATOR

DR. EMAN AZAB



9

Op-amp based Differentiator


𝑣𝑂𝑣𝑖

(𝑠) = −𝑠𝐶𝑅

VOLTAGE WEIGHTED SUMMER

DR. EMAN AZAB



10Figure from Sedra/Smith Copyright © 2010 by Oxford University Press, Inc.

VOLTAGE COMPARATOR

DR. EMAN AZAB




Positive Feedback is employed

The output voltage is either the high or the low voltage supply

𝑣𝑖 < 𝑣+ 𝑣𝑂 = 𝑉𝐶𝐶

𝑣𝑖 > 𝑣+ 𝑣𝑂 = 𝑉𝑆𝑆

VOLTAGE LOGARITHMIC AMPLIFIER

DR. EMAN AZAB



12

Non-linear logarithmic Amplifier

BJT operates in the Active Region

𝑉𝑜𝑢𝑡 = −𝑉𝐵𝐸 = −𝑉𝑇𝑙𝑛𝐼𝐶𝐼𝑜

𝐼𝐶 =𝑉𝑖𝑛𝑅1

𝑉𝑜𝑢𝑡 = −𝑉𝐵𝐸 = −𝑉𝑇𝑙𝑛𝑉𝑖𝑛𝐼𝑜𝑅1

VOLTAGE ANTI-LOGARITHMIC AMPLIFIER

DR. EMAN AZAB



13

Non-linear Anti-logarithmic Amplifier

BJT operates in the Active Region

𝑉𝑖𝑛 = −𝑉𝐵𝐸 = −𝑉𝑇𝑙𝑛𝐼𝐶𝐼𝑜

𝐼𝐶 =𝑉𝑜𝑢𝑡𝑅1

𝑉𝑜𝑢𝑡 = 𝐼𝑜𝑅1exp−𝑉𝑖𝑛𝑉𝑇

EXAMPLE

DR. EMAN AZAB



14

For the 4127 IC showed in figure, find the output voltage (Vout) as a function in the input currents (Ix and Iy).

Using the 4127 IC and the linear/nonlinear op-amp applications, design the following functions with minimum number of op-amps and derive K, n and m as a function in the circuit parameters.

Note that: Q1 and Q2 are matched and β is large.

𝑉𝑜𝑢𝑡 = 𝐾𝐼𝑥𝐼𝑦

𝑚

𝑉𝑜𝑢𝑡 = 𝐾𝐼𝑥𝐼𝑦

𝑚−𝑛

WAVE-FUNCTION GENERATORS

Introduction

DR. EMAN AZAB



15

INTRODUCTION

DR. EMAN AZAB



16

Oscillators (Wave-Function Generators) are used in all

communication systems

They are used to generate sinusoidal or triangular wave

forms with adjustable magnitude and frequency

There is different architectures and designs for these

circuits, we will focus on the designs using voltage op-

amps

Op-amp based Oscillators are critically stable closed-

loop systems designed using positive feedback

Op-amp comparators are the basic building block for the

oscillators

VOLTAGE COMPARATOR

DR. EMAN AZAB





The output voltage is either the high or the low voltage

supply

𝑣𝑖 < 𝑣+ 𝑣𝑂 = 𝑉𝐶𝐶

𝑣𝑖 > 𝑣+ 𝑣𝑂 = 𝑉𝑆𝑆

VOLTAGE COMPARATOR

DR. EMAN AZAB



18



The output voltage is either the high or

the low voltage supply

By varying vi with time to be greater

and smaller than VR we obtain a

square wave form at the output

SQUARE WAVE-FUNCTION GENERATOR

DR. EMAN AZAB



19


The circuit consists of a voltagecomparator and RC circuit

Assume that the initial voltage ofcapacitor is low, thus the output ofcomparator is high at L+, thus thevoltage at the positive input terminalof the op-amp is high tooThe comparator will maintain the

value L+ while the capacitor will startcharging

Once the capacitor charge to V+value the output of the comparatorwill change to L- (the negativeterminal of the op-amp becomesgreater than the positive one)

1

1 2

TH

RV L V

R R

SQUARE WAVE-FUNCTION GENERATOR (CONT.)

DR. EMAN AZAB



20

At this moment the capacitor voltageis greater than the output voltage L-and V+

Thus the capacitor will start todischargeThe comparator will maintain the

value L- while the capacitor isdischarging

Once the capacitor discharge to V+value the output will change to L+again (the negative terminal voltageof the op-amp becomes less than thepositive one)

Then the capacitor will start chargingagain!

1

1 2

TL

RV L V

R R


DR. EMAN AZAB



21


The output of the comparator is a

square wave with amplitudes L+

and L- (maximum and minimum

op-amp supply)


DR. EMAN AZAB



22

To calculate the frequency of theoutput wave form, we must calculatethe charging and discharging timeof the capacitor

Where R is the charging resistor, Cis the capacitor used, VSt is thesteady state voltage of thecapacitor (L+ or L-), Vini and VF is theinitial and final capacitor voltagerespectively

𝑇 = 𝑅𝐶 ln𝑉𝑆𝑡 − 𝑉𝑖𝑛𝑖𝑉𝑆𝑡 − 𝑉𝐹


DR. EMAN AZAB



23

T1 and T2 is the charging and

discharging time respectively

The output wave form frequency is:

Note: for symmetric wave forms

1

1 21

1

1 2

ln

RL L

R RT RC

RL L

R R

1

1 22

1

1 2

ln

RL L

R RT RC

RL L

R R

1 2

1f

T T

1 2T T

TRIANGULAR WAVE-FUNCTION GENERATOR

DR. EMAN AZAB




A Triangular wave

function generator can be

realized by integrating a

square wave form

Thus adding an op-amp

based integrator after

the square wave function

generator will realize a

triangular waveform

1

1 2

TH

RV L

R R

1

1 2

TL

RV L

R R

TRIANGULAR WAVE FUNCTION GENERATOR (CONT.)

DR. EMAN AZAB



25

To calculate the

frequency of the wave

form, we need to

calculate the slope of the

capacitor voltage

changing with time

CC

dVI C

dt

, argC ch e

LI

R

, argC disch e

LI

R

1 1

1 2 1 21

R RL L

R R R RT RC

L

1 1

1 2 1 22

R RL L

R R R RT RC

L

EXAMPLE

DR. EMAN AZAB



26

A voltage Controlled SQW generator (VCO) is shown in

Figure .The frequency of the oscillator is controlled by a

multiplier with an input D.C. Voltage Vref .

Sketch the output waveform and derive an expression

for the output frequency as a function of Vref .

microelectronics elct 703 (w19) op-amp …eee.guc.edu.eg/courses/electronics/elct703...example find...

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