Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering

School of Electrical and Computer Engineering

Introduction to Electronics

An introduction to linear electric components and a study of circuits containing such devices.

Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering

School of Electrical and Computer Engineering

Introduce Integrating and Differentiating Op Amp Circuits

Differentiators and Integrators

Basic Op Amp Amplifier Configurations

Previous Lesson

3

Introduce Differentiators and Integrators Demonstrate the performance of both circuits on an

oscilloscope

Lesson Objectives

4

Differentiator Circuit

dtdVRCV ino =

+

-

vin

vo

R

Cv-v+

cc V

dtdVCi=

5

Differentiator Circuit

Derivation:1. KVL: Vin = Vc + Ri + Vo2. Vin = Vc3. Vo = -Ri = -RC(dVin / dt)

dtdVRCV ino =

+

-

vin

vo

R

Cv-v+

6

Differentiator Example

+

-

vin

vo

1000

1Fv-v+

vin v+

vo+VS= 15v

-VS = -15v

-VS

v-

+VS

7

Results

dtdVRCV ino =

8

Integrator Circuit

dtVRC

Vt

ino

=0

1

cc V

dtdVCi= =

t

c idtCV

0

1

+

-

vin

voR

v-v+

C

9

Integrator Circuit

Derivation:For t0: Vin = iR i = Vin/RVin = iR + Vc + VoVo = -Vc = -1/C

t Vin/R dt0dtV

RCV

t

ino

=0

1

cc V

dtdVCi= =

t

c idtCV

0

1

+

-

vin

voR

v-v+

C

10

Integrator Examplevin v+

vo+VS= 15v

-VS = -15v

-VS v-

+VS

+

-

vin

vo1000

v-v+

1F

11

Results

dtVRC

Vt

ino

=0

1

12

Summary

Differentiator and Integrator Op Amp circuits examined

13

Active Filters

Next Lesson

14

Slide Number 1Slide Number 2Previous LessonLesson ObjectivesDifferentiator CircuitDifferentiator CircuitDifferentiator ExampleResultsIntegrator CircuitIntegrator CircuitIntegrator ExampleResultsSummaryNext Lesson