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"Handbook of Operational Amplifier Active RC Networks" Application Report
SBOA093A October 2001
1
Handbook Of Operational Amplifier Active RC Networks
Bruce Carter and L.P. Huelsman



ABSTRACT
While in the process of reviewing Texas Instruments applications notes, including those
from the recently acquired Burr-Brown I uncovered a couple of treasures, this handbook
on active RC networks and one on op amp applications. These old publications, from
1966 and 1963, respectively, are some of the finest works on op amp theory that I have
ever seen. Nevertheless, they contain some material that is hopelessly outdated. This
includes everything from the state of the art of amplifier technology, to the parts
referenced in the document even to the symbol used for the op amp itself:

These numbers in the circles referred to pin numbers of old op amps, which were potted
modules instead of integrated circuits. Many references to these numbers were made in
the text, and these have been changed, of course.
In revising this document, I chose to take a minimal approach to the material out of
respect for the original author - L.P. Huelsman, leaving as much of the original material in
tact as possible while making the document relevant to present day designers. I did clean
up grammatical and spelling mistakes in the original. I even elected to leave the original
RC stick figure illustrations, which have minimal technical content but added to the
readability of the document. SBOA093A
2
Handbook Of Operational Amplifier Active RC Networks

Contents
CHAPTER 1........................................................................................................................................... 6

Introduction..................................................................................................................................... 6

CHAPTER 2......................................................................................................................................... 11

The Infinite-Gain Single-Feedback Circuit .................................................................................... 11

The Operational Amplifier ............................................................................................................. 11

The Basic Single Feedback Circuit ............................................................................................... 12

The Voltage Transfer Function ..................................................................................................... 13

The Passive Networks.................................................................................................................. 16

Network Design ............................................................................................................................ 18

Conclusions.................................................................................................................................. 20

CHAPTER 3......................................................................................................................................... 21

The Infinite-Gain Multiple-Feedback Circuit .................................................................................. 21

The Basic Multiple Feedback Circuit............................................................................................. 21

The Voltage Transfer Function ..................................................................................................... 21

Network Design ............................................................................................................................ 23

Conclusions.................................................................................................................................. 26

CHAPTER 4......................................................................................................................................... 27

The Controlled Source Circuit....................................................................................................... 27

The Voltage-Controlled Voltage Source........................................................................................ 27

Network Design ............................................................................................................................ 28

Other Realizations with Voltage-Controlled Voltage Sources........................................................ 33

Conclusions.................................................................................................................................. 34

CHAPTER 5......................................................................................................................................... 36

The NIC In Active RC Circuits....................................................................................................... 36

The NIC (Negative-Immittance Converter).................................................................................... 36

A Realization for the INIC ............................................................................................................. 38

Stability of the INIC....................................................................................................................... 39

The Basic INIC Circuit .................................................................................................................. 40

Network Design ............................................................................................................................ 41

Conclusions.................................................................................................................................. 44

CHAPTER 6......................................................................................................................................... 45

Another Active Device: The Gyrator............................................................................................. 45

Definition of a Gyrator................................................................................................................... 45

Properties of the Gyrator .............................................................................................................. 45

A Gyrator Realization ................................................................................................................... 46

Circuit Realizations....................................................................................................................... 47

Conclusions.................................................................................................................................. 48

CHAPTER 7......................................................................................................................................... 49

A Summary................................................................................................................................... 49

SECTION II .......................................................................................................................................... 51

Circuits ......................................................................................................................................... 51

Introduction................................................................................................................................... 51

APPENDIX A ....................................................................................................................................... 80

References................................................................................................................................... 80

Chapter 1 ..................................................................................................................................... 80
SBOA093A


Handbook Of Operational Amplifier Active RC Networks
3
Chapter 2...................................................................................................................................... 80

Chapter 3...................................................................................................................................... 80

Chapter 4...................................................................................................................................... 81

Chapter 5...................................................................................................................................... 81

Chapter 6............................................................................................