Passive RC network was designed with zeros of transmission in the right half of the complex frequency plane in the feedback loop of a simple negative-gain amplifier. The proper positioning provides any desired trade-off between amplifier gain and sensitivity to amplifier gain

Kerwin, W. J.

Shaffer, C. V.

English

NASA Technical Reports Server

December 1968
	
Brief 68-10539 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151. 
Active RC Filter Permits Easy Trade-Off 
of Amplifier Gain and Sensitivity to Gain 
The problem: 
Active RC filter amplifiers are preferred to RLC 
filters in applications where the presence of inductors 
is undesirable for reasons of size, weight, cost, or mag-
netic field considerations. They are required if the 
circuit is to be integrated monolithically. However, the 
performance of active RC filters tends to be sensitive 
to component values and particularly to the gain of 
the amplifier. Designs which reduce this sensitivity to 
acceptable values often require amplifiers of very high 
gain or operational amplifiers (which may prohibit 
applications at intermediate radio frequencies). 
The solution: 
A passive RC network with zeros of transmission in 
the right half of the complex frequency plane used in 
the feedback loop of a simple negative-gain amplifier. 
These "phantom zeros" do not appear in the overall 
system transfer function, but their proper positioning 
provides any desired trade-off between amplifier gain 
and Q sensitivity to amplifier gain. 
How it's done: 
The desired rational transfer function can always 
be realized by a cascade of filter amplifiers each of 
which realizes, at most, two poles. Here we consider 
a single bandpass stage having two complex poles.
For this application, a twin-tee RC network or a dis-
tributed RC notch network may be used to generate 
the phantom zeros. Position of the phantom zeros can 
be controlled by using the results of closed-form 
analysis of the twin-tee or of a computer analysis that 
has been carried out for the uniformly distributed 
notch network. 
The amplifier can be a simple phase-inverting design 
permitting reliable operation in the radio frequency 
range. For example, when a Q of 50 is desired, a ta-
pered (10:1) twin-tee passive structure requires an am-
plifier gain of only —10.3 if the phantom zeros are 
positioned at +0.1 ±i 0.995 (normalized values) a 
position which reduces the Q sensitivity to amplifier 
gain, S, to 10.3 or 0.206 Q (compared with about 
2Q for some well known circuits). A model of this de-
sign with the center frequency scaled up to 4.78 MHz 
has been successfully tested in the laboratory. 
A design chart is given in reference I for the version 
using a uniformly distributed notch network and sev-
eral models have been successfully tested. However, 
the uniform line increases the gain required (over the 
tapered twin-tee) for the same Q and S. 
For low frequency applications where operational 
amplifiers can be used, the state variable method de-
scribed in reference 2 can be used, and is capable of 
(continued overleaf) 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19680000495 2020-03-12T06:30:42+00:00Z
exceptionally low sensitivity to both amplifier gain 
and components. 
References: 
I. "An Integrable IF Amplifier of High Stability," 
by W. J. Kerwin and Charles V. Shaffer presented 
at Eleventh Midwest Symposium on Circuit 
Theory, University of Notre Dame, Notre Dame, 
Indiana, May 13-14, 1968. 
2. "State-Variable Synthesis for Insensitive Inte-
grated Circuit Transfer Functions" by William 
J. Kerwin, Lawrence P. Huelsman, and Robert W. 
Newcomb printed in fEE Journal of Solid-State 
Circuits, Vol. SC-2, No. 3, September 1967.
Note: 
Documentation for this invention, consisting of the 
two reference papers, is available from 
Clearinghouse for Federal Scientific 
and Technical Information 
Springfield, Virginia 22151 
Price $3.00 
Reference: B68-10539 
Patent status: 
Inquiries about obtaining rights for the commercial 
use of this invention may be made to NASA, Code 
GP, Washington, D.C. 20546. 
Source: William J. Kerwin

and Charles V. Shaffer

Ames Research Center

(ARC-10042) 
Brief 68-10539	 Category 01
	 -


Active rc filter permits easy trade-off of amplifier gain and sensitivity to gain

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