IEEE TRANSACTIONS
ON
CIRCUITS
AND
SYSTEMS,
VOL.
CA.%21,
NO.
6,
NOVEMBER
1974
729
Realization of Ideal Gyrators
ALAN N. WILLSON, JR., AND H. J. ORCHARD, FELLOW, IEEE
Abstract-A
proof is given that it is impossible to realize an ideal
gyrator by connecting a controlled soarce across one of the ports of any
well-defined constant passive reciprocal three-port network (composed of
positive resistors and ideal transformers) with the controlling variable
being some voltage or current appearing inside the three-port network.
I. INTRODUCTION
0
VER the past eight years, the gyrator has come to
play an important role as a practical circuit element
in network design, quite distinct from its use as a theoretical
circuit element in the various nonreciprocal synthesis
schemes devised during the first two decades of its existence.
As a consequence of this, there now exists a multitude of
published papers describing different ways of making a
gyrator using components which are available in the
laboratory.
A gyrator is essentially a nonreciprocal element, so any
practical gyrator circuit must contain at least one non-
reciprocal component. At present, the only practicable
nonreciprocal component is a transistor, or combination
of transistors, arranged to operate as a linear amplifier,
of which very cheap and compact versions are now available
as integrated operational amplifiers. Nearly all good gyrator
circuits are built with these devices.
It has been found, by many different people, that, using
two such amplifiers and a few resistors, one can make a
variety of two-port networks which, with ideal amplifiers,
will behave as an ideal gyrator with an admittance matrix
y= -z;,
[ 1
a # 0.
The principal imperfections of any such practical gyrator
arise almost exclusively at high frequencies due to the
bandwidth limitations of the amplifiers.
Neglecting for the moment this bandwidth limitation and
assuming, as is quite reasonable for lower frequencies,
that the amplifiers are ideal, one is naturally led to wonder
whether the two amplifiers are in fact necessary
for the
construction of an ideal gyrator. Could one, by some
ingenious interconnection of components, manage with
only one amplifier?
Although
several one-amplifier gyrator-type circuits
have been described
in the literature [I], the quality of the
gyrators so produced, even with an ideal amplifier, is very
poor; specifically, the main-diagonal entries in the Y
matrix depart substantially from the desired zero value.
So far, not a single one-amplifier circuit for an ideal gyrator
Manuscript
received
November
9, 1973;
revised February
8, 1974.
This work was supported
by the National Science
Foundation
under
Grants GK35904x
and GK42722.
The author
is with the Electrical Sciences and Engineering Depart-
ment, Los Angeles,
Calif. 90024.