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110_1_Realization of Ideal Gyrators_Orchard&Willson

110_1_Realization of Ideal Gyrators_Orchard&Willson...

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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 cheapand 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, LosAngeles, Calif. 90024.
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