The simulation of floating inductors with high Q-factors at audio frequencies is so challenging that such achievements deserve publication.The refs [1,2,3,4,5] cited below list just a few of such publications presented by professional engineering societies on floating inductance simulation. This page and its subsequent linked webpages (see above) will demonstrate that such simulations are really quite simple, quite in contrast to the original contentions of the several professional institutes that became involved with it for several decades. So just what was their problem? This and the subsequent pages on impedance simulation address that very question, while showing how simple it is, using Collier's Method, to simulate a floating impedance of arbitrarily chosen value.
The equivalent circuit for a simulator of an ordinary (bidirectional) electrical impedance Zsim is shown in Figure 2(a), below, and the equivalent monodirectional impedance is shown in Figure 2(b).
This value of I determines the impedance Zsim seen by the external charge source of potential E, and this critical value of I must appear faithfully at the terminal of potential E for all expected values E and EA.The terminal of potential E is referred to as the "passive terminal" of the monodirectional impedance. Because this critical value of current needs only be realized in the passive terminal of the monodirectional impedance, the monodirectional simulator is much easier to simulate, its structure is simpler, its behavior is more reliable, and it is quieter in its performance.
Riordan [2] simulated a grounded ideal inductor, a device that Collier's later works showed could serve as a floating monodirectional inductor. Because Riordan didn't understand the nature of monodirectional impedances, he never viewed that his grounded inductance device could have served, just as it was, as a floating monodirectional inductor. Consequently, the floating impedance simulator that Riordan proposed in that same publication was a more complicated (bidirectional) simulator, a circuit that required about twice as many components as the grounded inductance simulator he had presented. If it's not already obvious, means are demonstrated later for transforming two monodirectional impedances into one bidirectional impedance.
To help overcome the societies' problems arising from not understanding the monodirectional feature of their grounded simulator devices, several later efforts pursued the simulation of grounded frequency dependent negative resistances (FDNRs), with which inductances could be excluded entirely from the networks requiring simulators. It was Collier that introduced the equivalent circuit of monodirectional impedance simulators, and who established that any monodirectional simulator can serve just as well in any floating application for which its virtual follower amp is not a detriment.
To use a monodirectional impedance, the potential EA, driving the virtual follower of the monodirectional impedance device, must be supplied by an autonomous voltage source; that is, a source that does not rely on the impedance's current I for governing its potential. This autonomous potential EA can be the output of virtually any amplifier or signal source with a voltage output, or it can be the zero-signal voltage supplied by virtually any ground terminal. Riordan and the entire engineering community were for decades after Riordan's work familiar only with use of the monodirectional device with EA = 0 (grounded). As Collier straightforwardly showed, monodirectional impedances can be flotated, and provided that its autonomous terminal is driven by an autonomous voltage source, it will perform more accurately than its more complicated bidirectional equivalent, despite being simpler, quieter, more accurate, and less accident proned.
The latter work by Singh echos clearly the long-held scholastic inertia of the Electrical Engineering community, which held that floating impedances must have equal (albeit opposite) currents in their two terminals. Even though monodirectional impedances have been simulated since the work of Riordan, it was not until Collier's work presented in the 1989 American Journal of Physics [6] that the general nature of monodirectional impedances became clear. Until then it was thought that the autonomous terminal must be grounded (That is, it was thought its frequency distribution must be concentrated entirely at the zero frequency). Indications of this mistaken belief are published in some of electrical engineering's most profound journals. Until Collier's work it was thought to be impossible to simulate a floating impedance without realizing equal currents in its two terminals. Some examples demonstrating the prevailing engineering difficulties of this theoretical error were presented in such works as [1-5]. And of course, these cite references to preceeding errors in the scholastic inertia. The works by Singh [4,5] were published about the time Collier's patent was granted. In each of Singh's works, even though his circuit uses the excessive circuitry needed to simulate a bidirectional inductor, his experimental configuration for testing the simulator drives one of the terminals with an autonomous voltage source. Clearly, a much simpler, monodirectional inductor could have performed more quietly and with better accuracy in Singh's test circuit used to demonstrate his simulator's flotation capability.
Of course, a great deal more info about all this is available in the file wrapper of Collier's U.S. Patent 4963845, in the United States Patent and Trademark Office.
1. B. D. H. Tellegen, Philips Res. Rep. 3, 81 (1948).
2. R. H. S. Riordan, Electronics Letters 3, 50 (1967).
3. D. F. Sheahan and H. J. Orchard, IEEE J. Solid State Circuits SC-5, pp.108-118 (1970).
4. V. Singh, "On floating impedance simulation," IEEE Transactions on Circuits and Systems, 36, pp. 161-162, January 1989.
5. V. Singh, "An implementation of CCII-current conveyor, with application," IEEE Transactions on Circuits and Systems, 36, p 1250, September 1989.
6. R. L. Collier, American Journal of Physics, 57, 4 (April 1989, pp.362-365).
What IS an impedance?
What is a monodirectional impedance, and why is it so much easier to simulate?
How can one simulate a monodirectional impedance?
Some sample simulators