| Remarks by Dr. Middlebrook: "I have finally been able to solve a problem I
have been struggling with for more than 40 years, namely, that of how to express the internal
properties of feedback, such as loop gain, directly in terms of circuit elements without first
inventing a block diagram in which the blocks are not really separable. In the first attempt [1], a
primitive "feedback theorem" showed that the closed-loop gain could be assembled from three transfer
functions calculated by breaking the loop at a dependent generator and applying a test signal at the
break. In the second attempt [2], it was shown that the loop gain could be found by injection of
both voltage and current test signals at a "nonideal" point, that is, one that is not at an ideal
dependent generator. In parallel, I was developing the Extra Element Theorem (EET) [3] and realized
that it is just the same as the "feedback theorem."
" Extension of the EET to the 2EET [4] and the NEET [5] followed, and at 4am on July 31st 2001 I
had a 'Eureka Moment,' that flash of insight that we all wish would occur more often: the 2EET is
actually the General Feedback Theorem (GFT) that I had long searched for.
" If the significance of this escapes you, it doesn't matter: the bottom line is that the GFT is
an extension of the primitive theorem in which all three constituent transfer functions can be found
by injection of both voltage and current test signals, regardless of whether or not the forward
and/or the feedback path is bidirectional, both of which "nonidealities" invariably exist in real
circuits. A valuable consequence is that a block diagram built of unidirectional blocks emerges as
part of the result, and doesn't have to be guessed at or approximated at the start.
"In the DVD Technical Therapy you can get a thorough background in the techniques you need to
take maximum advantage of the GFT, and at the same time you can practice the many examples of the
techniques covered in Dr.
Vatché Vorpérian's book Fast Analytical Methods in Electrical and Electronic Circuits [6]."
[1] R.D.Middlebrook, "Design-Oriented Analysis of Feedback Amplifiers," Proc. National
Electronics Conference, vol. 20, Oct. 1964; pp. 234-238.
[2] R.D.Middlebrook, "Measurement of Loop Gain in Feedback Systems," Intl. J. of Electronics,
vol. 38, Apr. 1975; pp. 485-512.
[3] R.D.Middlebrook, "Null Double Injection and the Extra Element Theorem," IEEE Trans. on
Education, vol. 32, no. 3, Aug. 1989; pp. 167-180.
[4] R.D.Middlebrook, "The Two Extra Element Theorem," Proc. IEEE Frontiers in Education, 21st
Annual Conf., Purdue Univ., Sept. 21-24, 1992; pp. 702-708.
[5] R.D.Middlebrook, Vatché Vorpérian, and John Lindal, "The N Extra Element Theorem," IEEE
Trans. on Circuits and Systems, vol. 45, no. 9, Sept. 1998.; pp. 919-935.
[6] Vatché Vorpérian,
Fast Analytical Techniques for Electrical and Electronic Circuits,,
Cambridge Univ. Press, 2002. |
