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Power Gain in Feedback Amplifier

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1 Author(s)

A linear three-terminal device Z is imbedded in a lossless passive network N and the properties of the complete system, as measured at two specified terminal pairs, are described by the open-circuit impedances Z_{11}, Z_{12}, Z_{21}, and Z_22 . A search for properties of Z which are invariant under the transformation N leads to the quantity U = frac{|Z_{21}-Z_{12}|^2}{4(R_{11}R_{22}-R_{12}R_{21})} where R_{jk} is the real part of Z_{jk} . Quantity U is independent of the choice of N and is (consequently) invariant under permutations of the three terminals and also under replacement of the open-circuit impedances by short-circuit admittances. If U exceeds unity at a specified frequency, then N can always be chosen to make R_{11} and R_{22} positive and Z_{12} zero at that frequency. Quantity U is identifiable as the available power gain of the resulting unilateral structure. An arbitrary coupling network may be decomposed into a portion which accomplishes unilateralization and a remaining complementary portion which provides feedback around the unilateralized structure. Such decomposition brings some of the notions of elementary feedback theory to bear upon nonunilateral circuit analysis and offers a viewpoint from which signal flow and power flow are simply related.

Published in:

Circuit Theory, Transactions of the IRE Professional Group on  (Volume:CT-1 ,  Issue: 2 )