Power Gain in Feedback Amplifier

Abstract

A linear three-terminal deviceZis 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 impedancesZ_{11}, Z_{12}, Z_{21},andZ_22. A search for properties ofZwhich are invariant under the transformation N leads to the quantityU = \frac{|Z_{21}-Z_{12}|^2}{4(R_{11}R_{22}-R_{12}R_{21})}whereR_{jk}is the real part ofZ_{jk}. QuantityUis independent of the choice ofNand is (consequently) invariant under permutations of the three terminals and also under replacement of the open-circuit impedances by short-circuit admittances. IfUexceeds unity at a specified frequency, thenNcan always be chosen to makeR_{11}andR_{22}positive andZ_{12}zero at that frequency. QuantityUis 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.