chapter  3

General Feedback Theory

ByWai-Kai Chen

This chapter aims to develop H. W. Bode’s feedback theory, which is applicable to the general network configuration and avoids the necessity of identifying the transfer functions μ(s) and β(s). Bode’s feedback theory is based on the concept of return difference, which is defined in terms of network determinants. The chapter shows that the return difference is a generalization of the concept of the feedback factor of the ideal feedback model. It examines the notion of null return difference and discusses its physical significance. The chapter reviews briefly the formulation of the indefinite-admittance matrix. It presents present elegant, compact, and explicit formulas that express the network functions in terms of the ratios of the first and/or second-order cofactors of the elements of the indefinite-admittance matrix. The chapter explores the notion of null return difference, which is found to be very useful in measurement situations and in the computation of the sensitivity for the feedback amplifiers.