# Loop, cutset, hybrid and state analyses of linear multiple-loop feedback systems

Abstract (Summary)

The return difference plays a very important role in the analysis and design of feedback systems. It has the advantage of being easily measured physically from the network itself and possesses many interesting properties. Among them, it has been shown that the return difference is a generalization of the concept of feedback factor of the ideal feedback model, that the return difference is basic to the study of the stability of the network and that it is closely related to the sensitivity function. It has also been shown that the return difference can be used in determining the transmission and driving-point properties of a system. The return difference matrix and the null return difference matrix are the generalizations of the concepts of the return difference and the null return difference to the multiple-loop systems. It has been shown that these two matrices possess similar interesting properties. The purpose of this investigation is to find a general formulation of the return difference matrix and the null return difference matrix of the multiple-loop feedback networks and their determinants in terms of either the loop-impedance matrix, the cut-admittance matrix, the hybrid matrix or the coefficient matrices of the state equations. The loop, cutset, hybrid and state variable methods of analysis were employed with the use of some transformation matrices which can be obtained for most of the practical multiple-loop feedback networks by inspection of their equivalent circuits, to obtain such formulation. In this dissertation, it has been shown, with the aid of some practical illustrative examples, that this formulation is very useful in the analysis of multiple-loop feedback systems. The general formulation of the return difference, the null return difference and the transfer function matrices and their determinants in terms of either the loop-impedance matrix, the cut-admittance matrix or the hybrid matrix of the network which has been derived in this research is especially useful in the analysis of large multiple-loop feedback networks containing more than two active devices, because it eliminates the explicit determination of the transfer function matrices of the fundamental matrix feedback-flow graph which are used in the computation of the return difference and the null return difference matrices. This has been fully illustrated at the end of the dissertation by applying the cutset method to the computer analysis of a practical three-transistor multiple-loop feedback amplifier. The general formulation of the return difference, the null return difference and the transfer function matrices and their determinants in terms of the coefficient matrices of the state equations of the network as it has been derived in this research is especially useful in the analysis of multiple-loop feedback networks which are characterized by their state equations.
Bibliographical Information:

Advisor:

School:Ohio University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:linear multiple loop systems hybrid and state analyses

ISBN:

Date of Publication:01/01/1980