# Accession Number:

## AD0605264

# Title:

## CASCADE SYNTHESIS OF PASSIVE N-PORTS,

# Descriptive Note:

# Corporate Author:

## POLYTECHNIC INST OF BROOKLYN N Y MICROWAVE RESEARCH INST

# Personal Author(s):

# Report Date:

## 1964-08-01

# Pagination or Media Count:

## 200.0

# Abstract:

This report presents a theory of cascade synthesis for lumped, passive n-ports based on a generalization of Richards theorem to the matrix case. It is first shown that there is a natural way to define the zeros of transmission of a rational positive-real matrix Zp and that the number of such zeros equals precisely Z, the McMillan degree of Zp. By applying the generalized Richards theorem at a zero of transmission, it is possible to induce a degree reduction in the terminating impedance matrix. If the degree reduction is restricted, from the outset, to equal, at most, one, two, or four units, the process generates the 2n-port analogues of the Richards, type E and Darlington 4-terminal A A, B, C and D sectioons. The synthesis procedure encompasses nonreciprocal as well as reciprocal networks and economic realizations are achieved for all the primitive reciprocal sections and most of the nonreciprocal ones. Author