Identification of Certain Networks with Reflection Coefficient Zero Locations

In this paper, the coefficients of return loss expansions are found for certain low-pass, LC ladder networks which havenlossless elements and which exhibit Tchebycheff (or equal ripple) pass band and monotonic stop band transmission behaviors. The return loss expansion is the Taylor expansion of In (1/\rho_{1}(s)) aboutsequal to infinity, the variable s being the familiar complex frequency variables = \sigma + j{\omega}, and\rho_1being the reflection coefficient between a resistive termination and the remainder of the network. The return loss coefficients are tabulated according to reflection zero locations for odd and evenn. Methods for synthesizing low-pass, LC ladder networks from return loss coefficients are available. A presentation of the modifications necessary to adapt these methods for use with the particular coefficients discussed above is given. Thus, it is possible to synthesize certain Tchebycheff networks through use of return loss coefficients which are, in turn, directly identified with reflection zero locations. The paper concludes with a brief discussion of the extension of existing tables of Tchebycheff network element values for finding the element values for several reflection zero distributions and LC ladder arrangements.