Some Techniques for Network Synthesis

Part I: Synthesis of Immittances with Two Poles and Two Zeros. Cauer's continued-fraction technique is generalized for use in realizing RLC network immittances. Using this method, element values are determined by simple processes of "forward" and "reverse" division. Immittances F(p) with two poles and zeros may be grouped in three classes according to the frequency jω
_m
at which Re F(jω) is a minimum. For Class I, ω
_m
= 0; for Class II, ω
_m
= ∞; and for Class III, ∞
_m
is finite. Class I and II F(p) can be realized immediately by making a continued-fraction expansion. If both F(p) and 1/F(p) are Class III, to obtain a realization without unity-coupled coils the function must be split into two terms which may then be expanded in continued fractions. Simple formulas are presented which enable one to easily classify F(p) and determine an appropriate realization method. Part II: A Constant-Resistance Ladder for Transfer Function Synthesis. The physical factors that determine the poles and zeros of a transfer function are examined. By use of physical insight, a design procedure for a constant-resistance ladder network is arrived at. This ladder network is found to have the same realm of application as the conventional, RLC, constant-resistance bridged-T. However, the ladder has the advantages of: fewer elements, more flexibility, and requiring less flat loss if the bridged-T requires flat loss. Complicated transfer functions may be realized in a chain of ladder sections having arm immittances with only two poles and two zeros.