Algorithms for the element values in a class of stub‐unit‐element cascades

Attempting to unify the various papers in the literature revolving around the classical ideas of moment theory, this paper by considering various generalizations of the orthogonal polynomial concept, examines the microwave equivalent of the lumped ladder structure. The stub‐unit‐element cascades that result are shown to be synthesizable in terms of the properties of Hurwitz generalized orthogonal polynomials. Using this concept, the synthesis procedure leads to element value algorithms, both for the reactance ladder case, and the case where the unit‐elements become redundant (in the sense that they do not contribute to synthesis). As an example, explicit element value formulas are derived for lowpass and bandpass reflection filters using stub‐unit element‐cascades, that exhibit maximally flat delay and amplitude characteristics. Lastly, using the concept of a complex weight function, the relationship between the approximation of a transfer impedance and the synthesis of the resulting structure, is considered. The considerations discussed here appear to have many possible lines for extension: to multivariable networks; alternative one‐variable structures; and to the question of the existence of explicit element value formulas for particular filters.