Linearly variable networks— I. analysis

Abstract

A linearly variable element is any passive two-terminal network element in which the immittance varies linearly with respect to an independent (of frequency) real variable, x. A definite set of fundamental passive two terminal network elements (F- elements) consisting of fixed passive elements and linearly variable elements is presented. It is shown that any network consisting of only F-elements has a driving point immittance, D(s,x), that is positive real for s complex, x real and positive real for x complex, s real. Conditions on the variable coefficients, degree and location of zeros and poles of D(s,x) are established. A method of testing whether D(s,x) is positive real for one complex and one real variable is developed. This testing is accomplished by extending the Hurwitz and Sturm test to one complex and one real variable.