Rapid design procedures for the Brune and Bott-Duffin circuits

Assuming that a driving-point impedanceF(s)=N(s)/D(s)is known by the coefficients of the rational function, both polynomials of the same degree and normalized, theA-type (resistance series) and/or theB-type (resistance parallel) Brune circuit can rapidly and with high accuracy be designed using the results of evaluatingN(j\omega)andD(j\omega)only. In a few steps the circuit can be transformed into the Bott-Duffin circuit. The suggested procedure becomes especially advantageous whenF(s)is a function of high rank.