Rapid design procedures for the Brune and Bott-Duffin circuits

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