Minimum-Phase Transfer-Function Synthesis

This paper presents a means for realizing a minimum-phase transfer-function
H(p)
to within a constant multiplier, provided that
H(p)
has no poles on the
j \omega
-axis including infinity. The network is in ladder form, without coupled coils, and every coil has an associated series resistance if
H(j \omega) \neq 0
for any finite
\omega
Synthesis is illustrated for the specification of resistance termination at input and output, and for the specification of a resistor-capacitor termination at both ends. Regardless of the complexity of
H(p)
, the synthesis problem can always be reduced to the problem of synthesizing driving-point functions that are no more complicated than the ratio of quadratic polynomials in
p
. The method to be described is an extension of constant-resistance ladder network synthesis.