Necessary and sufficient conditions for the realizability of biquadratic functions

The necessary and sufficient condition for the positiverealness of a general biquadratic function
Z(s)
is presented. It is shown that for each given pair of conjugate-complex poles of
Z(s)
with negative-real parts, the zeros of
Z(s)
are graphically restricted in a realizability region, which is an open region bounded by two curves. One of these curves is the locus of the zeros for which
Z(s)
is a minimum positive-real function. A theorem is given stating the realizability conditions for
Z(s)
as a driving-point immittance with passive elements.