Sharp Inequalities for Driving Point Impedance Functions

In this brief, positive real functions are considered as driving point impedance functions,
$Z(s)$
, which are utilized in electrical engineering for characteristic representation of circuits. Accordingly, for the real part of
$Z(s)$
, sharp inequalities are presented with their extremal functions by using zeros and poles of
$Z(s)$
. For these extremal functions, corresponding generic circuit schematics are given with their spectral analyses. According to the obtained results, it has been shown that various circuits can be obtained by using the extremal functions of the inequalities presented in this brief.