Darlington's Synthesis and RMS Error Evaluation

A theorem relating the integrated square of the impulse and step response of a two terminal-pair network to its input impedance is developed; this theorem is in a sense the time domain equivalent to the gain-bandwidth relationship in steady state. As an application, a simple method is presented for evaluating the integrated square,
\int_{0}^{\infty} [r(t)-r_{ss}]^2 dt
, of the difference between a signal
r(t)
and its steady state value
r_{ss}
; the method is based on Darlington's procedure for determining a reactive network from its transfer function.