A Practical Method for Time-Domain Network Synthesis

This paper presents a method of network synthesis for a prescribed unit-impulse response
f(t)
, taken to be zero outside the interval
(0, t_{0})
. The imposed response
f(t)
is approximated by another one
h(t)
, whose Laplace transform
H(s)
is always physically realizable as the transfer function of a passive network with lumped parameters. A finite number of equidistant values of the specified function
f(t)
is used for the approximation. The pulse transfer function that has been used in elaborating the method no longer appears in the final design relations. The approximation criterion is the mean-square error in the interval
(0, t_{0})
, and outside this interval
h(t)
is smaller than some imposed value. The transfer function
H(s)
results are expanded into partial fractions. The necessary computations are simple. As a particular case, the method permits the determination of the response
h(t)
in such a way, that it takes certain given values at regular intervals of time, thus making the method also useful for sampled-data systems. Illustrative examples and experimental results are given.