A General Theory of Commutated Networks

A state-space approach is used to derive an exact closed-form solution for the steady-state and transient response of a general commutated network terminated in a multiport. By expanding the time-varying transfer function
N(p, t)
in a Fourier series, the transfer function at input frequency
N_{0}(p)
, and the transfer functions at harmonic frequencies
N_{m}(p)
are then calculated. A necessary and sufficient condition for the recovery of the input signal, without distortion due to the harmonics, is given. From the general analysis, we immediately obtain previously available results on comb filters,
n
-path filters, sample-data filters, etc., as special cases. The resulting closed-form solutions in terms of element values are most suitable for computer simulation in which the performance of the commutated network is to be evaluated as the element values are varied.