Interreciprocity in Linear Periodically Time-Varying Networks With Sampled Outputs

We consider a linear periodically time-varying (LPTV) network (varying with frequency f_s) excited by an input x(t). We show (using frequency-domain arguments) that if its output is sampled at f_s, one can find a linear time-invariant (LTI) filter, which, when excited by x(t) and output sampled at f_s, yields the same sequence as the LPTV network. We then use Tellegen´s theorem to demonstrate interreciprocity in LPTV networks with sampled outputs. This enables the determination of the equivalent LTI filters from multiple sources in the LPTV network to the sampled output, using just one time-domain simulation. A first-order continuous-time delta sigma modulator is used to illustrate the theory.