A network containing a periodically operated switch solved by successive approximations

This paper concerns itself with the analysis of a type of periodically switched network that might be used in time multiplex systems. The economics of the situation require that the ratio of the switch closure time τ to the switching period T be small. Using this assumption, the analysis is performed by successive approximations. More precisely the zeroth approximation to the transmission is obtained from a block diagram analogous to those used in sampled servomechanisms. From the convergence proof of the successive approximation scheme, it follows that when τ/T is small, the zeroth approximation is very close to the exact transmission. A discussion of some examples is included.