Two-Port Analysis of SC Networks With Continuous Input Signals

Previous publications by the author and G. S. Moschytz showed that sc networks can be analyzed in the time domain by using nodal 1297 charge equations with time-varying coefficients.1'2"' This led to a representation of sc networks as time-variant sampled-data networks, which can be modeled by a discrete, time-series, sampled-data system in cascade with sample-and-hold devices. Ultimately, it was shown that any sc network can be represented by a four-port equivalent circuit in the Z-domain.2 Throughout this analysis, it was assumed that the sc network is fed by a staircase voltage function to be compatible with the inherent staircase nature of a voltage across any internal capacitor of the sc network. The charge transfer occurs at the end of the closing time of the switches; consequently, the magnitude of the voltage at every node of the network must be constant over the previous inactive interval of the switches. This leads to a staircase approximation of a compatible input function, as shown in Fig. 1. The closing t i m e s ri a n d r2 of t h e t w o sets of switches are a s s u m e d to be