Using the Miller Theorem in LPTV Networks to Analyze Miller N-Path Filters

This paper revisits the Miller theorem in linear periodically time-varying networks. Using this, we provide an intuitive technique to analyze Miller N-path filters. Earlier works either considered the amplifier to be a voltage-controlled voltage source (VCVS) instead of a voltage-controlled current source (VCCS) or analyzed the Miller N-path filters from scratch. As an alternative, we show how the analysis can be greatly simplified even in the presence of a VCCS by using the Miller theorem appropriately. Using this, we reduce the Miller N-path filter as a cascade of two regular N-path filters. Unlike the equivalent circuit shown in earlier works, this is an exact model and has no approximations. Hence, by re-using the extensive analysis already done for regular N-path filters, the Miller N-path filter is readily analyzed. The model obtained also helps us make the following observations in a more intuitive manner: i) the overall bandwidth depends on the transconductance, ii) the out-of-band gain can be optimized by choosing the switch resistance to be 1/G<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf>. Simulation results validating the model and the observations are also presented.