Generalized Analysis of High-Order Switch-RC N-Path Mixers/Filters Using the Adjoint Network

This paper presents a systematic method to analyze N-path mixers and filters consisting of periodically switched $RC$ -networks of arbitrary order. It is assumed that each capacitor periodically exchanges charge with the rest of the network during the on-phase of the switching clock, then samples its charge, and holds it perfectly until the next on-phase. This assumption allows for using the adjoint network for simplified analysis of the harmonic transfer functions that describe the signal transfer and folding. Moreover, harmonic transfer cancellations due to the N-path implementation with N equal capacitors switched by N non-overlapping clocks are systematically analyzed. The method is applied to a recently published N-path filter-mixer combination and verified by simulations.