Frequency-Domain Analysis of $N$-Path Filters Using Conversion Matrices

N-path filters are finding increased prominence in recent architectures for tunable transceivers. The clock-programmable center frequency together with programmable baseband bandwidth makes it a natural fit for wide programmability required in software-defined radios and cognitive radios. However, the analysis of such filters remains difficult due to their linear periodically time-varying (LPTV) nature. This brief presents an analysis of N-path filters using conversion matrices. Conversion matrices allow for the analysis of an LPTV circuit with equivalent frequency-domain circuits that can, in turn, be analyzed similar to a linear time-invariant circuit. On applying this method to N-path filters, results already established in prior art are accurately reproduced. Furthermore, the effects of a few important nonidealities, such as clock overlaps, nonideal clock duty cycles, and parasitic elements, are also calculated and verified.