Frequency-Domain Analysis of N-path Filters Using Conversion Matrices

Abstract

N-path filters are finding increased prominence in recent architectures for tunable transceivers. The clockprogrammable 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 remain difficult due to their linear, periodically time-varying (LPTV) nature. This paper presents an analysis of N-path filters using conversion matrices. Conversion matrices allow analysis of an LPTV circuit with an equivalent frequency domain circuits that can in turn be analyzed similar to a linear time invariant (LTI) circuit. On applying this method to N-path filters, results already established in prior art are reproduced accurately. Further, effects of a few important non-idealities, such as clock overlaps, non-ideal clock duty cycles, and parasitic elements are also calculated and verified