Universal Frequency-Domain Analysis of N-Path Networks

N-path commutated capacitive networks provide a practical solution to implement highly sought on-chip high-Q filtering applications in which the use of lumped inductors is undesirable due to their significant footprints and low Q-factors. Recently, it has been also revealed that N-path networks can also exhibit other interesting functionalities, such as nonreciprocal phase-shifting and ultra-wideband true time delay, providing a path to miniaturization of various reciprocal and nonreciprocal devices. The analytical treatment of these networks, however, remains challenging, because their operation involves frequency mixing produced by the time modulation. In this article, we present a highly accurate frequency-domain approach for the analysis of N-path networks based on perturbation theory. Our method compares favorably to the state-of-the-art polyphase analysis by being much simpler mathematically, yet providing results essentially indistinguishable from numerical simulations, while offering physical insights into the N-path filter operation. We particularize the solution for the high-Q operation regime and obtain simple closed-form analytical expressions for harmonic transfer functions, scattering parameters and baseband impedance.