Expressions for the Harmonic Transfer Functions of N-Path Filters With Arbitrary Source and Load Impedances

We derive analytical expressions for the harmonic transfer functions (HTFs) of N-path filters with arbitrary source and load impedances. We start with first-order approximations of the HTFs based on a simplified "Ohm's-law" characterization of filter operation, and then show how these can be corrected via a feedback visualization to obtain infinite-series expressions. We apply our expressions to study the impact of variations in the source and load impedances. Overall, our approach provides a way to visualize and understand the individual terms contributing to the HTFs and adds to the existing analytical methods to explore N-path filter response.