N-Path Filtering and Mixing Analysis—A General Approach Based on Fourier Transform

This article proposes a general approach to accurately model the N-path filters and mixers, with the double purpose of bringing a better insight in the frequency transposition phenomena and opening the door towards a more general discussion concerning NPF-NPM and their outstanding properties as passive circuits. Thanks to a Fourier transform analysis, some mathematical equations are rigorously derived for both filtering and mixing voltage gains. The analysis is compared with ideal simulations for various sets of parameters: source impedance
$R_a$
, load impedance
$R_L$
, switch resistance
$R_{sw}$
, capacitive path
$C_L$
. Some error curves are extracted validating the initial hypotheses for the model in a given range of capacitances values. As a proof of concept, it is shown that the model complies with the measurements results with very good accuracy. The error is less than 10.5
$\%$
on the two first harmonics prediction.