LAUSR

The N-path circuit serves both as a mixer and as a radio frequency (RF) filter. Certain performance aspects, such as noise, linearity, and out-of-band (OOB) rejection dictate large switches size. However, such increment raises the value of the parasitic RF capacitance, which causes further in-band (IB) loss and peak frequency shift. In this brief, we derive simplified equations for the assessment of the mentioned non-ideal properties, using the novel linear periodically time-variant (LPTV) state-space analysis, by making derivations and approximations based on realistic circuit parameters. We present closed-form equations for the voltage gain peak frequency shift and a revised linear time-invariant (LTI) model for the assessment of $S_{11}$ dip frequency shift.