Analysis of the Effect of Source Capacitance and Inductance on $N$ -Path Mixers and Filters

Abstract

Switch $R-C$ passive $N$ -path mixers and filters enable interference-robust radio receivers with a flexibly programmable center frequency defined by a digital multi-phase clock. The radio frequency (RF) range of these circuits is limited by parasitic shunt capacitances, which introduce signal loss and degrade noise figure. Moreover, the linear periodically time varying nature of switch $R-C$ circuits results in unwanted signal folding which needs to be suppressed by linear time- invariant (LTI) prefiltering by passive LC filters. This paper analyzes the interaction between capacitive or inductive LTI prefiltering and an $N$ -path mixer or filter, leveraging an analysis technique based on the impulse response of the adjoint network. Previously reported results for an inductive source impedance are derived in a simpler fashion, while providing circuit intuition. Moreover, new results for $N$ -path receivers with a shunt capacitor, and a combination of a series inductor and shunt capacitor are derived, as well as design criteria to minimize loss and frequency shifting in the peak response of these circuits.