Simplified Unified Analysis of Switched-RC Passive Mixers, Samplers, and $N$ -Path Filters Using the Adjoint Network

Recent innovations in software defined CMOS radio transceiver architectures heavily rely on high-linearity switched-RC sampler and passive-mixer circuits, driven by digitally programmable multiphase clocks. Although seemingly simple, the frequency domain analysis of these linear periodically time variant (LPTV) circuits is often deceptively complex. This paper uses the properties of sampled LPTV systems and the adjoint (inter-reciprocal) network to greatly simplify the analysis of the switched-RC circuit. We first derive the transfer function of the equivalent linear time-invariant filter relating the input to the voltage sampled on the capacitor in the switched-RC kernel. We show how a leakage resistor across the capacitor can be easily addressed using our technique. A signal-flow graph is then developed for the complete continuous-time voltage waveform across the capacitor, and simplified for various operating regions. We finally derive the noise properties of the kernel. The results we derive have largely been reported in prior works, but the use of the adjoint network simplifies the derivation, while also providing circuit insight.