Unified Frequency-Domain Analysis of Switched-Series-$RC$ Passive Mixers and Samplers

A wide variety of voltage mixers and samplers are implemented with similar circuits employing switches, resistors, and capacitors. Restrictions on duty cycle, bandwidth, or output frequency are commonly used to obtain an analytical expression for the response of these circuits. This paper derives unified expressions without these restrictions. To this end, the circuits are decomposed into a polyphase multipath combination of single-ended or differential switched-series-RC kernels. Linear periodically time-variant network theory is used to find the harmonic transfer functions of the kernels and the effect of polyphase multipath combining. From the resulting transfer functions, the conversion gain, output noise, and noise figure can be calculated for arbitrary duty cycle, bandwidth, and output frequency. Applied to a circuit, the equations provide a mathematical basis for a clear distinction between a “mixing” and a “sampling” operating region while also covering the design space “in between.” Circuit simulations and a comparison with mixers published in literature are performed to support the analysis.

I. Introduction

In radio front ends, mixers normally perform frequency conversion, with continuous-time input and output signals. Samplers convert a continuous-time input into a discrete-time output signal but can also provide frequency conversions (aliasing). Mixing and sampling seem to be quite different functions and are analyzed differently but can be implemented by similar circuits. Some examples are shown in Fig. 1. Fig. 1.

Switched- application examples. (a) Switching mixer. (b) Sampling mixer/track and hold. (c) In-phase/Quadrature mixer with (d) polyphase clocks A–F.