Simplified Harmonic Rejection Mixer Analysis and Design Based on a Filtered Periodic Impulse Model

Abstract

Hard-switched mixers have attractive linearity and noise properties, but are plagued by spurious responses due to the harmonic content of square-wave local oscillator (LO) signals. Harmonic rejection mixers (HRMs) reject (some of) these responses and can be constructed combining polyphase mixing and amplitude weighting. This paper presents a generalized model for the analysis of the harmonic rejection (HR) of such HRMs, based on circular convolution. We show that the effective LO signal can be modeled as a periodic Dirac impulse filtered by a time-discrete filter. For a multi-stage HR system, this filter consists of multiple stages as well, and the coefficients of each stage can be found simply by inspection. The total HR is shown to be the sum (in dB) of the rejection of the individual filtering stages, highly simplifying analysis and design of HRMs.