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

Pieter-Tjerk  de Boer; Mark Stefan Oude Alink; Eric A.M. Klumperink

doi:10.1109/TCSII.2021.3051769

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

Pieter-Tjerk de Boer^*, Mark Stefan Oude Alink, Eric A.M. Klumperink

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

Hard-switched mixers have attractive linearity and noise properties, but are plagued by spurious responses due to the harmonic content of square-wave 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 of such HRMs, based on circular convolution. We show that the effective signal can be modeled as a periodic Dirac impulse filtered by a time-discrete filter. For a multi-stage system, this filter consists of multiple stages as well, and the coefficients of each stage can be found simply by inspection. The total is shown to be the sum (in dB) of the rejection of the individual filtering stages, highly simplifying analysis and design of HRMs

Original language	English
Number of pages	5
Journal	IEEE transactions on circuits and systems II: express briefs
Early online date	14 Jan 2021
DOIs	https://doi.org/10.1109/TCSII.2021.3051769
Publication status	E-pub ahead of print/First online - 14 Jan 2021

Keywords

Circular convolution
Frequency conversion
Harmonic rejection
Mixer

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title = "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 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 of such HRMs, based on circular convolution. We show that the effective signal can be modeled as a periodic Dirac impulse filtered by a time-discrete filter. For a multi-stage system, this filter consists of multiple stages as well, and the coefficients of each stage can be found simply by inspection. The total is shown to be the sum (in dB) of the rejection of the individual filtering stages, highly simplifying analysis and design of HRMs",

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