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

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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 brief 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.

Original languageEnglish
Article number9324800
Pages (from-to)2292-2296
Number of pages5
JournalIEEE transactions on circuits and systems II: express briefs
Issue number7
Early online date14 Jan 2021
Publication statusPublished - Jul 2021


  • Circular convolution
  • Frequency conversion
  • Harmonic rejection
  • Mixer
  • circular convolution
  • Switches
  • Harmonic analysis
  • harmonic rejection
  • Mixers
  • Power harmonic filters
  • Analytical models
  • Convolution
  • frequency conversion
  • mixer.
  • Gain


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