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Design Constraints for Image-Reject Frequency-Translating \Delta \Sigma Modulators

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2 Author(s)
Philip M. Chopp ; Dept. of Electr. & Comput. Eng., McGill Univ., Montreal, QC, Canada ; Anas A. Hamoui

This brief derives design constraints for bandpass ΔΣ modulators that use mixers to perform frequency downconversion inside their ΔΣ loop. Such systems, which are referred to as frequency-translating ΔΣ modulators, facilitate direct analog-to-digital conversion (ADC) of high-frequency signals that cannot adequately be processed using classical bandpass ΔΣ modulator architectures. The derived constraints are required for the correct design of frequency-translating ΔΣ modulators: 1) The sampling constraints maintain the stability of the ΔΣ feedback loop and prevent the mixing of the undesired signal content into the input-signal band, thereby ensuring that the time-varying behavior of the mixers does not affect the ADC resolution; and 2) the noise- shaping constraints minimize performance loss during the recombination of the in-phase and quadrature feedback paths. This brief analyzes frequency-translating ΔΣ modulators that are designed with image-reject (quadrature) mixing and that are implemented using continuous- or discrete-time lowpass or complex-bandpass inner-loop ΔΣ modulators. Thus, the derived constraints offer a valuable reference for the design of image-reject frequency-translating ΔΣ ADCs.

Published in:

IEEE Transactions on Circuits and Systems II: Express Briefs  (Volume:56 ,  Issue: 12 )