The structure of the limit cycles in sigma delta modulation
- 1 January 1988
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Communications
- Vol. 36 (8) , 972-979
- https://doi.org/10.1109/26.3777
Abstract
It is shown that when the input to a sigma-delta modulator is a DC level that can be expressed as a rational number b/a, when normalized with respect to the quantizer step, the output bit string is periodic with a period that is multiple of the denominator a. On the basis of number theory, the structure of these cycles for single-loop modulators is determined and the noise contribution is computed. Around such levels the noise has two peaks, for which the maximum value and the width are proportional to the relative signal bandwidth and to the inverse of the period of the cycle, respectively. The effect of the limit cycles on the performance of the A/D and D/A converters using sigma-delta modulation is discussed. A comparison between single-loop and double-loop modulators from the point of view of this phenomena is made. >Keywords
This publication has 9 references indexed in Scilit:
- Oversampled Sigma-Delta ModulationIEEE Transactions on Communications, 1987
- A 16b oversampling A/D conversion technology using triple integration noise shapingPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1987
- A 120kHz sigma/delta A/D converterPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1986
- Double Interpolation for Digital-to-Analog ConversionIEEE Transactions on Communications, 1986
- Design Methodology for ΣΔMIEEE Transactions on Communications, 1983
- The Structure of Quantization Noise from Sigma-Delta ModulationIEEE Transactions on Communications, 1981
- Single-chip per channel codec with filters utilizing Δ-Σ modulationIEEE Journal of Solid-State Circuits, 1981
- A Voiceband Codec with Digital FilteringIEEE Transactions on Communications, 1981
- Exact model for delta-modulation processesProceedings of the Institution of Electrical Engineers, 1971