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Bandpass Sigma Delta Modulators - Stability Analysis, Performance and Design Aspects (Hardcover, 2000 ed.)
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Bandpass Sigma Delta Modulators - Stability Analysis, Performance and Design Aspects (Hardcover, 2000 ed.)
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Sigma delta modulation has become a very useful and widely applied
technique for high performance Analog-to-Digital (A/D) conversion
of narrow band signals. Through the use of oversampling and
negative feedback, the quantization errors of a coarse quantizer
are suppressed in a narrow signal band in the output of the
modulator. Bandpass sigma delta modulation is well suited for A/D
conversion of narrow band signals modulated on a carrier, as occurs
in communication systems such as AM/FM receivers and mobile phones.
Due to the nonlinearity of the quantizer in the feedback loop, a
sigma delta modulator may exhibit input signal dependent stability
properties. The same combination of the nonlinearity and the
feedback loop complicates the stability analysis. In Bandpass Sigma
Delta Modulators, the describing function method is used to analyze
the stability of the sigma delta modulator. The linear gain model
commonly used for the quantizer fails to predict small signal
stability properties and idle patterns accurately. In Bandpass
Sigma Delta Modulators an improved model for the quantizer is
introduced, extending the linear gain model with a phase shift.
Analysis shows that the phase shift of a sampled quantizer is in
fact a phase uncertainty. Stability analysis of sigma delta
modulators using the extended model allows accurate prediction of
idle patterns and calculation of small-signal stability boundaries
for loop filter parameters. A simplified rule of thumb is derived
and applied to bandpass sigma delta modulators. The stability
properties have a considerable impact on the design of single-loop,
one-bit, high-order continuous-time bandpass sigma delta
modulators. The continuous-time bandpass loop filter structure
should have sufficient degrees of freedom to implement the desired
(small-signal stable) sigma delta modulator behavior. Bandpass
Sigma Delta Modulators will be of interest to practicing engineers
and researchers in the areas of mixed-signal and analog integrated
circuit design.
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