Design Methodology for ΣΔM

The paper presents a design methodology based on correspondence between performance requirements, mathematical parameters, and circuit parameters of a sigma-delta modulator. This methodology will guide a design engineer in selecting the circuit parameters based on system requirements, in translating paper design directly into LSI design, in predicting the effect of component sensitivity, and in analyzing the operations of the sigma-delta modulator. The sigma-delta modulator is viewed as a device which distributes the noise power, determined by peak SNR, over a much broader band, compared to signal bandwidth, shapes and amplifies it, and allows filtering of the out-of-band noise. The shaping and amplification are quantified by two parameters,
F
and
P
, whose product is analogous to the square of step size of a uniform coder. These two parameters are related, on one hand, to the time constants or location of zero and poles. On the other hand, inequalities are set up between performance parameters, like signal-to-noise ratio and dynamic range, and
F
and
P
.