Environmental Engineering Reference
In-Depth Information
6.
Simulation Methods
Sigma-delta modulators are partitioned into (i) a linear block con-
sisting of the integrators, digital-to-analog converters, and other linear
components, and (ii) a nonlinear block composed of the quantizer. The
linear block is modeled at the circuit level and formulated using modified
nodal analysis while the nonlinear part is modeled using the behavioral
model given earlier and incorporated in simulation without using con-
ventional matrix approaches. Such a partition allows us to analyze the
behavior of these circuits in the time domain effectively in the following
way :
The linear part can be formulated and analyzed effectively using the
sampled-data simulation method for periodically switched linear cir-
cuits presented in Chapter 6. There are two inputs to the linear
blocks : the input signal of the sigma-delta modulator and the out-
put of the quantizer. The input signal of the sigma-delta modulators
varies with time continuously. The output of the clocked quantizer
changes with time in a piecewise constant manner and is treated as
a step input for each clock phase. Because the output of the clocked
quantizer is transparent to its input only at switching instants, the
output of the linear block is needed only at the clocking instants
when the quantizer updates its output. For sigma-delta modulators
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