Modeling techniques currently utilized in design of
Σ∆
- Modulator are based on MATLAB
Yi-Lung Shih
1
, Jia-Yarn Wong
2
Abstract
S
igma-Delta (
Σ∆
) Analogue-to-Digital Converters (ADC) have been hugely
successful in realizing high-resolution consumer audio products, such as MP3
players and cellular mobile phones, for some time now.
Matlab
7
offers
a
technical
computing
environment
for
high
-performance
numeric
computation. It integrates numerical analysis, matrix computation and
graphics in an easy-to-use
environment
without
the u se
of
tedious
language
syntax
.
The
M a lta
environment is ideal for the behavioral simulation of
Σ∆
converters
because signals can be treated as vectors (matrices with only one row or column) and
the modulator operation itself can be described simply as a set of
difference equations.
The output bit stream(s) from the modulators can be easily transformed into the
frequency domain by making use of
M a tlab’s
excellent
signal
processing
functions
,
such
as
the
various
windowing
functions and the Fast Fourier Transform (FFT).
Furthermore the results can be displayed graphically and the noise and signal
components can be quickly summed up separately to compute the SQNR. An example
of the difference equation modeling of a 3
rd
order feed- forward modulator (using a
4-level quintile
and over sampling rate of 76.8) is shown in Figure2 along with the
output spectrum and the computed SQNR.
1. INTRODUCTION
There is a great deal of interest in extending the bandwidth of sigma
-delta-modulators for wideband applications. There are many ways to increase
the bandwidth of a sigma-delta converter. Each method involves an alteration of one
or more of the parameters available to the designer, that is the sampling frequency,
the number of bits in the quantizer, the oversampling ratio and the modulator loop
order. An alternative to increase the effective sampling frequency is to lower
the OSR. There are several ways to do so. One solution is to improve the noise
-shaping characteristic by employing higher-order modulators, [1].
Another alternative
and perhaps the
most practical approach, is to replace the single-bit quantizer by a
multi-bit quantizer, [2]. This allows the OSR to be reduced without trading resolution to
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