The Delta-Sigma Toolbox
• Matlab functions for the design, simulation and
realization of delta-sigma modulators.
• Developed at OSU by Dr. Schreier
• Download sites:
ftp://ftp.mathworks.com/pub/contrib/v5/control/delsig.zip
http://www.mathworks.com/matlabcentral/fileexchange/Files.jsp?
fileId=19
• Documentation is in file DelSig.pdf
Installation
• Unzip file to ~/delsig
• In non-existent, create directory ~/matlab
• Copy file mexopts.sh into ~/matlab
• Edit file ~/matlab/startup.m to include:
path(path,’<full-path-to-home>/delsig’);
• Compile C functions using mex file.c
• Start matlab.
1
Noise Transfer Function
Simple NTF NTF with optimized zeros
NTF = (1 - z-1)L
Inband
noise
fB 0.5 f/f fB 0.5 f/f
Zeros CLK Zeros CLK
at DC
Even better
• Less in-band noise (optimized zeros)
• Meets stability requirements (Lee’s rule)
Lee’s
rule
6 dB
fB 0.5
f/fCLK
Zeros Poles
2
Design Flow
Key Functions (1)
• Modulator synthesis and simulation
synthesizeNTF Noise transfer function (NTF) synthesis.
clans Closed-loop analysis of noise shapers
(NTF synthesis for multi-bit modulators).
simulateDSM Simulate a delta-sigma modulator using
either its NTF or its state-space description.
simulateSNR Use simulateDSM to simulate a DSM with
sine wave inputs of varying amplitudes and
then determine the SNR for each.
predictSNR SNR prediction for binary modulators
(Ardalan & Paulos method)
3
Key Functions (2)
• Modulator Realization:
realizeNTF Compute coefficients for a particular modulator
topology.
stuffABCD Create state-space description of a modulator
given the coefficients for a particular topology.
mapABCD Convert state-space description back to
coefficients.
scaleABCD Perform dynamic-range scaling.
Key Functions (3)
• Demonstrations and Examples:
dsdemo1 Synthesize 5th-order lowpass and 8th-order
bandpass NTF.
dsdemo2 Time-domain simulation and SNR calculation.
dsdemo3 Modulator realization and dynamic range
scaling.
dsdemo4 Continuous-time bandpass modulator design
using LC tanks.
dsdemo5 Find positively-invariant sets for second and
third-order modulators.
dsdemo6 Simulate element selection logic of mismatch-
shaping DAC.
dsdemo7 Design hardware-efficient halfband filter.
dsexample1 Discrete-time lowpass modulator.
dsexample2 Discrete-time bandpass modulator.
8
4
Design Example
• Delta-sigma ADC for digital audio applications:
– SNR > 98 dB (16-bit resolution)
– Output data rate: 44.1 KS/s
– Use 1-bit quantizer
– Second-order noise transfer function (NTF)
• Quick lookup shows that oversampling ratio needs to
be > 128.
=> Select OSR = 256 , and check later.
• Start code with:
order = 2; OSR = 256; nlev = 2;
9
Synthesize Noise Transfer Function
>> ntf = synthesizeNTF(order,OSR,opt)
opt=1
Zero/pole/gain: Optimize zeros
(z^2 - 2z + 1)
------------------------
(z^2 - 0.7639z + 0.2361)
>> [NUM,DEN] = tfdata(ntf,’v’)
NUM =
1.0000 -1.9999 1.0000
DEN =
1.0000 -0.7639 0.2361
10
5
Modulator Simulation
N=8192; f=N/(2*OSR); u=0.5*sin(2*pi*f*[0:N-1]/N);
[v,xn,xmax,y]=simulateDSM(u,ntf,nlev);
fB = 1/(8*OSR); Au = [-100:5:-10 -9:1:0];
[snr,Au] = simulateSNR(ntf,OSR,Au,0,nlev,fB,14);
11
Calculate Coefficients
>> form = ’CRFB’; [a,g,b,c] = realizeNTF(ntf,form,1)
a = 0.4721 0.7639
Other forms:
g = 5.0199e-05
b = 0.4721 0.7639 1.0000 CRFF
c = 1 1 CIFB
CIFF, etc
12
6
Scaling
• Scale coefficients for optimum dynamic range:
ABCD = stuffABCD(a,g,b,c,form)
threshold for
[ABCDs,umax]=scaleABCD(ABCD,nlev,0,1,7) judging stability
umax = 0.9000
ABCDs = 1.0000 -0.0003 0.7286 -0.7286
0.1530 0.9999 0.2919 -0.2919 signal limit
0 4.2349 1.0000 0
[a,g,b,c] = mapABCD(ABCDs,form)
a = 0.7286 0.1804
g = 3.2808e-04
b = 0.7286 0.1804 1.0000
c = 0.1530 4.2349
13
Circuit Level Implementation
fCLK = 2 × fB × OSR = 11.29 MHz
14
