sigma-delta modulator issues

1) Many sigma-delta modulator's simulink models include some gain blocks, whose gain value may be 0.5/1.0/2.0. How to decide whether the gain block is needed and how to decide these gain values?

P.S., The pic (SDM.jpg) is an example. The a1(a2,b1,b2,b3,c1,c2) block is what I mentioned gain block. This pic is from Richard Schreier’s manual.


2) I downloaded the free sigma-delta modulator toolbox from
h**p://www.mathworks.com/matlabcentral/fileexchange
I do as the example says(write a plot.m file which contains the lines on the right of spectrum) and find the frequency-domain plot cannot work(the time-domain plot can work if I write a plot.m file which contains the lines on the right of time-domain figure).

The matlab prompt hints:
??? Attempt to execute SCRIPT plot as a function.
Error in ==> plot at 21
plot(linspace(0,1,N/2),dbv(spec(1:N/2)));

I am sure that the dbv.m exists in the same path with plot.m
P.S., The pic (Toolbox.jpg) is also from Richard Schreier’s manual.

What are your opinions?


Thank you very much.

The gain blocks are the sigma-delta modulator loop filter coefficients. They are used to stabilize the loop filter for given specs.
The noise transfer function (NTF) of your modulator indeed depends on the loop filter transfer function. The coefficients of the loop filter and hence the loop filter transfer function is the results of a tradeoff between noise suppression and stability. In schreier toolbox, it is the out-of-band gain which will give that tradeoff (higher gain more suppression but lower stability).
So the coefficients will depend on this tradeoff (set by you) and by the architecture of your loop filter (Butherwoth, Chebyshev, ... also set by you) but the good news is that
they are generated by functions like synthesizeNTF in the toolbox.

Hi shpongle,
Thank you very much for your reply.

The loop filter mentioned in your post is the low-pass filter which is used in sigma-delta ADC/DAC to suppress the high frequency quantization noise?

My sigma-delta modulator is used in phase-locked loop in order to finish a fraction-N PLL. In such application, the pll dynamics will suppress the high-frequency quantization noise. So the gain block is still critical?

no, the loop filter is total pic of your post.
for delta sigma pll, the gain block is still critical becasue you must make the loop stability.