how to simulate the instability of sigma-delta modulator?

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i want to simulate the instability of sigma-delta modulator in matlab.
but when i change the integrator's gain (3rd order), i found only alternating bit stream at the output of quantizor , which is quite similar.

so could anyone tell me how to figure out the instability in matlab simulation.
thanks a lot!
 

is there anyone could answer my question?
 

Re: how to simulate the instability of sigma-delta modulator

A sigma delta modulator is called stable when for a certain class of input, the states of the system are bounded and the modulator is free of large sginal limit cycles.

large gain of filter may saturate the cirucit, that's one reason that alternating bit stream are at the output. Reduce the gain, and input and see it.
 

Re: how to simulate the instability of sigma-delta modulator

You can try use full scale rectangle wave as your input signal, the frequency is about half of you sample rate.
 

large than 3-order is generally not stable if you don't do some improvement for the modulator, search my previous post , I have give some models of matlab and a toolbox for delta-sigma modulator design.
Regards
carl
 

Re: how to simulate the instability of sigma-delta modulator

My may is to sumulate more and more pattern in Matlab. And check every SNR for every pattern.

In design, make sure the high frequency gain is limit in some value based on your order and topology.

Yibin.
 

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