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Design >> Mixed-Signal Design >> Problem with a 3rd order CIFB sigma-delta modulator
https://designers-guide.org/forum/YaBB.pl?num=1302855650

Message started by b3k on Apr 15^th, 2011, 1:20am

Title: Problem with a 3rd order CIFB sigma-delta modulator
Post by b3k on Apr 15^th, 2011, 1:20am

Hi,

I'm trying to simulate a 3rd-order SDM using Simulink. I followed the approach Schreirer used in his text "Understanding Delta-Sigma" to calculate the coefficients by simply comparing the powers of z of the required NTF, which is (1-z^-1)^3 in my case, and the general NTF of a 3rd order CIFB structure given by eq. (4.33) on page (116).

My calculated coefficients are:

a1 = 1, a2 = 3, a3 = 3
b1 = 1, b2 = 3, b3 = 3, b4 = 1 (to give an STF = 1)

Input is a sine-wave with frequency = 812.5Hz, amplitude = 0.5v, OSR = 32 and 1-bit quantizer.

However, it appears to be unstable for an unknown reason to me and I'm really confused, any suggestions?

Thanks

Title: Re: Problem with a 3rd order CIFB sigma-delta modulator
Post by jefkat on Apr 16^th, 2011, 9:50am

Just thinking ..
Scale down the coefficients such that the biggest is 1.
May be that helps.

Title: Re: Problem with a 3rd order CIFB sigma-delta modulator
Post by b3k on Apr 17^th, 2011, 6:50am

Same result.
Thanks anyways jefkat.

Title: Re: Problem with a 3rd order CIFB sigma-delta modulator
Post by jefkat on Apr 21^st, 2011, 4:02am

An "odd" thing I notice is that you dont have any delay in the loop. I have not seen any SC architecture of this sort so far. So may be somehing lies in there--

Title: Re: Problem with a 3rd order CIFB sigma-delta modulator
Post by jefkat on Apr 21^st, 2011, 4:04am

On the other hand may be also try playing with the input amplitude may be your input is beyound OL level to begin with .

Title: Re: Problem with a 3rd order CIFB sigma-delta modulator
Post by nrk1 on Apr 30^th, 2011, 10:25am

b3k,

1 bit delta sigma modulators of order > 2 are unstable for out of band gain(OBG) more than about 1.5. Your OBG is 8 (absolute value of NTF at z=-1). You need to realize a 3rd order modulator of the form (1-z^-1)^3/D(z) where D(z) will make the OBG to be 1.5. You can use Schreier's DS toolbox to synthesize the right NTF and get the coefficients etc. (As an aside, you can make stable multibit DSMs with OBG > 1.5, but not as high as 8. OBG=3 is probably a reasonable practical limit).

Nagendra