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b3k

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Problem with a 3rd order CIFB sigma-delta modulator
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

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jefkat Community Member Offline Posts: 69	Re: Problem with a 3rd order CIFB sigma-delta modulator Reply #1 - Apr 16^th, 2011, 9:50am Just thinking .. Scale down the coefficients such that the biggest is 1. May be that helps.
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b3k New Member Offline Posts: 2	Re: Problem with a 3rd order CIFB sigma-delta modulator Reply #2 - Apr 17^th, 2011, 6:50am Same result. Thanks anyways jefkat.
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jefkat Community Member Offline Posts: 69	Re: Problem with a 3rd order CIFB sigma-delta modulator Reply #3 - 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--
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jefkat Community Member Offline Posts: 69	Re: Problem with a 3rd order CIFB sigma-delta modulator Reply #4 - 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 .
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nrk1

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Re: Problem with a 3rd order CIFB sigma-delta modulator
Reply #5 - 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

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