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Design >> Mixed-Signal Design >> Second order Sigma Delta
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Message started by solanojedi on Mar 27^th, 2010, 1:17pm

Title: Second order Sigma Delta
Post by solanojedi on Mar 27^th, 2010, 1:17pm

Hi everybody,
I'm reading about sigma delta adc, the basic theory. I've read about the first order modulator and now the second order, but I have a problem (maybe stupid) with a phrase of my book (Data Converters by F.Maloberti), when he describe the 'passage' from first order to second order. He says: "Better performances and features are secured by using two integrators around the loop thus forming a second-order modulator as shown in the conceptual scheme of Fig. 6.11 (a). Since the use of two integrators in a feedback loop can
cause instability, it is necessary to dump one of the two integrators by using one of the two options represented by the dotted lines of Fig. 6.11 (a)." (Fig. 6.11 (a) is attached) Why two integrators can cause instability? I can't see... Thank you very much!

Title: Re: Second order Sigma Delta
Post by panditabupesh on Mar 27^th, 2010, 3:47pm

I suggest go through the section "Stability of MOD2" (page 74) of "Understanding Delta-Sigma Data Converters"

Bupesh

Title: Re: Second order Sigma Delta
Post by solanojedi on Mar 28^th, 2010, 2:12am

Thanks for your answer!

I've read the stability of second order modulator on Temes' book but he talks only about the 'classic' configuration of the second order modulator.. where can I find a discussion about the modulator of mine figure? [i.e, a first order modulator with two integrators in series instead of one]
Thank you!

Title: Re: Second order Sigma Delta
Post by loose-electron on Mar 29^th, 2010, 8:09am

Take a look at a simplified model - linear in nature - it is a crude approximation - but it illustrates the stability issue quite well.

Each integrator contributes 90 degrees of phase. 2X90 = 180
Thus you get into oscillation issues.

Title: Re: Second order Sigma Delta
Post by solanojedi on Mar 29^th, 2010, 10:12am

You're absolutely right! I didn't think about using continous techniques [like the L-transform] to analyze the stability but I tried to use the Z-transform, and that is a little more unfriendly to me. :)

Thank you very much!!