Sigma Delta Coeficients

Hello

I'm trying to design a DAC, using a DT 3rd order Sigma Delta with feedforward (CIFF) , using verilog.

I applied the coefficients specified by Shreier's Delsig toolbox, but the output wave is distorted. I investigated a bit and discovered that these coeficients DO NOT account for accumulator (or integrator) saturation. The coefficients returned by the toolbox only guarantee Transfer Function stability, ignoring implementation issues such as the saturation.

Does anyone know how to calculate the coefficients that make the modulator stable and avoid saturation?

Also, if anyone already knows the coefficient values for this topology, i would really apreciate you tell me. At least I could test right away to see if it works.

Thanks

Yes I did see the same issue.

The coefficients from Richard's toolbox can not be applied into circuit without any change, even after scaling. I did have to rescale manually by myself before applied into the circuit for all modulators to be bounded in supply range.

But it took many times' simulation to obtain the final coefficients(switch to different sets every time). What is the better way to do it?

Guoke2000 said:

Yes I did see the same issue.

The coefficients from Richard's toolbox can not be applied into circuit without any change, even after scaling. I did have to rescale manually by myself before applied into the circuit for all modulators to be bounded in supply range.

But it took many times' simulation to obtain the final coefficients(switch to different sets every time). What is the better way to do it?

Click to expand...

The problem with every Sigma-Delta is that all of them presents as certain integrator saturation probability. This probability becomes worst as you increase Full-Scale, modulator order, or reduce integrator swing range and the number of quantization levels. To make matters worse, the theoreticall model does have some weaknesses and does not model the real modulator with a 100% accuracy. In order to get good coefficients from Richard's toolbox your Sigma-Delta requirements should not be too hard to meet (keep Full-Scale low, do not use very high-order modulators etc.). Even if your requirements are not very demanding, the requirements you define in the toolbox should always be more demanding than what you really need, to increase the probability of generating good coefficients.

I would sugest you read some good book about the subject, if you have the time. I does really help to understand some of these things and why the toolbox doesn't work 100%.

Try to avoid changing the coefficients by trial and error. I did that too, and it took me a lot of time and the results were not so good. When possible, try to stick to mathematical methods, such as the toolbox, and use he tricks I told you to increase your chances of sucess.

fcfusion said:

The problem with every Sigma-Delta is that all of them presents as certain integrator saturation probability. This probability becomes worst as you increase Full-Scale, modulator order, or reduce integrator swing range and the number of quantization levels. To make matters worse, the theoreticall model does have some weaknesses and does not model the real modulator with a 100% accuracy. In order to get good coefficients from Richard's toolbox your Sigma-Delta requirements should not be too hard to meet (keep Full-Scale low, do not use very high-order modulators etc.). Even if your requirements are not very demanding, the requirements you define in the toolbox should always be more demanding than what you really need, to increase the probability of generating good coefficients.

I would sugest you read some good book about the subject, if you have the time. I does really help to understand some of these things and why the toolbox doesn't work 100%.

Try to avoid changing the coefficients by trial and error. I did that too, and it took me a lot of time and the results were not so good. When possible, try to stick to mathematical methods, such as the toolbox, and use he tricks I told you to increase your chances of sucess.

Click to expand...

Thank you for your inputs. I agree that with lower-order and lower swing level setting in toolbox, it increases the probably of success of coefficients. However, I even tried very conservative settings in toolbox, like reduce out-of-band gain to <1.5, reduce the swing level, and increase zeros distribution, finally I still need to go through trial/error at transistor-level to make it work. The thing is, we are using toolbox because we don't need to go through the detailed analog filter process, but finally when all transistor-level is done we found the coefficients do not work! The trial/error process may be never successful!

Actually rarely saw book or paper mentioned this problem, seems scaling is always the solution, but maybe not.

Guoke2000 said:

The thing is, we are using toolbox because we don't need to go through the detailed analog filter process, but finally when all transistor-level is done we found the coefficients do not work! The trial/error process may be never successful!

Click to expand...

There are other issues aside poor coefficients that can cause your Sigma-Delta to fail, such as problems in your integrators or the quantizer. These problems include insufficient open-loop gain, low input voltage range, low output voltage range, high output impedance, poor frequency response (this happens quite often, integrators that do not behave as integrators), distortion, etc.

At the moment you should ask yourself "what's causing the modulator to fail? Poor coefficients or problems in your amplifier?"

In my opinion, you should have tested the modulator architecture with ideal amplifiers before starting the transistor-level design. That would allow to quickly determine if the coefficients you obtained with the toolbox were good or bad, without much effort. If your circuit is failing, you have no way to determine were the problem is without using an ideal modulator first.

I would bet your sigma-delta problems are due to amplifier problems instead of architecture or coefficients. Could you specify your sigma-delta specifications (order, quantization leves, Full-Scale, etc.) and what kind of amplifier did you use on your integrators and quantizer?

I thought opamp is fine as I used it to get higher SNR before. Anyway here is the situation: Opamp has ~50dB gain, output with 1.2Vpp differential swing, 1-bit quantizer. Vref is 1.1V. It is feedforward, 4-order and with two local feedback for distributed zeros. OSR of 28 and target ~65db SNR for the ADC.
Still need to rescale after getting coefficients from toolbox.

Guoke2000 said:

I thought opamp is fine as I used it to get higher SNR before. Anyway here is the situation: Opamp has ~50dB gain, output with 1.2Vpp differential swing, 1-bit quantizer. Vref is 1.1V. It is feedforward, 4-order and with two local feedback for distributed zeros. OSR of 28 and target ~65db SNR for the ADC.
Still need to rescale after getting coefficients from toolbox.

Click to expand...

As I suspected your amplifier has some problems. Let's start with the open-loop gain: you said your target SNR is 65 dB and your open-loop gain is 50 dB. Do you see the discrepancy? If the open-loop gain is 50 dB the SNR can NEVER be greater than 50 dB, because in real Sigma-Delta modulators, the SNR performance is directly limited by the amplifier's open-loop gain. I bet you looked at some graph wich plotted the relation between modulator's OSR and/or order with the respective SNR performance. Do not forget that these graphs were plotted for theoretical Sigma-Delta modulators which always use infinite open-loop gain. In reality your open-loop gain must be at least 65 dB, but professionals always give some margin of error, around 20 dB , and any of them would tell you to use amplifiers with at least 80 or 85 dB open-loop gain.

Since your open-loop gain is so low, you'll also experience another problem: you integrator does not behave as an integrator. An ideal integrator presents a Y(S) = X(S)/S frequency response. A real integrator presents Y(S) = X(S)/ (S+1/β) where β is the open-loop gain. As you can see, the smaller the open-loop gain the greater is the difference between the real and the ideal integrators. This results in a flat frequency response for low frequency signals instead of the expected -20dB\decade slope for all frequencies presented by an ideal integrator.

Third and last issue is the low OSR you selected. Typically, OSR below 64 is never used because the results are poor. This will not make your sigma-delta fail, it just means that your Sigma-Delta could be more optimized, using a 3rd order modulator with a 64 OSR would probably give you better results. Anyway, you can ignore this for now if you want, since I dont know what were your motives to select such a low OSR.

Output swing looks good but you gave no information about input voltage swing, which can give problems as well. Don't forget to check it as well eventually.

hi i want to design sigma delta ADC and start using delta sigma toolbox would you introduce me good document to start using this delsig toolbox ? i am totally new to this toolbox
thanks in advanve

membership said:

hi i want to design sigma delta ADC and start using delta sigma toolbox would you introduce me good document to start using this delsig toolbox ?

Click to expand...

If you would like to use Schreier's Toolbox, you need to read the following book at least.
https://www.amazon.com/Understandin...F8&qid=1355150691&sr=1-1&keywords=delta+sigma

pancho_hideboo said:

If you would like to use Schreier's Toolbox, you need to read the following book at least.
https://www.amazon.com/Understandin...F8&qid=1355150691&sr=1-1&keywords=delta+sigma

Click to expand...

Thank you, you mean the part of the book relate to delta sigma toolbox? (appendix B)? do you have the e-book?

membership said:

Thank you, you mean the part of the book relate to delta sigma toolbox? (appendix B)?

Click to expand...

No.
Appendix-B is no more than an old version of "DSToolbox.pdf" which is included in up-to-date "delsig".
https://pub.maruzen.co.jp/book_magazine/support/analog_digital/AppendixB.pdf

membership said:

do you have the e-book?

Click to expand...

No. I have hard cover book of this.

Again, if you would like to use Schreier's Toolbox, you need to read the following book at least.
https://www.amazon.com/Understandin...F8&qid=1355150691&sr=1-1&keywords=delta+sigma
Background theories required for Schreier's Toolbox are descripted in this book.
So purchase this book, if you would like to use Schreier's Toolbox.

Some useful but too simple materials might be available in the followings.
https://individual.utoronto.ca/schreier/ece1371.html
https://individual.utoronto.ca/schreier/ece1371-2012.html

pancho_hideboo said:

No.
Appendix-B is no more than an old version of "DSToolbox.pdf" which is included in up-to-date "delsig".
https://pub.maruzen.co.jp/book_magazine/support/analog_digital/AppendixB.pdf

No. I have hard cover book of this.

Again, if you would like to use Schreier's Toolbox, you need to read the following book at least.
https://www.amazon.com/Understandin...F8&qid=1355150691&sr=1-1&keywords=delta+sigma
Background theories required for Schreier's Toolbox are descripted in this book.
So purchase this book, if you would like to use Schreier's Toolbox.

Some useful but too simple materials might be available in the followings.
https://individual.utoronto.ca/schreier/ece1371.html
https://individual.utoronto.ca/schreier/ece1371-2012.html

Click to expand...

aha,, and just another question: I want to design Digital Sigma-Delta ADC to be implemented on FPGA, does this toolbox help me to design the modulator part of my ADC? as of course it should be in digital...
thanks a lot for our time

membership said:

I want to design Digital Sigma-Delta ADC to be implemented on FPGA,
does this toolbox help me to design the modulator part of my ADC?
as of course it should be in digital...

Click to expand...

Do you understand Delta-Sigma-ADC correctly ?

The modulator part, that is, loop filter of Delta-Sigma-ADC can't be in digital.
On the other hand, it is in digital for Delta-Sigma-DAC.

For Delta-Sigma-ADC, decimation filter and DEM or shuffler are implemented in digital.

Anyway if you can understand Delta-Sigma-ADC correctly, Schreier's Toolbox is very useful.
Of course, it can't give you necessary bitwidth directly for required accuracy of numerical operation.

http://www.cypress.com/?docID=40297
http://www.ijecse.org/wp-content/uploads/2012/08/Volume-1Number-2PP-508-513.pdf