The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Mixed-Signal Design >> Another difficult fundamental question: about delta sigma modulator
https://designers-guide.org/forum/YaBB.pl?num=1253702751

Message started by tony_taoyh on Sep 23^rd, 2009, 3:45am

Title: Another difficult fundamental question: about delta sigma modulator
Post by tony_taoyh on Sep 23^rd, 2009, 3:45am

Hi, All,

I have another difficult fundamental question for the first order delta sigma modulator.

ff
|
x -----(+) ----- {z^-1/(1-z^-1)} ------(+) ------> [8-bit ADC] ------> y
| |
-----------------------------------------------------------------

The feedback is a negative one, with 8-bit ideal DAC.

The ADC is also a ideal one.

ff is white noise. x is a DC input.

According to the linear model, the TF is as:
y = x*z^-1 + (ff+qq) * (1-z^-1), where qq is the quantization noise.

According to this model, the ff will also be first-order shaped. Right?

However, from the Matlab behavioral model, ff is NOT shaped.

Is there anybody who can explain this well?

Thanks a lot.

Title: Re: Another difficult fundamental question: about delta sigma modulator
Post by tony_taoyh on Sep 23^rd, 2009, 6:12pm

Some additional information.

In the matlab program, the integrator output will be:

v1(n) = v1(n-1) + 1*(x(n-1) - y(n-1)) + ff(n-1)

It is equivalent to:

v1(n) = v1(n-1) + 1*({x(n-1) + ff(n-1) } - y(n-1))

Assuming the gain of the integrator is 1.

Then, the x + ff can be considered as the input of the modulator.

Both x and ff will NOT be shaped inside the behavioral simulation.

There shoud be some breaking point somewhere, to explain the
contradition between behavioral simulation and linear model.

Thanks.

Title: Re: Another difficult fundamental question: about delta sigma modulator
Post by Berti on Sep 23^rd, 2009, 11:01pm

I think your conclusion is wrong. The output y will contain ff and x. You basically consider the modulator open-loop.

When you close the loop you get y(n) = x(n-1) + (ff(n) - ff(n-1)).

How do you simulate this modulator?

Cheers