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# difficult fundamental question: about delta sigma modulator

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#### tony_taoyh

##### Full Member level 2
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
..........|__________________________________________|

Because the website will automatically remove those long whitespace in typing.

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.

In the matlab program, the integrator output can be written as:

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

It is equivalent to:

v1 = 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.

Is there anybody who can explain this well?

Thanks a lot.

Is there anybody who can explain this well?

Thanks a lot.

if the ff is the kt/c noise, it should appear at the input of the integrator along with x.

i don't get this equation:
v1 = v1(n-1) + 1*(x(n-1) - y(n-1)) + ff(n-1)

Re: difficult fundamental question: about delta sigma modula

From the block diagram it appears that ff is the quantization noise and not qq. qq seems to be thermal noise because its not shown in the diagram. But anyway thermal noise doesn't undergo noise shaping.

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