Hi,

I am using the toolbox from Richard Schreier for a sigma-data ADC.

>> ntf=synthesizeNTF(3,16,1.5,1)

Zero/pole/gain:
    (z-1) (z^2  - 1.977z + 1)
-----------------------------------
(z-0.9942) (z^2  - 1.994z + 0.9942)

>> [a,g,b,c]=realizeNTF(ntf,'CIFF')
realizeNTF Warning: The ntf's zeros have had their real parts set to one.

a =
   0.0116   -0.0229   -0.0003
g =
   0.0230
b =
    1     0     0     1
c =
    1     1     1

However, from the flow-diagram of CIFF structure, it only uses
cascaded 1/(z-1), and there is a feedback from the output of
the third integrator to the input of the second.
This can only achieve z^2-2*z+1+r ,where r is the small feedback
facto.  It has no way to realize the zeros
in z^2-1.977*z+1.

Is something wrong with my understanding?

Acutally, I am using
> ntf=synthesizeNTF(3,16,1,1.5)

Zero/pole/gain:
    (z-1) (z^2  - 1.977z + 1)
-----------------------------------
(z-0.6657) (z^2  - 1.524z + 0.6599)

Anyway, there zeros are at
1,  0.9885 + 0.1512i, 0.9885 - 0.1512i

They are all on unit circle.

However, if I use the CIFF stucture, there is no way I can get
complex conjugate zeros on unit circle,

I can only get zeros where z^2-2*z+1+g1=0.

Please see the attached derivation, I asume k1=k2=k3, which
is the case on pp. 22 of Richard's toolbox v7.2 documentation.

if you use
freqz([ 1 -2 1.023]) which is realizable via CIFF
and compare with
freqz([ 1 -1.977 1]), whose zeros are  on unit circle.

you can tell the frequency response is quite different.
The first reponse has quite less attenduation at desired zero frequency.

Hi Berti,

I agree that for high or moderate OSR, the difference is not big. For low OSRs, how do you achieve the desired NTF?

1) use CRFF or CRFB structure, which has a z/(z-1)^2 in their transfer
function. It is easy to realize z^-1/(1-z^-1), how do you realize
1/(1-z^-1). I know some switch-capacitor implementation can
realize z^1/2, is there any other way?

2) use CIFB structure, but you have need extra DACs need to build and
Feed forward structure can achieve lower distortion since it only
process mostly quantization noise only.

3) how do you achieve the NTF in continuous-time Sigma-Delta?
I know you can use d2c with zoh to converter the NTF from Z domain
to S domain and the 'zoh' will take care NRZ dac pulse, however,
usually you get a transfer function H(s) that has poles like
Num(H(s))=s(a*s^2+b*s +c).
However, if you use two 1/s in cascade and feedback from the
output of the second 1/s to the input of the first 1/s, you will get
something like K(s)=(x*s^2+y), unless you feedback from the
output of the second 1/s to the input of 1/s as well.
However, if you look at most published continuous-time sigma-delta,
nobody actually feedback from the output of the second 1/s to the
input of the second 1/s. All of them only feedback from the output
of the second 1/s to the input of first 1/s.