Hi,

I'm simulating a second order Sigma-Delta Modulator (Cascade of Integrators Feedback) with a 1.5 bit quantizer (3 quantization levels); a behavioural model has been implemented and all the simulations are performed in Simulink. The results are compared with the results obtained simulating Temes and Schreier toolbox and good agreement is proved.

The fft results in odd harmonics according to the odd quantization function and the noise floor is compatible with the expected value.
The fft calculation is performed using Hann windowing and coherent sampling (fin=fs*127/2^19, fft n.of points=2^19).

The power spectrum however includes unexpected even harmonics.

Since the model is perfectly balanced and ideal, why the modulator described above shows even harmonics? Is this problem intrinsic of the architecture?

Many works in literature show sigma-delta spectra with both even and odd harmonics but none explanation is reported.

Could someone help me to undertand the phenomenon?

Many thanks,
Matteo

Thank Sheldon for your attention,

the fft result (2^22 points, Hann windowing) is attacched.

Further details:

The oversampling ratio is 2048; the input sine wave is at fs*1023/2^22 where fs is the sampling frequency.

The 2nd order (cascade of integrators feedback)  modulator is based on a 1.3 bits quantizer; in other terms the quantization curve performs a mid-tread characteristic with three quantization levels

Thanks in advance,
Matteo