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Design >> Mixed-Signal Design >> sigma deltas, coherent averaging, PSD
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Message started by svensl on Jun 27^th, 2005, 5:07am

Title: sigma deltas, coherent averaging, PSD
Post by svensl on Jun 27^th, 2005, 5:07am

When a sigma delta modulator is used without dithering the quantizer properly, then it will produce limit cycles and idle tones. These limit cycles and idle tones will manifest themselves as spectral lines and high frequency oscillation observable in the frequency domain of the output. However, often they are buried in the noise floor and a ordinary PSD plot will not reveal them. I would like to know how it is possible to "bring out" the tones by reducing the random noise and revealing all the periodic components. When reading papers people often refer to coherent averaging but I don't know what it is. Does anyone know how to do such a thing in matlab or refer me to the corresponding literature?

Thanks,
Svensl

Title: Re: sigma deltas, coherent averaging, PSD
Post by Eugene on Jun 27^th, 2005, 10:58am

I have found sometimes that strobing the data helps, especially if you can tie the strobe rate to some multiple of the highest frequency clock, or the some multiple of the frequency of interest, if you know it. You must also make sure the sample rate for the PSD calculation coincides with the strobe rate in the analysis options.

Linking the strobe and PSD sample rate saves PSD from having to interpolate between data points in the transient analysis. The strobe command forces the simulator to place time points at regular intervals, which is what the PSD analysis needs. Spectre will still adjust time steps to control error propagation but it will also guarantee uniformly spaced time points and also only record those time points. You might be surprised at how much the noise floor can drop when you eliminate interpolation through strobing.

Title: Re: sigma deltas, coherent averaging, PSD
Post by sheldon on Jul 6^th, 2005, 4:32pm

Svensl,

If the goal is just to lower the noise floor why not just
increase the length of the FFT. Tested this recently for an
Oversampling ADC.

1) Baseline simulation was 4096 conversions with an
input frequency of 7/4096.

2) Re-ran the simulation with a 4x longer simulation and
the same input frequency.

The noise floor of the second simulation was signficantly
lower, normally we would expect the noise floor to be
10 log 4 better or about 6dB better. Since data from
oversampling ADCs need to be windowed anyway, the
only penalty is longer simulation time.

This increasing the number of time points is complementary
to the approach Eugene suggests. Strobing eliminates the
interpolation error in the data. Increasing the number of
FFT points, decreases the resolution bandwidth of the FFT.
Since the noise in fixed, decreasing the bandwidth
decreases the noise, noise(V/rt Hz) * bandwidth(rt Hz).
Since noise is uncorrelated, noise decreases by 3dB/oct.

So if you runnning the simulation with MATLAB, this is
probably not an issue. If you are running SPICE, this
may be more problematic.

Best Regards,

Sheldon

Title: Re: sigma deltas, coherent averaging, PSD
Post by svensl on Jul 6^th, 2005, 10:43pm

Thanks for the feedback.
Increasing the number of samples taken does decrease the noise floor as there are more points to spread the noise to. I am just curious as coherent averaging is often mentioned in papers. For example in : "Why 1-Bit Sigma-Delta Conversion is Unsuitable for High-Quality Applications" by Stanley P. Lipshitz and John Vanderkooy it is mentioned on page 4, right column, that coherent averaging reduces the noise by 48dB when averaging four 2^14 windows.

http://sjeng.org/ftp/SACD.pdf

Is it that they just take 4 periodigrams and just average them, or have the 4 windows overlap? I tried both and did not get the promised results.

Sven