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Simulators >> Circuit Simulators >> psd in Cadence Waveform Calculator
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Message started by fran2k5 on Mar 31^st, 2006, 7:33am

Title: psd in Cadence Waveform Calculator
Post by fran2k5 on Mar 31^st, 2006, 7:33am

Hello everybody,

I have some problem to understand the psd function of the Cadence Calculator.
In particular I do not get the meaning of the Number of Samples.

The Window Size represents the number of time points that are considered by the FFT.
The total number of points (in time) will be divided by overlapping segments. The length of each segment
is Window Size.
Where does the Number of Samples come in?

Thank you very much,

fran2k5

Title: Re: psd in Cadence Waveform Calculator
Post by Jess Chen on Mar 31^st, 2006, 7:58am

fran2k5,

You are right about the window size and the overlapping segments. But the overlapping segments are selected from the total time record. The total time record consists of uniformly sampled time points and the total number of points is specified by the "Number of Samples" parameter. Spectre does not generate uniform time steps by default. However, the Fourier analysis in the psd function requires uniform samples. The Number of Samples determines how many uniformly sampled points to interpolate from the complete (non-uniformly sampled) record for use with the overlapping segments. The window width determines the frequency resolution. The Number of Samples, together with the start and stop times, determines the sampling period, which in turn determines the maximum frequency of the psd analysis.

-Jess

Title: Re: psd in Cadence Waveform Calculator
Post by fran2k5 on Apr 1^st, 2006, 7:53am

Thank you very much Jess,

Your explanation has been enlightening. I have got another question though.
I want to compare the SNR of two delta-sigma ADCs that work with different sampling frequencies, let's say one 2 times faster than the other.
I run the simulation for the same time (long enough to have several period of the sampled signal).
The number of samples has to be large enough to correspond to a sampling frequency (for the analysis) higher than the actual sampling frequency of the ADC. This means that the number of samples has to be doubled in the analysis of the faster ADC.

If I pick a number of samples high enough such that I satisfy Nyquist principle for both cases, is the comparison of the two psd fair?
I think that it would not be fair but I do not get why...could you help me out?

Thank u again,

fran2k5

Title: Re: psd in Cadence Waveform Calculator
Post by Jess Chen on Apr 4^th, 2006, 11:26am

fran2k5,

Cadence displays the psd in units of Volts**2/Hz for the vertical axis and Hz for the horizontal axis. Consequently, you can mix and match psd parameters and the overlaid plots still make for fair comparisons.

One thing that is not obvious is that the psd displays a double sided density; if you integrate only over positive frequencies to compute the rms value, you will need to double the integral.

-Jess

Title: Re: psd in Cadence Waveform Calculator
Post by fran2k5 on Apr 5^th, 2006, 3:09am

Jess,

when I talk about fair comparison I am wandering about the effect of the reduction of the noise floor when I increase the number of FFT points. It is not clear to me how to make a fair comparison of SNRs in the two delta-sigma ADCs . The one that goes faster is gonna need more points. But if I use the same number of points for the one that goes slower it is going to lower its noise floor more.

I hope my problem is a bit more clear now.:)

fran2k5

Title: Re: psd in Cadence Waveform Calculator
Post by Jess Chen on Apr 5^th, 2006, 8:32am

fran2k5,

One trick I use when studying noise floors is to strobe the data. Set the strobe period under transient options to be consistent with the number of points you plan to use in the psd so that the psd function does not have to interpolate. This will drop the noise floor considerably and perhaps make your comparison more robust. As it was explained to me, in different words, strobing sweeps numerical noise under the "signal rug"; the noise still exists but it is in the signal lines instead of the noise floor. As part of the signal, the noise should have less of an effect on the SNR and thus give you a more robust comparison...I think. I suspect it would be even better if you could find a strobe period that lines up with both ADC rates.

-Jess

Title: Re: psd in Cadence Waveform Calculator
Post by Ken Kundert on Apr 5^th, 2006, 9:50am

The comparison would not be fair if each bin had a different noise bandwidth. IN this case you could correct the results by computing the noise power per hertz. However, the noise bandwidth of each bin is dependent on the window size and shape, and you are using the same window on both converters, so the noise bandwidth per bin should be the same. The effect of doubling the sampling rate for one converter is that the spectrum extends to a maximum frequency that is twice as high.

-Ken

Title: Re: psd in Cadence Waveform Calculator
Post by fran2k5 on Apr 6^th, 2006, 2:24am

Thank you very much to both of you!!
I finally understood the right way of proceeding.

I need to perform the comparison keeping the same bin NBW for the 2 converters. The bin size can be kept the same if the simulation time is the same and if the ratio between Nunber of FFT points and window size is kept constant. For the same time, in the converter that goes faster I need more points because of the higher sampling rate. If I consider a number of FFT points that satisfy both cases (equivalent to a sampling frequency for the FFT higher than the highest ADC sampling frequency) it will mean considering more interpolated points for the slower converter and therefore more noise. As Jess suggested, strobing at the actual frequency of the converter gets rid of this problem:for the same simulation time the faster ADC will give more points and as consequence if I keep the n.ro points/window size the same in both cases I will get the same bin NBW.

Thank you again,

fran2k5