After reading Ken Kundert's "Simulating Switched-Capacitor Filters with SpectreRF" and played with some PXF simulations, I have some question regarding the concept of k (as in Equation (33), f_in = k*f_clk+f_out) and sidebands. Allow me to illustrate my question by an example.

Assume that my circuit's f_clk is 100kHz, and I perform two PXF analyses. In the first analysis, I run my simulation from 1Hz to 4*100kHz (that is, 4 times clock frequency), with number of sideband set to 0; in the second analysis, I run my simulation from 1Hz to 100kHz, with number of sideband set to 3. It appears to me that in both cases, the "actual" f_in would be from 1Hz to 400kHz (in the second analysis, k varies from 0 to 3 while the sweep frequency varies from 1Hz to 100kHz, resulting in an overall sweep range of 1Hz to 400kHz.) So will the two analyses produce the same result? Of course, depending on how I set freqaxis, the results may be plotted differently, but physically, should the actual response be the same? If not, under what circumstances will they differ? Thanks a lot!

Thanks Ken for the reply. I understand the general idea of f_in = k*f_clk+f_out, but I still have some confusion.

In current version of SpectreRF, PXF analysis has a "Specialized Analyses" option which can be set to "Sampled." If I understand it correctly, with this option, the simulator first samples the output at specific time points, resulting in discrete-time values, and then performs spectrum analysis on these samples. If I set this feature to sample at f_clk, and f_in=400kHz, what I get at the output is a set of sampled, discrete-time values spaced at time interval of 1/100kHz (i.e. 1/f_clk.) Then how do I interpret this one set of sampled values as both a 400kHz signal (for k=0) and a 100kHz signal (for k=3)? Physically, this set of sampled values have one amplitude. Then how can the transfer functions for k=0 and k=3 be different?

Can I say that the implicit assumption behind f_in = k*f_clk+f_out is that we do not do such sampling, and that the output signal is a continuous-time signal, so it has frequency components shifted from f_in by integer multiples of f_clk?

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No, it is true regardless of the sampling.
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They are different transfer functions because the output frequency is different. However, they may have the same value (same magnitude and phase), as you would expect with a sampled system.

The interpretation of sampled PXF is that of traditional PXF applied to your original circuit with a sampler added to it. And it is not an ideal sampler. It is a sampler that uses the time points of the underlying PSS analysis, that is why the transfer functions tend to droop with frequency.

-Ken

Thanks Ken and Frank for the replies. As Ken mentioned:

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I'd like to confirm my understanding here. Conceptually, the signal at the output of this added sampler is still considered a continuous-time signal (that is, vout(t)), not a discrete-time signal (i.e. vout[n]) as I originally thought. I understand that as a numerical tool, the simulator still needs to look at the continuous-time signal at specific time points for the purpose of computation, but that is an implementation issue; the signal itself is still a continuous-time signal. Is this correct?

Also, if this added sampler is not an ideal sampler, what kind of sampler is it, and how will it shape the output signal spectrum? Will it introduce any sinc-like characteristics at all? If drooping the only effect, how much drooping should I expect?

I probably missed something here. If I configure the "Sampled" option in "Specialized Analyses" in such a way that PXF samples the output once per clock cycle (this can be easily done by triggering sampling on a clock edge), I would expect that (1) within one clock cycle, there are one track phase and one hold phase, and (2) the track interval and hold interval add up to a clock cycle time. If these time intervals are related to time steps, then within one clock cycle, very likely it will sample the output many times (assuming the time step is much smaller than clock cycle), which contradicts the configuration that it samples once per cycle.

I understand that the numerical method needs to "look at" the sampled signal at many points within the cycle to calculate the spectrum, with the interval between these points being the time step, but is that kind of "interval" the same as the sample interval/hold interval in a sample-and-hold situation?

So, is it correct to say that the sampler has a sample phase and hold phase, which add up to clock cycle time?

Frank Wiedmann wrote on Nov 6^th, 2012, 6:26am:



Hi Frank,

Now I am using sampled pxf to analyze relaxation oscillator which has comparator(very non-linear component) in it to compare a referecne votage and a sawtooth wave derived from charging and discharging a capacitor. Does the pxf still work since there is a very non-linear component in circuit? The analyzed output signal may be delayed from the comparator output? Does the delay and heavy non-linear component make the pxf fail?

BTW, I encounter convergence problem when running pss on the relaxation oscillator.

Any comment would be highly appreciated.

Thx,
Winston