I have been trying to intuitively understand how pnoise is computed after running a PSS simulation. My grasp is that a circuit is linearized about its periodic operating point when driven by a periodic waveform. During pnoise analysis, the spectrum of the noise sources (provided by device model) is then translated to the output via the transfer function obtained in PSS. As a result, the output noise has the correlation/folding effects of all the noise sources.

My questions is with regard to the following statement in the cadence manual: ...the simulation computes the total time-average noise at an
output over a given frequency range...

Also, in a separate presentation (unfortunately, I forgot the source), it is mentioned that "pnoise computes the time-averaged noise over one period of the periodic steady state".

I have a tough time thinking through what "time-average noise" means. I gather from K. Kundert's "Introduction to RF simulation and its application" that pnoise is similar to a spectral analyzer which computes the time-averaged PSD of one particular node. I understand this in the sense that PSD displayed can be thought of as taking the average of multiple FFT over the span of time in a cyclostationary system to get an idea of noise performance of a system because its PSD is never constant. Is that what "time-average" means in the simulator as well?

If so, why does the simulator need to do time-average? It already has the PSD of the devices provided by the model. Doesn't the simulator just take the PSD and use the PXF to transfer the noise profile to the output? What is actually "time-averaged"? Also, why is it "time-averaged" over the period of the PSS? What does this statement mean?

Any insight is appreciated. Thanks.

I found the following thread:
https://designers-guide.org/forum/YaBB.pl?num=1554838519

which is a similar question. Quoting there:
"SpectreRF performs a detailed noise analysis including all correlations, and then presents the time-average of the noise. So the time-averaging only occurs after the noise leaves the circuit and is being processed for display.

This is very analogous to the case where you are observing the noise of a circuit with a spectrum analyzer. The circuit processes the noise including the effect of all correlations, and the result is observed by the spectrum analyzer when then computes the time-average of the noise before displaying it."

Unfortunately, I am still not able to picture what pnoise is doing which is "time-averaging". For example, let's say PSS is obtained at period = 1 second. If we have 1024 data points of system output voltage within 1 second, we will observe 1024 different noise values due to operating point change of the circuit (cyclostationary nature). What is getting time-averaged exactly?

PNoise starts with a PXF analysis on the periodically time varying linear representation of the circuit about it periodic operating point, which is used to compute the transfer functions from every noise source to the output. The output noise is then computed by processing the raw noise sources by these transfer functions and accumulating the resulting output noise. The averaging is effectively done in the frequency domain rather than the time domain, so it is done 'over all time'. The PSS period and time points are only used when constructing the periodically time-varying linear representation. As such, they play no role in the averaging.

-Ken

All real spectrum analyzers have a bandwidth. That bandwidth sets the effective averaging period. If the characteristics of the signal are changing at a rate that is above the bandwidth they are averaged, if they change at a rate below the bandwidth, then output of the spectrum analyzer follow the changes.

To see this, imagine you have a high frequency signal generator that turns on and off once a second. If you set the bandwidth of the spectrum analyzer to be significantly above 1Hz, then you will see the signal level displayed by the analyzer pop up and down at a rate of 1Hz.  If you set the bandwidth of the analyzer to be significantly below 1Hz, then you will see an averaged result.  Of course, in this second case the spectrum analyzer updates much more slowly, taking well over 1 second for each update.

With PNoise the effective bandwidth is 0Hz, meaning it is as if the analysis starts averaging before the big bang and continues beyond the heat-death of the universe, and then displays the results.

Thus, I would say you have it backward. It is not the results from PNoise that are inaccurate for slow variations, it is the spectrum analyzer. After all what is promised is the time-average of the result, which is what PNoise provides. The averaging provided by the spectrum analyzer breaks down if the characteristics of the signal are changing slowly.

-Ken

I also have been confused on how pnoise is computed, I'm learning a lot here.

Pstb analysis is little more than two PAC analyses combined with some post processing. To understand it you need to understand two rather unrelated topics: how PAC works, and how STB analysis work.

PAC:
The first step in PAC is to compute the POP, the periodic operating point. This is the LTV representation of the circuit with the large-signal clock applied. The second step is to apply a small signal stimulus at a single frequency. This signal is modulated by the POP as it traverses the circuit, resulting in a comb spectrum that is offset by the stimulus frequency.  PAC then outputs the offset comb spectrum. The only averaging that occurs is done by the Fourier analysis when computing the coefficients of each member of the comb spectrum (the sidebands).

STB:
Loop gain is only easily defined and measured on abstract feedback loops, loops where the amplifier and feedback are ideal (unilateral with no loading effects). Abstract loops do not exist in real circuits, however because we are linearizing the circuit, we can play all kinds of tricks with linear equivalent circuits. The easiest way to understand this is to think about Grey & Meyer's method. They replace the circuit with a linear two port equivalent circuit, and then mathematically compute the loop gain using two-port parameters. Tian's method, which is used in Spectre, is similar.

-Ken

A swept frequency domain  analysis is nothing more than a collection of independent single frequency analyses. No averaging is performed over frequency.

In the context of this thread, the averaging occurs over time. Specifically, in a noise analysis the noise is averaged over a clock cycle.

To be more specific, imagine examining the detailed noise waveform over many many clock cycles. Chop the waveform into individual cycles and line them up. There will be small differences between them due to the noise. Because of modulation effects from the circuit, the variation between the cycles will vary over the cycle. At some points in the cycle the variation will be large, at other points it will be small. Consider the output being a digital signal. The variation will tend to be small when the signal is high or low, but the variation will be high as it is transitioning between high and low. In this case, imagine sampling the output waveform once per cycle, and the same phase in each cycle. If you sample when the output is either high or low, then the variation will be small. If you sample during the transition it will be large. Now imagine sampling the noise at 100 points over the cycle and averaging them. That would be the time-average noise.

PNoise is like that, but it breaks each output frequency into a different analysis. So it starts by limiting the noise to a single frequency and computing the average noise over one cycle. Then it repeats that process over and over for each of the frequencies.

-Ken

Quote:


No, the comb spectra are not summed. Each Fourier coefficient in a spectrum is placed into a different transfer function. Each Fourier coefficient represents a different sideband, and there is a different transfer function represents a different sideband.

With PSTP, you are interested only in the 0 sideband.