How to convert pnoise to time domain process

Not entirely sure why it being an oscillator means you're interested in voltage noise rather than jitter - normally with oscillators (since they are amplitude limited) it's normally the voltage noise at the transitions that matter, i.e. the PM rather than the AM noise, which results in phase noise or jitter. Either way, not sure that's important for your question.

Why do you want to convert this back into the time domain? The noise output from pnoise analysis gives you the power spectral density of the noise, and so in transient noise you'd only see a similar shape after averaging over multiple cycles (because it's random) - seeing a single period in the time domain is not going to be terribly useful (I'd have thought).

There is the ability with the "Sampled Phase" mode of "sampled" pnoise (formerly known as tdnoise or time domain noise as the Noise Type in older versions) to sample the noise at various strobe points throughout the period. This adds a sampler at the output of the circuit and allows  you to see how the noise varies throughout the period (so you can see the noise PSD at instants in time throughout the period, for example). Not sure if that's what you want though.

So put simply, I'm not sure what your real objective is here, so I don't know how to answer!

Regards,

Andrew.

Sorry, I made a typo. I meant "not oscillator", an amplifier for example.

The reason why I want to convert it back to time domain is because the specification is in time domain. I am not so confident the integrated noise from noise summary is 1:1 to what I want to "the way I want to measure" in time domain. At least, I want to "measure" the deviation in time domain to at least get confidence level that it matches with integrated pnoise roughly. 

Well, I don't think you can really convert back into the time domain anyway, so this is probably a moot point. Often time domain metrics would be to measure the RMS noise power, which should be similar to the integrated noise power. Perhaps you can compare with transient noise to convince yourself that the results are reasonable (generally speaking though there's more scope for inaccuracy with transient noise if you don't set it up right - e.g. not high enough fmax, or not a long enough simulation, or not high enough accuracy to resolve the small noise signals).

Andrew.

Well, I don't think you can really convert back into the time domain anyway, so this is probably a moot point. Often time domain metrics would be to measure the RMS noise power, which should be similar to the integrated noise power. Perhaps you can compare with transient noise to convince yourself that the results are reasonable (generally speaking though there's more scope for inaccuracy with transient noise if you don't set it up right - e.g. not high enough fmax, or not a long enough simulation, or not high enough accuracy to resolve the small noise signals).

Andrew.

Dear Excalibur,

If I may intrude a bit on your question and your need for a “time domain” representation (and perhaps add to Andrew’s responses). Even a specification such as an rms noise is defined over a limited bandwidth. Hence, you need the frequency domain information to determine if your amplifier meets its requirement. If you recall, Parseval’s theorem expresses the equivalence of the energy in the time and frequency domain results for a signal. Hence, I also agree with Andrew that converting from the frequency domain to the time domain should not be necessary with enough knowledge about the actual circuit requirement for your amplifier.

Shawn 

Hi ShawnLogan,

I do not understand why "Even a specification such as an rms noise is defined over a limited bandwidth". How I see it is just measuring the noise during a defined time window, e.g. 1us. The frequency content is of no relevance, e.g. is it 90% 1/f and 10% white noise or is it 10% 1/f noise and 90% thermal noise.

I do know Parseval’s theorem. The trick is, the theorem is about when time is infinite and when frequency is infinite. It does not apply to a process that is limited in time. I read quite some papers on this topic. The impression I get is that the power of a time domain process start from t=0, e.g. noise, at a time T is equal to integrating the process's spectrum from f=1/T to f=+inf, scaled by some factor involving pi. 
Of course, if somebody took the task of translating time domain spec to the amplifier noise spec, then I dont need to deal with time domain here. 

Dear Excalibur,

ExcaIibur said:

I do not understand why "Even a specification such as an rms noise is defined over a limited bandwidth". How I see it is just measuring the noise during a defined time window, e.g. 1us. The frequency content is of no relevance, e.g. is it 90% 1/f and 10% white noise or is it 10% 1/f noise and 90% thermal noise.

Let me try to answer your question as best I can to explain my comment. Even when you measure the "noise during a defined time window", you are imposing frequency limits on your rms measurement. Why? Suppose you measure the noise over a time period Tsample with measurements of the noise taken every Tstrobe interval within that time window Tsample as shown in the attached illustration. The fact that you are observing the noise over a total time period of Tsample suggests that your measurement will not fully capture the contributions of noise whose frequencies fall below 1/(Tsample). Simply put, you will only capture a portion of the noise whose frequency components is less than 1/(Tsample). Now consider the effect of Tstrobe on your noise measurement. If the noise has frequency components that exceed the frequency of 1/(Tstrobe), it also will not be accurately captured in your noise measurement. As a result of this explanation, hopefully you will agree with me that the use of a 1 us time period to measure your noise and whatever value of Tstrobe your simulation data provides, does not capture the full rms noise power.  In fact, the noise power of even thermal noise is infinite over the full frequency band. Hence, any real noise measurement has in inherent limited bandwidth. This is the basis for the use of the thermal noise estimate of -174 dBm/Hz in a 50 Ω system at room temperature.

ExcaIibur said:

I do know Parseval’s theorem. The trick is, the theorem is about when time is infinite and when frequency is infinite.

While the integration over time and frequency in Parseval's theorem are infinite, the signals in time and frequency do not have to extend to infinity in their respective domains. In the example I provided, the noise frequencies are limited by the filter corner frequencies of 1/(Tsample) and 1/(Tstrobe). The time domain data is also limited by Tsample and Tstrobe. Hence, the time and frequency signals of the two integrals are not infinite.

Let me know if this helps explain my comments a bit better.

Shawn

Hi ShawnLogan,

That is quite impressive explanation and way beyond my expectation. It really helps.

Dear Excalibur,

I am just glad it helped explain my thoughts a bit better and that it made sense to you (and helped!)

Shawn