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Phase noise to phase jitter for square waves

yizh

Hi,

I'm simulating a free running oscillator for jitter and I have the following question:

I have to run a "PNOISE - sources" simulation in order to recieve phase noise, since I have to filter the phase noise before integrating in to extract jitter (in order to mimic a PLL / CDR transfer function).

A few papers were written on the subject, some of them state that the integration upper limit is Fc/2 while others state that it is a few Fc. I assume that it should be a few Fc if the tested wave is a sine wave (i.e. no harmonics appear in the phase noise) and Fc/2 if it is a square wave.

As far as I understand, for square waves the jitter behavior of the first harmonic is similar to the jitter behavior of the square wave, thus it is assumed that integration up to Fc/2 takes into account only the first harmonic, otherwise the jitter will be summed more than once.

Please correct me if so far I'm wrong. Otherwise, here is a correction that I would like to do in my PNOISE simulation settings: instead of mixing the noise with many harmonics (i.e. Maximum sideband >> 1) and then integrating up to Fc/2, I might set maximum sideband to 1, thus the noise will be mixed only with the first harmonic, such that I will see a phase noise as if I had a pure sine wave at the input and not a square wave. Then, I would integrate up to a few Fc and see a more accurate jitter result.

In my simulations I see substantial difference between the two options, that's why the question is very important.

Any respose will we appreciated. I would especially like to hear Andrew Beckett's opinion on this.

Thanks!

 

Parents
  • Quoting:

    I think there are some assumptions you are making here which aren't necessarily correct. In general you should use the "jitter" noisetype if you want to measure jitter. There are two approaches - "FM" jitter (which uses a conversion from the PM part of the noise, as computed with the "modulated" noise type to a time metric), and "PM" jitter (which samples the noise at the specified threshold crossing, and then uses this in conjunction with the slope of the signal at the threshold crossing to compute the equivalent time variation).

    The FM approach (which is not disimilar to what you are trying to do) is best suited to sinusoidal (or near-sinusoidal signals) rather than square-ish waveforms; for those (particularly when used in decision making circuits, or clock recovery circuits), the PM jitter approach is better.


    Thanks for the answer.

    First, a word about my motivation or - why pnoise-jitter does not suit my needs. In my application, jitter has to be filtered prior to integration with a physical (i.e. not a "brick wall") filter. Take for example IEEE KX spec (annex 70.7.1.9) which states: "For the purpose of jitter measurement, the effect of a single-pole high-pass filter with a 3 dB point at 750 kHz is applied to the jitter". Pnoise-jitter does not have this capability as far as I've seen, thus I must run jitter-sources, extrace phase noises, multiply it with the filter and then integrate.So, even though the wave I measure is a square-ish wave, I don't see an option to run the PM approach.Please correct me if I'm wrong.

    Quoting:

    I don't think it makes sense to set maxsideband to 1 and then integrate over multiples of the carrier. For a start, the noise will be infinite at multiples of the carrier (1/f is infinite at f=0 - of course, noise is not really that large at low frequencies, because non-linear effects start to come into play), but more importantly if you are only including noise contributions from up to the first side band, high frequency noise is being excluded! In many oscillators the noise in sidebands 0 and +/-1 are the biggest, but of course it depends...


     I think that the noise will not be infinite at multiples of the carrier since maxsideband=1, so no harmonic is viewed at the phase noise plot. The plot is smooth at the harmonics.

    High frequence noise, as my understanding goes, is not excluded since integration goes up to a high frequency. This is equivalent to folding the noise around half the carrier frequency. Only in my proposition noise is folded only "implicitly" since I don't actually fold but instead integrate up to a high frequency.

     It is true that noise mixing with high harmonics is not taken into account, but this is due to the assumption that I described at the first post of this thread.

    Quoting:

    Whilst the phase variation of the fundamental harmonic of a square wave will be similar to that of a sine wave, it won't be precisely the same, and I don't think that means that jitter is the same either - the PM jitter approach will be better.

    Note that it doesn't make sense to sweep past half the fundamental frequency when using PM jitter, because it adds an ideal sampler at the fund frequency rate to the output of the circuit, which naturally folds the noise from higher frequencies - so it is sufficient to sweep to half the fundamental. Sweeping beyond that will mean you double count the noise. Maybe that's what you're read?


    No, I'm speaking of phase noise integration, i.e. FM jitter. See for example here:

    http://www.maximintegrated.com/app-notes/index.mvp/id/3359

    Or in the Cadence app note titled "Jitter Measurements Using SpectreRF", eq. 1-17.

Reply
  • Quoting:

    I think there are some assumptions you are making here which aren't necessarily correct. In general you should use the "jitter" noisetype if you want to measure jitter. There are two approaches - "FM" jitter (which uses a conversion from the PM part of the noise, as computed with the "modulated" noise type to a time metric), and "PM" jitter (which samples the noise at the specified threshold crossing, and then uses this in conjunction with the slope of the signal at the threshold crossing to compute the equivalent time variation).

    The FM approach (which is not disimilar to what you are trying to do) is best suited to sinusoidal (or near-sinusoidal signals) rather than square-ish waveforms; for those (particularly when used in decision making circuits, or clock recovery circuits), the PM jitter approach is better.


    Thanks for the answer.

    First, a word about my motivation or - why pnoise-jitter does not suit my needs. In my application, jitter has to be filtered prior to integration with a physical (i.e. not a "brick wall") filter. Take for example IEEE KX spec (annex 70.7.1.9) which states: "For the purpose of jitter measurement, the effect of a single-pole high-pass filter with a 3 dB point at 750 kHz is applied to the jitter". Pnoise-jitter does not have this capability as far as I've seen, thus I must run jitter-sources, extrace phase noises, multiply it with the filter and then integrate.So, even though the wave I measure is a square-ish wave, I don't see an option to run the PM approach.Please correct me if I'm wrong.

    Quoting:

    I don't think it makes sense to set maxsideband to 1 and then integrate over multiples of the carrier. For a start, the noise will be infinite at multiples of the carrier (1/f is infinite at f=0 - of course, noise is not really that large at low frequencies, because non-linear effects start to come into play), but more importantly if you are only including noise contributions from up to the first side band, high frequency noise is being excluded! In many oscillators the noise in sidebands 0 and +/-1 are the biggest, but of course it depends...


     I think that the noise will not be infinite at multiples of the carrier since maxsideband=1, so no harmonic is viewed at the phase noise plot. The plot is smooth at the harmonics.

    High frequence noise, as my understanding goes, is not excluded since integration goes up to a high frequency. This is equivalent to folding the noise around half the carrier frequency. Only in my proposition noise is folded only "implicitly" since I don't actually fold but instead integrate up to a high frequency.

     It is true that noise mixing with high harmonics is not taken into account, but this is due to the assumption that I described at the first post of this thread.

    Quoting:

    Whilst the phase variation of the fundamental harmonic of a square wave will be similar to that of a sine wave, it won't be precisely the same, and I don't think that means that jitter is the same either - the PM jitter approach will be better.

    Note that it doesn't make sense to sweep past half the fundamental frequency when using PM jitter, because it adds an ideal sampler at the fund frequency rate to the output of the circuit, which naturally folds the noise from higher frequencies - so it is sufficient to sweep to half the fundamental. Sweeping beyond that will mean you double count the noise. Maybe that's what you're read?


    No, I'm speaking of phase noise integration, i.e. FM jitter. See for example here:

    http://www.maximintegrated.com/app-notes/index.mvp/id/3359

    Or in the Cadence app note titled "Jitter Measurements Using SpectreRF", eq. 1-17.

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