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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
  • yizh

     Edouard,

    I read your post once and again (and again). You seem very confident, and besides it is much easier to walk in a beaten path than build a new one, but I couldn't get myself conviced that you are right.

    However, at this point it I feel that it will not be appropriate to continue the discussion as it is since it seems that we begin to walk in circles. Some points I would still like you to clarify, if you could:

    1.  You write "your theory is somehow going against math evidences upon which the simulator has been built". Could you ellaborate?

    2. Andrew forwarded to you a while ago what I think might be a proof to my theory. Could you review it?

    3. I didn't understand your response to my proposed Matlab example.  You wrote "you’ll find identical zero crossing jitter for both waves, which is obviously  wrong for the square wave:   Ideal square wave has a  zero crossing jitter (infinite slew rate)". Since the square wave was created from the sine wave (say, by defining: if the sine wave is >0 then the square wave is =1, otherwise it is =-1), then clearly both waves have similar jitter. What do the infinite slew rate has to do here?

    4. How would YOU simulate jitter, given that you have a square wave and want to run the FM jitter ("sources"). Please relate to the following:

    a. Number of harmonics

    b. Integration limits

    c. Noise folding (aliasing of noise from higher frequencies due to the sampling of the signal edge)

     

    Thanks,

    Yizhak

Reply
  • yizh

     Edouard,

    I read your post once and again (and again). You seem very confident, and besides it is much easier to walk in a beaten path than build a new one, but I couldn't get myself conviced that you are right.

    However, at this point it I feel that it will not be appropriate to continue the discussion as it is since it seems that we begin to walk in circles. Some points I would still like you to clarify, if you could:

    1.  You write "your theory is somehow going against math evidences upon which the simulator has been built". Could you ellaborate?

    2. Andrew forwarded to you a while ago what I think might be a proof to my theory. Could you review it?

    3. I didn't understand your response to my proposed Matlab example.  You wrote "you’ll find identical zero crossing jitter for both waves, which is obviously  wrong for the square wave:   Ideal square wave has a  zero crossing jitter (infinite slew rate)". Since the square wave was created from the sine wave (say, by defining: if the sine wave is >0 then the square wave is =1, otherwise it is =-1), then clearly both waves have similar jitter. What do the infinite slew rate has to do here?

    4. How would YOU simulate jitter, given that you have a square wave and want to run the FM jitter ("sources"). Please relate to the following:

    a. Number of harmonics

    b. Integration limits

    c. Noise folding (aliasing of noise from higher frequencies due to the sampling of the signal edge)

     

    Thanks,

    Yizhak

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