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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

  •  Andrew, Frank,

    Let me get back to my original claim before I answer your two latest comments. Let's leave the filtration aside for now.

    My claim was that it is enough  to look at the first harmonic's jitter when analyzing a square wave's jitter.

    Using what I just learnt on ponise -> jitter -> pm, I thought of the following experiment: Let us take the "Jee" result of PM jitter simulation as a reference point, with integration at the range [1K, Fc/2] and maxsideband=fullspectrum. Next, let us see if my claim holds, by running a "sources" simulation with maxsideband=1 at the range [1K,300*Fc], then integrate phase noise and extract the phase jitter. If results are close, that would be an indication for the correctness of my claim (I will speak about theory later).

    So, I ran the simulation on the crystal oscillator that I currently design (fullspectrum resulted in 3).

    For the PM option, jitter was 1.9ps for one of the edges and  1.96ps for the other.

    For the "sources" option, jitter was 1.94ps.

    I also tried a third option: "sources",  fullspectrum, integration [1K, Fc/2]. Result was 1.2ps.

    So I think that this is a strong indication to my claim's correctness.

     

    Back to thoery, qouting:

    If maxsideband is 1, you are only including the noise contributions from sidebands +/-1 and 0 (so you will get very high up-converted flicker noise if you sweep near to the carrier frequency). You won't get noise contributions from higher frequencies "folded" by the harmonics of the carrier because you simply are not including them. Sweeping over a wide frequency range is NOT the same as including lots of sidebands - you are sweeping the output frequency yes, but you've removed the simulator's ability to compute all the transfer functions from the noise sources to the output - you've only included three noise transfer functions.

    I definitely agree that folding the high frequency content of the base harmonic noise is not the same as integrating the high frequency content of the high order harmonics, that were folded by the higher harmonics into the frequency range of interest (say [0,Fc/2]). BUT this is done on purpose, assuming that the claim is correct. A nice illustration of this is below, taken from spectreRF user guide.

    So the point is that I believe that (1) only one skirt should be taken and (2) that skirt is folded by the sampling nature of the signal's edges hence its high frequency content should be integrated.

     

     

Reply

  •  Andrew, Frank,

    Let me get back to my original claim before I answer your two latest comments. Let's leave the filtration aside for now.

    My claim was that it is enough  to look at the first harmonic's jitter when analyzing a square wave's jitter.

    Using what I just learnt on ponise -> jitter -> pm, I thought of the following experiment: Let us take the "Jee" result of PM jitter simulation as a reference point, with integration at the range [1K, Fc/2] and maxsideband=fullspectrum. Next, let us see if my claim holds, by running a "sources" simulation with maxsideband=1 at the range [1K,300*Fc], then integrate phase noise and extract the phase jitter. If results are close, that would be an indication for the correctness of my claim (I will speak about theory later).

    So, I ran the simulation on the crystal oscillator that I currently design (fullspectrum resulted in 3).

    For the PM option, jitter was 1.9ps for one of the edges and  1.96ps for the other.

    For the "sources" option, jitter was 1.94ps.

    I also tried a third option: "sources",  fullspectrum, integration [1K, Fc/2]. Result was 1.2ps.

    So I think that this is a strong indication to my claim's correctness.

     

    Back to thoery, qouting:

    If maxsideband is 1, you are only including the noise contributions from sidebands +/-1 and 0 (so you will get very high up-converted flicker noise if you sweep near to the carrier frequency). You won't get noise contributions from higher frequencies "folded" by the harmonics of the carrier because you simply are not including them. Sweeping over a wide frequency range is NOT the same as including lots of sidebands - you are sweeping the output frequency yes, but you've removed the simulator's ability to compute all the transfer functions from the noise sources to the output - you've only included three noise transfer functions.

    I definitely agree that folding the high frequency content of the base harmonic noise is not the same as integrating the high frequency content of the high order harmonics, that were folded by the higher harmonics into the frequency range of interest (say [0,Fc/2]). BUT this is done on purpose, assuming that the claim is correct. A nice illustration of this is below, taken from spectreRF user guide.

    So the point is that I believe that (1) only one skirt should be taken and (2) that skirt is folded by the sampling nature of the signal's edges hence its high frequency content should be integrated.

     

     

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