Phase noise and jitter simulation

Dear Lawrence,

Lawrence Guan said:

he beat frequency is set to be fin/2 so that pss can converge.

Great! This totally consistent with the recommendations for computing an accurate estimate of jitter components of a driven circuit or oscillator that contains dividers at the On-line support URL:

support.cadence.com/.../ArticleAttachmentPortal

2. Use Edge phase Noise in the same form to plot phase noise, and integrate the noise 1M~fin/2, convert it to Rj with respect to 2*pi*fin

Now the problem is that the Jee gives exactly twice the number of method 2. Does this mean that Jee rely on beat frequency to calculate the phase jitter instead of the real frequency?

Perhaps I am not understanding your computation of random jitter when you stated "...and integrate the noise 1M-fin/2, convert it to Rj with respect to 2*pi*fin", but if the output signal used for the edge phase noise Jee is defined as the divider output, whose frequency is fin/2, then you are sampling the noise every 1/(fin/2) seconds - not every 1/fin seconds. Therefore the frequency spectrum ion its Jee is limited to 50% of fin/2 or fin/4. Hence, should your upper limit on the integration frequency be fin/4 and not fin/2? In other words, any frequency components over fin/4 will be aliased. The spectrum of the output of the buffer at frequency fin will extend to fin/2.

Put another way, the random jitter when measured over the same frequency interval and expressed in time units, is invariant to whether the jitter measurement is made on a signal whose frequency is fin or a signal that is fin/2 (assuming the division does not add significant noise). If the measurement is made in units of per unit interval, the jitter measurement using a reference frequency of fin/2 will be 50% of the value of that using a reference frequency of fin as a result of the period difference in the two signals - not the result of a difference in jitter expressed in time units.

Once again Lawrence, I apologize in advance if I am not understanding your computation or your simulation set-up for the two cases (i.e., phase noise of buffer output and phase noise of divider output)!

Shawn

Dear Lawrence,

Lawrence Guan said:

he beat frequency is set to be fin/2 so that pss can converge.

Great! This totally consistent with the recommendations for computing an accurate estimate of jitter components of a driven circuit or oscillator that contains dividers at the On-line support URL:

support.cadence.com/.../ArticleAttachmentPortal

2. Use Edge phase Noise in the same form to plot phase noise, and integrate the noise 1M~fin/2, convert it to Rj with respect to 2*pi*fin

Now the problem is that the Jee gives exactly twice the number of method 2. Does this mean that Jee rely on beat frequency to calculate the phase jitter instead of the real frequency?

Perhaps I am not understanding your computation of random jitter when you stated "...and integrate the noise 1M-fin/2, convert it to Rj with respect to 2*pi*fin", but if the output signal used for the edge phase noise Jee is defined as the divider output, whose frequency is fin/2, then you are sampling the noise every 1/(fin/2) seconds - not every 1/fin seconds. Therefore the frequency spectrum ion its Jee is limited to 50% of fin/2 or fin/4. Hence, should your upper limit on the integration frequency be fin/4 and not fin/2? In other words, any frequency components over fin/4 will be aliased. The spectrum of the output of the buffer at frequency fin will extend to fin/2.

Put another way, the random jitter when measured over the same frequency interval and expressed in time units, is invariant to whether the jitter measurement is made on a signal whose frequency is fin or a signal that is fin/2 (assuming the division does not add significant noise). If the measurement is made in units of per unit interval, the jitter measurement using a reference frequency of fin/2 will be 50% of the value of that using a reference frequency of fin as a result of the period difference in the two signals - not the result of a difference in jitter expressed in time units.

Once again Lawrence, I apologize in advance if I am not understanding your computation or your simulation set-up for the two cases (i.e., phase noise of buffer output and phase noise of divider output)!

Shawn

Hi Shawn,

Thank you in advance for your kind reply, and sorry that I did not state the computation clearly.

What is concerned is the Rj of "1st stage buffer" whose output frequency is still fin. I have put that node in pnoise analysis setting and select the correct output in direct plot form for both method 1 and 2.

The computation for method 2 is like this:  Rj_from_phase_noise = sqrt( integ(10**(phase_noise(f)/10), 1M, fin/2)*2 ) / (2*pi*fin)

Rj_from_phase_noise = 0.5 *Jee, while I expect the two methods should give the same results. I suspect that this is because beat frequency = fin/2 is used in PSS because a divider exists in the total clock path, and Jee result is affected by the beat frequency.

If I use a smaller beat frequency (say fin/6), the Rj_from_phase_noise is still the same, but Jee changes.

Is this as expected by the tool?

Dear Lawrence,

First, thank you for the additional information - it is helpful to me anyway! Unfortunately for me, I am still not clear if you are comparing the random jitter number in units of absolute time or in unit intervals. Clearly if the comparison is made on random jitter and Jee on a unit intervall basis, the two will differ dependent on the frequency ratio (factor of 2 in your case). 

Lawrence Guan said:

If I use a smaller beat frequency (say fin/6), the Rj_from_phase_noise is still the same, but Jee changes.

Is this as expected by the tool?

In any case, the value of Jee provided by Cadence spectre is computed from the edges of the signal defined in your phase noise simulation. Hence, it will be 0.50*fin when your divider is set as the phase noise output and fin when our pnoise output is defined as the buffer output. If you include a sample ratio in the analysis, see URL:

https://support.cadence.com/apex/ArticleAttachmentPortal?id=a1O0V000009ETPrUAO&pageName=ArticleContent&oMenu=People%20who%20viewed%20this%20also%20viewed

that will also impact the result.

I am not convinced I've answered your question, but maybe I am closer?

Shawn

Hi Shawn,

I compare the random jitter in the unit of "second".

I then simulated the buffer alone with different beat frequency for PSS, but keep the input clock frequency the same. The noise plot is different with different beat frequencies fbeat=fin, fin/2, fin/3. This result is weird. Shouldn't the phase noise be independent from the beat frequency?

Below is a snapshot of the PNOISE setting:

Phase noise is always calculated with respect to the PSS "beat frequency". The same amount of jitter corresponds to half the phase deviation (or 6 dB less phase noise) if you reference it to half the frequency (= twice the period length). 

Dear Frank,

Frank Wiedmann said:

The same amount of jitter corresponds to half the phase deviation (or 6 dB less phase noise) if you reference it to half the frequency (= twice the period length).

Thank you for emphasizing this to :Lawrence! I mentioned it to him two posts back, but apparently he overlooked it or my comment was not sufficiently clear.

Shawn

Frank and Shawn,

I read the manual about pnoise settings and put the number into sample ratio. So for buffer, the sample ratio is 2 (fin/fbeat). For divider, the sample ratio is 1 (fin/fbeat). This is giving consistent results from both phase noise and Jee. Thank you very much.

Dear Lawrence,

Lawrence Guan said:

I read the manual about pnoise settings and put the number into sample ratio. So for buffer, the sample ratio is 2 (fin/fbeat). For divider, the sample ratio is 1 (fin/fbeat). This is giving consistent results from both phase noise and Jee. Thank you very much.

Excellent!  I am glad you had some time to review the information in the manual. I find for many of the more complex simulations, perusing the documentation can be very helpful in bot understanding the nature of the simulation, the background, and interpreting the results.

Thank you for letting us know!

Shawn