Designer’s Guide Community

Ken Kundert

Global Moderator

Offline

Posts: 2386
Silicon Valley

Re: Positive values of phase noise in dBc/Hz??
Reply #30 - Jul 06^th, 2005, 9:41pm

There are several noise metrics that are often confused. They are:
S_phi - The power spectral density of the phase noise with units of rad²/Hz
S_v - The power spectral density of the voltage noise with units of v²/Hz
L - The power spectral density of the voltage noise normalized to the power in the carrier with units of dBc/Hz

As f -> 0, S_v and L are bounded but S_phi goes to infinity.

Three things add to this confusion:
1. When you request the "phase noise" from Artist, it actually gives you L, which is technically is not phase noise.
2. When computed with SpectreRF, S_v and L are unbounded as f -> 0 as a direct result that the noise analysis is a small signal analysis, as discussed starting at (9) in www.designers-guide.org/Analysis/rf-sim.pdf.
3. S_phi and L are often confused because they can have the same value (S_phi = L when using the double sided transform and S_phi = 2L when using the single sided transform, as can be seen from (27) of www.designers-guide.org/Analysis/PLLnoise+jitter.pdf).

Finally, it is possible to separate S_v (L) into its AM and PM component pieces. These would have units of v²/Hz (dBc/Hz) and could be plotted on the same graph.

-Ken

Back to top

IP Logged

chlai

Junior Member

Offline

Save the earth~

Posts: 13
Taipei, Taiwan

Re: Positive values of phase noise in dBc/Hz??
Reply #31 - Jul 11^th, 2005, 8:26pm

Hello Ken,
Thanks very much for your answer, which is quite enlightening me.

Indeed, not only the S_v and S_phi noise are confusing, but also AM and PM noise are.

In the limiter cycle, we have:
Quote:

Delta y(t) = �(1 + a(t))y(t + phi(t)/2*pi*fc) - y(t)

Can I determine a(t) means all the AM noise, and (phi(t)/2*pi*fc) means all the PM noise? And are these two noise observable at SpectreRF simulation result as AM and PM noise?
Besides, due to S_v includes AM and PM noise, and S_phi is only for PM noise. Does that mean a(t) belongs only to S_v noise, and (phi(t)/2*pi*fc) belongs to S_v and S_phi noise?

I am very appreciated for your answers, those help me a lot.
with Best regards,
Daniel lai

Back to top

« Last Edit: Jul 11^th, 2005, 10:54pm by chlai »

IP Logged

Ken Kundert Global Moderator Offline Posts: 2386 Silicon Valley	Re: Positive values of phase noise in dBc/Hz?? Reply #32 - Jul 12^th, 2005, 8:32am Daniel, I believe you've got it. -Ken
Back to top	IP Logged

chlai

Junior Member

Offline

Save the earth~

Posts: 13
Taipei, Taiwan

Re: Positive values of phase noise in dBc/Hz??
Reply #33 - Jul 14^th, 2005, 7:37pm

dear Ken,

Because S_V including AM and PM noise, the PM noise should equals to phi(t)/2*pi*fc in:
Quote:

Delta y(t) = (1 + a(t))y(t + phi(t)/2*pi*fc) - y(t)

At the question of my last post, the PM noise (phi(t)/2*pi*fc) contribued not only in S_V but S_phi. However, does PM noise contribute the same noise in S_V and S_phi? If yes, we may use small signal approximation to calculate all the PM noise to voltage noise to generate S_V. If no, maybe we need to know which parts in PM noise contributed in S_V.

Thanks you for answering my questions with great patience.
Best regards,
Daniel

Back to top

IP Logged

Ken Kundert

Global Moderator

Offline

Posts: 2386
Silicon Valley

Re: Positive values of phase noise in dBc/Hz??
Reply #34 - Jul 17^th, 2005, 8:43am

Remember that the phase and voltage are related in a nonlinear way (because y is a nonlinear function). So S_phi and the PM component of S_V are not the same. However, in oscillators at high offset frequencies the phase noise is small and so through a small-signal assumption there is a linear relationship between them. The relationship depends on which form of the transform you use:
For single-sided transform (assuming large f_m):
S_phi = L
For double-sided transform (assuming large f_m):
S_phi = 2L
where in this case the AM component of S_V is assumed negligible and L is S_V normalilzed to the total power in the fundamental component.

-Ken

Back to top

IP Logged

chlai

Junior Member

Offline

Save the earth~

Posts: 13
Taipei, Taiwan

Re: Positive values of phase noise in dBc/Hz??
Reply #35 - Jul 18^th, 2005, 7:38pm

Hi Ken,
Thanks very much for your response, that really helps me a lot.

Assumed that thermal noise generates AM and PM noise in a VCO system as a(t) and phi(t):
Quote:

V(t) = (1 + a(t)) * cos(2*pi*fc*t + phi(t))
=(1 + a(t)) * [cos(2*pi*fc*t) * cos(phi(t)) - sin(2*pi*fc*t) * sin(phi(t))]
If sin(phi(t)) is very small (much smaller than 1),
then V(t) ~ (1 + a(t)) * [phi(t) * sin(2*pi*fc*t)]

To be more clear, phi(t) should be at one specified large offset frequency fm, which is phi(t) * cos (2*pi*f_mt). Besides, all PM noise phi(t) transfer to voltage (power) domain and value is:
Quote:

|V(t)| = |1+a(t)| * |phi(t)|

However, if all PM noise use this way transfering to power domain noise S_V, S_phi and the PM component of S_V should be the same. Actually, if I assume there are three kinds of noise in nature: AM+PM noise, pure PM noise, and pure AM noise. AM+PM noise (for example: thermal noise) should contribute same PM noise in S_phi and S_V. In S_V, PM noise transfer to power domain using above formula. On the other hand, if we have a pure PM noise, it couldn't generate power and transfered its PM noise to power domain.

My opinion is all PM noise (not only AM+PM noise but PM noise) contribute to S_phi, and only PM components of AM+PM noise contributes to S_V, pure PM noise couldn't. So S_phi and the PM component of S_V are not the same. Is this correct?

Sincerely yours,
Daniel

Back to top

IP Logged

Ken Kundert Global Moderator Offline Posts: 2386 Silicon Valley	Re: Positive values of phase noise in dBc/Hz?? Reply #36 - Jul 18^th, 2005, 9:38pm I'm afraid I do not understand your question. Nor do I understand why or how you have broken noise into three components, AM, PM, and AM+PM. -Ken
Back to top	IP Logged

chlai

Junior Member

Offline

Save the earth~

Posts: 13
Taipei, Taiwan

Re: Positive values of phase noise in dBc/Hz??
Reply #37 - Jul 18^th, 2005, 10:54pm

dear Ken,
Sorry to confuse you.

Noise in nature are from several reasons: (Information from noise book)
Thermal noise: Due to random thermal fluctuation
Shot noise: Due to the discrete nature of charge flow
Flicker noise: Due to random capture and release of charge
Because the noise are generated from different reasons, they also have different properties, such as AM+PM noise or pure PM noise only.

In MOSFET, the flicker noise is generated from the capturing and releasing charge at discrete interface between SiO₂ and Si. My opinion is the charge captured and released behavior should be periodic without generating new noise power. (The period of this behavior depends on the charging and releasing frequency.) So, I would regard flicker noise as a pure PM noise, and this PM noise would not transfer to power domain noise, which makes S_V.

My question is S_phi are not the same with the PM components of S_V, but we don't distinguish the noise properties to which PM noise part would transfer to S_V. I assumed that noise should be seperated into several group as AM+PM noise, and pure PM noise. (and even more the pure AM noise) If the noise is AM+PM noise, such as thermal noise, could transfer all its PM part to S_V; on the contrary, pure PM noise, such as flicker noise, could not transfer any PM noise to S_V.

with best regards,
Daniel

Back to top

IP Logged

Ken Kundert

Global Moderator

Offline

Posts: 2386
Silicon Valley

Re: Positive values of phase noise in dBc/Hz??
Reply #38 - Jul 19^th, 2005, 12:09am

Whether noise is a PM or AM noise is not a property of the noise source, it is a property of the circuit. Thermal noise produces PM noise when present in an oscillator, and additive noise (what you call AM+PM noise) when produced by a resistor in a linear circuit. And if thermal noise were present on the control line of a variable gain amplifier, it would produce AM noise at the output of the VGA.

The M in both AM and PM stands for modulation, which implies that there must be a carrier signal present that is being modulated by the noise. Without the carrier, there can be no AM or PM noise.

-Ken

Back to top

IP Logged

chlai

Junior Member

Offline

Save the earth~

Posts: 13
Taipei, Taiwan

Re: Positive values of phase noise in dBc/Hz??
Reply #39 - Jul 19^th, 2005, 12:58am

dear Ken,

Thank you very much for the correction and fast reply.

You are right, the noise property would be specified as AM or PM when it applied on a circuit. So, I should modify my last question to the situation in a VCO (or an oscillator).

Some kinds of noise exist and have different properties in VCO. Thermal noise and flicker noise exist together with different effects to the phase noise. As Ken's last post (or in cyclo-paper.pdf), thermal noise generates PM noise and suppress AM noise in VCO. However, this PM noise should transfer to power noise at S_V. (observable with a conventional Spectrum Analyzer.) Is that right?
Question in last post is: PM parts of S_V is different (and less than) to S_phi, the total PM noise. Can we determine which part of PM noise would contribute to S_V?

Sorry to ask so many basic questions, but these questions are really difficult to me, and I couldn't find them in all the papers. (rf-sim.pdf, cyclo-paper.pdf, PLLnoise+jitter.pdf) Your paper and post are quite useful to me to go ahead to understand the VCO noise.

Sincerely yours,
Daniel

Back to top

IP Logged