When running SpectreRF's PNoise analysis within Artist, the environment provides a "Phase Noise" button as part of its direct-plot capability. The label on this button is misleading, which has caused a substantial amount of user confusion.

It is important to know that when you press this button you are actually plotting the normalized voltage noise, or L, and not the phase noise (this is why the result has units of dBc). This function was added when we added support for oscillators. Oscillator designers use L as a way of characterizing the phase noise of their oscillators. This works because for oscillators the phase noise dominates, especially close to the carrier, and so they need not distinguish between phase noise and voltage noise. Furthermore, in oscillators the values of L and S_phi (the phase noise) are actually the same in most cases, which adds to the confusion.

However, problems arise when engineers who are not designing oscillators use the phase noise direct plot function thinking that this function is decomposing the total noise into amplitude and phase noise components and plotting only the phase noise. It is not doing that. Rather it is plotting L = S_v(df)/V₁², where S_v is the power spectral density of the voltage at an offset frequency of df and V₁ is the amplitude of the fundamental. Thus, it is plotting the noise power normalized to the power of the fundamental.

Whoops! I spoke too hastily.

Your right, L is S_v(df) divided by the power of the fundamental, and so L = S_v(df)/(2V₁²)
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With L and S_phi, we can both claim to be right. L = S_phi when using double-sided (complex exponential) Fourier representation, and L = S_phi/2 when using a single-sided (trigonometric) Fourier representation.

Good eye, and thanks for keeping me honest.

-Ken

No, I am not convinced I have it right yet either. Let me look into this and get back to you.

Ken,
I found a fairly concise explanation of Sphi and L in Egan's book:

William F. Egan, "Phase-Lock Basics", John Wiley & Sons, Inc.  1998. ISBN 0-471-24261-6,   pages 304-310.

Egan gives a simple example showing that L = Sphi/2  where  L is a single-sided, single-sideband, passband PSD shifted down to baseband and Sphi is a single-sided baseband PSD.

However, as I read Demir's May 2000 Circuits and Systems paper ( at least the part I can follow),

L(fm) ~ 10log10(a*(fc/fm)^2), which differs from your expression by 3dB but perhaps you define L differently.

Now all I need to do is figure out why my code still produces a 3dB error but that is something I must deal with myself.

Ken,
I believe I discovered why the phase domain model seemed to give 3dB less phase noise. I believe the Analog Artist's waveform calculator's PSD function is 3dB off. I checked a simple sinusoid as well as a filtered noise signal. In both cases, the variance of the signal as computed from the time domain waveform was twice the area under the PSD function.

That makes my voltage domain model 3dB high but I think that is probably just uncertainty in eye-ballling the value because the PSD was fairly jagged.

On the simple test case of white noise filtered by an RC circuit, I compared results using a Hanning window and a rectangular window. The two PSD's were nearly identical and both were 3dB in error. Should the factor of 1.5 also apply to the rectangular window?

The factor of 1.5 compensates for the equivlant noise bandwidth of the bins, which is dependent on the window function. So for a rectantular window, the factor would not be 1.5, but I don't believe it will be 1 either. I am currently unable to find my copy of Harris, nor can I find it on the web, so I cannot tell you what it should be though.  

You can look the number up yourself by finding a copy of  
F. Harris. On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE, vol. 66, no. 1, January 1978.

Eugene,
   There were several places in my phase noise and jitter papers where I was not careful in distinguishing single-sided and double-sided transforms. As a result, there were several factor-of-two errors. I believe I have identified and corrected all of them in the latest versions of the papers, which I uploaded today. Please let me know if you see any further issues.

Thanks,
-Ken