Frank,

I talk about these topics in my paper and presentation on cyclostationary noise, which can be found in the

*Theory* section of this website. To explore these questions, I like to work with a noisy signal

*v*_{n}(

*t*) that is constructed by starting with a noise-free

*T*-periodic signal

*v*(

*t*) where

*v*_{n}(

*t*) = (1 +

*a*(

*t*))

*v*(

*t* +

*p*(

*t*)

*T*/(2

*pi*))

where

*a* represents the amplitude noise and

*p* represents the phase noise.

**Quote:** Let me explain what I mean: If I have a sinewave signal with pure phase noise, the strobed noise will also have a sinusoidal variation and the maxima of the strobed noise will coincide with the zero crossings of the signal. If I have a sinewave signal with pure amplitude noise, the strobed noise will have a sinusoidal variation also in this case, but the maxima will coincide with the extrema of the signal. A sinewave signal with constant strobed noise can be regarded as having equal amounts of uncorrelated phase noise and amplitude noise as they will add up to a constant value.

This is the case where

*a* or

*p* are stationary. Note that even though the amplitude and phase noise contributions are stationary, the noise in

*v*_{n} is cyclostationary because the noise from

*a* or

*p* is being modulated by

*v*.

**Quote:**What happens now if we have a sinewave signal for which the strobed noise has an arbitrary waveform? Is there any unique way to decompose the noise into amplitude and phase noise? What happens if the signal also has an arbitrary waveform? Will there be a different phase noise value for each harmonic? What would be the combined phase noise of the entire signal in this case?

In this case,

*a* or

*p* become cyclostationary, meaning that the amount of amplitude and phase noise vary along the phase of

*v*. To see this variation you will have to be "observing"

*v*_{n} across multiple harmonics, but this does not imply that the amplitude or phase noise of each harmonic is different. You can see this by taking the Fourier expansion of

*v* before adding in the amplitude and phase noise.

**Quote:** The practical answer to my question is of course the one that is given in section 6 of Ken's paper on phase noise and jitter (

http://www.designers-guide.com/Analysis/PLLnoise+jitter.pdf). Here, the phase noise is defined with respect to a threshold level and is actually nothing else than timing jitter multiplied by the angular frequency of the fundamental. The consequence of this definition is, however, that it is not possible to determine a unique phase noise value for an arbitrary periodic signal. Instead, the phase noise will generally be different depending on the threshold level one chooses.

That particular section of the paper is discussing the phase noise of frequency dividers, which are logic circuits and so inherently have thresholds. And the thresholds play a critical role in the phase noise behavior of the divider. However, as I have shown above, one can define amplitude and phase noise without resorting to use of either thresholds or strobed noise. The same is also true with jitter. Though jitter is normally defined as the variation in the timing of discrete events, one can also talk about jitter simply being a "noise in time" in which case the jitter

*j* =

*p**T*/(2

*pi*).