Hello and welcome to the inaugural article for a new blog series, Timing 201. My previous blog series, Timing 101, ran for 12 articles over a period of roughly a year and a half.
As the name suggests, I intend to discuss timing topics with a little bit more breadth and depth than might be considered “Timing 101” material. However, that does not mean I won’t cover introductory material, if and when it’s called for, especially if readers ask for it.
When More is Less
You may recall that clock buffers are typically specified in terms of additive jitter. That is because they do not have an intrinsic phase noise source such as an XO (crystal oscillator) or a PLL’s VCXO. They consist of only amplifiers and perhaps dividers. So we would generally expect an XO followed by a clock buffer to have at least somewhat increased phase noise or jitter compared to the XO alone.
All things being equal, this will be the case, except when the amplifier has sufficiently high gain to act as a limiting amplifier or LA. In these situations, the apparent measured source + LA phase noise may actually decrease. I ran in to this phenomena years ago evaluating various clock + buffer combinations. The results weren’t always making sense and it turned out at the time that some of the noise I was measuring was in fact, not really phase noise, hence the title of this case.
To see how this might happen, let’s touch on what is meant here by apparent measured phase noise.
You may recall I discussed modulation spurs previously in Timing 101 #7: The Case of the Spurious Phase Noise Part II. In that article, I considered carriers with relatively small amounts of AM (Amplitude Modulation) and narrowband FM (Frequency Modulation) or equivalent PM (Phase Modulation). The general ideas comparing AM and FM/PM spurs also apply to AM and FM/PM noise.
One topic I did not touch on at that time was the phasor or phase vector representations of AM and NB FM as shown below. The carrier vector is shown as a thick red arrow and the modulation LSB (lower sideband) and USB (upper sideband) vector components are shown as thinner blue arrows. The vector sum or resultant of the modulation is the thick blue arrow. The modulating frequency is f<subscript>M and the rotating arrows indicate the change in the modulation vectors over time versus the carrier. For the figures below the overall vector sum is the geometric addition of the carrier + modulation resultant.
What’s useful about the phasor representation is that it indicates that random noise modulating the carrier can be regarded as consisting of both AM and PM components. That is, components of the noise contributing to carrier magnitude changes are the AM components. Likewise, components of the noise contributing to carrier angle changes are FM or equivalent PM components.
You may see authors emphasizing this distinction by using script L(f) or ℒ(f) to refer to PM noise or “real” phase noise and script M(f) or ℳ(f) to refer to AM noise. The first paper I know of using this notation is:
Spectral Density Analysis: Frequency Domain Specification and Measurement of Signal Stability, by Donald Halford, John H. Shoaf, and A. S. Risley, National Bureau of Standards, Boulder, CO, published in 27th Annual Symposium on Frequency Control, 12-14 June 1973, https://tf.nist.gov/general/pdf/1558.pdf
The magnitude of noise that is AM + PM will be the RSS or Root Sum Square of the individual modulation contributions. Instruments that treat these noise components the same will then “see” this RSS noise directly as phase noise. This is what is meant by apparent phase noise and it is a particular issue for Spectrum Analyzers as discussed below.
The Spectrum Analyzer in Brief
As I noted in Timing 101 #7, Spectrum Analyzers do not preserve phase information and so a low modulation AM spur appears similar to a narrow band low modulation FM spur.
Below is a block diagram for a classic swept spectrum analyzer which suggests why. It is essentially a calibrated frequency selective peak responding voltmeter. The difference in phase between the DUT (Device Under Test) and the LO (Local Oscillator) inputs at the mixer is arbitrary. The Spectrum Analyzer doesn’t “know” anything about their relative phases and AM and PM cannot be distinguished.
The Phase Noise Analyzer in Brief
By contrast, the Phase Noise Analyzer is much less susceptible to AM. The simplified block diagram below gives the basic idea behind the method typically used by Phase Noise Analyzers and Signal Source Analyzers. The mixer is usually a double-balanced mixer to suppress even-order mixing products.
Note that, unlike the Spectrum Analyzer, there is a PLL (Phase Lock Loop) that enforces a specific phase relationship between the DUT and the Reference. Further, it can be shown that AM and PM can be distinguished as follows.
As designed, the Phase Noise Analyzer will be superior to the spectrum analyzer for rejecting AM.
Take It to the Limit
So how exactly does the limiting amplifier or LA help us here? The clue lies in the behavior of the LA: It removes, or at least minimizes, amplitude variation from the clock signal. Therefore, if a source has both AM and PM noise components, then an ideal limiter will remove the AM component noise leaving only the PM noise (the genuine phase noise) behind. The exaggerated sketch below gives the basic idea.
Now getting back to the original work which prompted this post:
If a clock source had apparent phase noise that included both AM and PM noise contributions, then following it with a high gain clock buffer or LA would strip away the AM resulting in less than expected measured phase noise. Rather than yielding additive jitter the new component apparently yielded “subtractive” jitter. Thus the case of the phase noise that wasn’t.
When should AM be considered when making phase noise measurements?
The short answer is that AM is always a potential consideration when one is making careful jitter and phase noise measurements. Having a limiter on one’s lab bench is as important as a balun.
However, there are specific instances where AM can be more of an issue than others.
1. Measuring phase noise using a spectrum analyzer or any other instrument that does not sufficiently reject AM.
A limiter can be valuable even when working with a Phase Noise Analyzer by suppressing AM beyond the rejection capability of the mixer. This may be necessary when measuring very low phase noise sources.
2. Measuring low frequency low phase noise sources.
You may recall the 20log(N) rule, i.e. if the carrier frequency of a clock is divided down by a factor of N then we expect the phase noise to decrease by 20log(N); however, this rule only applies to phase noise. If there is significant AM noise also then this component will loom larger, as we decrease the carrier frequency, and potentially impact measurements.
3. Measuring a source known or suspected to have AM noise.
Clock sources with high common mode noise fall in to this category. For example, we specifically inject power supply ripple when testing oscillator power supply rejection. This is why you see a limiting amplifier shown in Figure 5. PSRR Setup in AN491: Power Supply Rejection For Low-Jitter Clocks. See the highlighted block in the diagram below which comes from that app note.
Finally, the ability to distinguish between phase noise and spurs, and AM noise and spurs, can be very helpful when troubleshooting a system and determining the root cause of performance issues. Additional testing may also be needed to determine how sensitive the ultimate receiver is to clock impairments that include AM noise.
I hope you have enjoyed this Timing 201 article. In the next article, I will give some measurement examples and offer a few rules of thumb.
As always, if you have topic suggestions for this blog or timing-related questions, please send them to firstname.lastname@example.org with “Timing 201” in the subject line. I will give them consideration and see if I can fit them in. Thanks for reading. Keep calm and clock on.