# Phase noise in spectrum analyzers

I'm reading about spectrum analyzers from Keysight's AN 150 and I have two questions regarding phase noise.

The AN states:

No oscillator is perfectly stable. Even though we may not be able to see the actual frequency jitter of a spectrum analyzer LO system, there is still a manifestation of the LO frequency or phase instability that can be observed. This is known as phase noise (sometimes called sideband noise).

Another paragraph that confuses me is this one:

If we reduce the resolution bandwidth by a factor of 10, the level of the displayed phase noise decreases by 10 dB.

My two questions are:

• Why is it that lack of accuracy in LO system leads to the skirt we see on the display when looking at phase noise? I would expect that, if the frequency of the LO shows some error, then the peak in amplitude on the display should by displaced by that error. Why is it that the peak is on the correct place and those weird skirts are produced? I'm not being able to intuitively understand how the display recieves that shape due to LO unstability.
• I think that if the IF filter is wide enough, then the phase noise would be hidden under the skirt of the filter itself, thus the phase noise wouldn't be easy to appreciate. If the IF filter is narrow, the phase noise shows up. Thus, I believe that reducing the RBW increases phase noise. So why does the AN state that reducing the RB decreases the level of phase noise?
• Read around the net for a primer on Phase Noise to get a better appreciation of where it comes from and what it looks like. It's not a fixed frequency offset, it's an ever-present variation in the frequency, or phase, of any oscillator. Jul 23, 2018 at 4:15

For your first question, it's necessary to distinguish between long-term and short-term frequency jitter. If the frequency is off by a fixed amount, and this offset changes slowly, then the peak in amplitude on the display will be displaced in frequency by that amount. If on the other hand the frequency changes back and forth extremely fast (short-term frequency jitter), this is similar to FM modulation, and shows up as phase noise. This short-term frequency jitter (as opposed to long-term frequency error) creates the noise "skirt" referred to in the application note.

For your second question, there is usually a given amount of phase noise for a given bandwidth: phase noise is expressed in units of dBc per Hz of bandwidth (dBc/Hz) at a given offset. This amount is not fixed, but varies depending on how away from the carrier you measure the noise. Nonetheless, as the bandwidth of measurement increases, the total noise within that bandwidth also increases. Thus if you set the RBW filter wider, then it is integrating and averaging noise over a wider bandwidth. If you set the RBW filter narrower, then it only picks up the noise over that narrower bandwidth.

• Thanks for your answer. I got the first part. But the second one I still don't get it. Why would the phase noise increase with increasing RBW? It's not like white noise that has "components" in all frequencies. So I even find the unit of dBc/Hz confusing for this magnitude. Could you provide a more intuitive explanation about this? Jul 23, 2018 at 15:58
• The units are dBc/Hz because the phase noise (and other sources of noise in general) aren't confined to a single frequency (if they were, they'd show up as a single pair of Dirac delta functions in the frequency domain). Phase noise is not necessarily like white noise in that in doesn't have components in all frequencies, but it does have components over a broad bandwidth, not just at a single frequency. (i.e. phase noise isn't so regular that it is directly equivalent to a perfect FM signal consisting of two Dirac deltas, but instead the frequency jitter is fairly random).
– JDW
Jul 23, 2018 at 16:30

Tendero

Lets talk about (2) first. Yes. A wide resolution-bandwidth filter would hide the phasenoise skirts, because the shape-factor of RB filter is explored by the energy in the central lobe of the oscillator. Good insight you have, not to overly trust your measuring equipment.

Now for (1). There are (at least) 2 situations to analyze, OpenLoop and ClosedLoop.

With OpenLoop, temperature changes and power-supply noise and changes in active-device operating-point will cause the carrier frequency to vary slightly. The last effect --- change in operating-point --- is exploited in the 1-transistor FM transmitter circuits, where a microphone signal is applied to the base of Colpitts. Even without intentional variation, the top of the carrier will wander, in a shape labeled "Lorentzian". This was proved about 30 years ago.

With ClosedLoop, especially with high-PLL loopgain, the carrier will appear to not wander, but under high (delta_frequency) resolution the carrier will be shown to wander in the Lorentzian of the Crystal Oscillator frequency reference.

You specifically ask about skirts. The skirts display several slopes (db per octave, or db per decade). The innermost (steepest) should be the shape of the phasenoise of the Frequency reference, if you have a LOW NOISE phase detector and LOWNOISE charge pump and LOW JITTER prescaler and LOW JITTER fracN pot of logic.

Outside the PLL loop bandwidth, the OpAmp noise floor will rear its head, as will Oscillator phase noise.

• Thanks for your answer. Regarding the 2nd question, I don't understand why in the AN it is stated that reducing the RBW reduces the phase noise. I thought exactly the contrary happened. Can you explain this too? Jul 23, 2018 at 15:18
• Given flat noise density as a first approximation, over small delta frequency, a 4:1 smaller bandwidth filter will have 4:1 less power (statistical variance) and 2:1 less standard-deviation (which is the RMS voltage). For 100:1 less bandwidth, the standard-deviation drops 10:1. Jul 24, 2018 at 5:02