# Link between phase noise and linewidth for a oscillator?

I was googling for a formula to transform the dbc/Hz value given in data sheets for VNA, spectrum analyzers and VCO is often given in dBc/Hz with offset. Now looking up research papers about future oscillator devices based on new nanophysical effects, the physical oscillator is often measured with a spectrum analyzer and the linewidth (f/delta_f) is given)

Is there any calculable link between both measures to see how well such devices compare to state of the art oscillators? Only very seldom a dBc/Hz value is given in research papers, as the measure makes less sense without a given standard carrier frequency and offset. The linewidth is more a physical than a technical measure and makes different published devices better to compare. Is this reasoning correct or is it also that to define the dBc/Hz measure you need a very accurate spectrum analyzer while the linewidth can be deduced basically from a plotted graph?

Is there a way to transform the dBc/Hz of a standard VNA @ 100 MHz being around 110-120 to a linewidth. I need a value here or order of magnitude. I also read here, the dbc/Hz of a function/waveform generator is often better than that of a spectrum analyzer, so determining it this way is also no option?

The line width is not 100% cleanly defined, as far as I know. What is common that you call it the "width" of the spectral main peak of an oscillator. "Width" needs to be defined, either in terms of "x % of the energy are within that bandwidth" or "outside of the bandwidth, the PSD is x dB below main peak".

In the first case, it becomes very easy: You just integrate the PSD of your oscillator, as given in dBc/Hz values.

An often good assumption is that the phase noise itself is white, so that the PSD of the oscillator generally has 1/f² behaviour; use that to fit a curve through the points given in the datasheet. Then integrate until you get e.g. 99.9% of the total energy of the noise.

In the second definiton, you'd simply plot your PSD and find the point where it cuts -80 dB (or whatever) of its main peak.

Notice that neither 99.9% nor -80 dB are something standardized. Whoever is supplying you with linewidth info hopefully defines what they mean.

• Oscillators are often locked to XTAL references. I've read of the XTALs having 1/F^3 behaviors, perhaps due to flaws in the quartz or in the active-amplifier element. Check out the work of Wenzel Associates, for their XTAL osc phasenoise curves. Jan 6, 2019 at 23:17
• hm, 1/f³ would be even better than 1/f²! I'm from a wireless comms background, and old-school receiver phase recovery PLLs were (white) noisy, so I knew the 1/f² for white phase noise sources. 1/f³ would be explainable by... hm. good question. Maybe I should read. Jan 6, 2019 at 23:20
• Thank you very much! But in the case I have no data points and want to compare oscillators from different research papers given in dbc/Hz and linewidth there is no way? The spectral density you can probably estimate from the area in the power vs. frequency graph in a paper, but for data sheets of VCO or VNA I only have the dbc/Hz value. So you would have to construct a formula with 1/f² and dBc/Hz to calculate the PSD from this and compare to linewidth based PSD in a paper? Jan 7, 2019 at 17:18