# Two details about phase noise have been confusing me for a long time. Hope to be resolved

1. Just like FLOYD M. GARDNER said in the PhaseLock Techniques, 3rd Edition: "In light of that success in spectrum analyzers, a practitioner’s answer to the question above is: The spectrum of phase noise consists of the data delivered by a phase-noise spectrum analyzer.", the value of zero frequency of phase noise PSD should be infinite in theory. But in reality, what should the value of zero frequency of phase noise PSD showed on phase-noise spectrum analyzer be? In other words, what is the value of zero frequency of phase noise PSD stored in phase-noise spectrum analyzer? If I simulate phase noise PSD in Matlab using discrete data, what the zero frequency value should be or should be set? Hope these two problems can be solved.
2. What is the VCO DC power? What is the relationship between VCO DC power and VCO output phase noise PSD which has a 1/f^2 shape? Hope to be resolved.

The Lorentzian describes that flat-topped behavior. [I initially wrote Lambertian, in error]

Regarding the DC power, cyclo-stationary statistics work in the 1990s validated the classic Leeson Equation.

Today the simulators extend that statistical work into trusted predictors, to be within 1dB; fundamentally, the active device parameters including any distortion (and the spreads of those parameters) must be accurately known. This knowledge must include substrate-path modeling of charge flows; I suspect the non-linear effects of device isolation junctions become part of the cyclo-stationary modeling to describe transient behaviors and the resultant spectral folding.

Note the deterministic energy environment surrounding the active device may be quite large, and even balanced layouts may not overcome energy injection into inductors. varactors, differential-pairs, etc.

Most of this work has been written up in "The Red Rag" of the US's IEEE, the Journal of Solid State Circuits.

Here is a fine paper from Hewlett Packard (Keysight) on Lorentzian: https://www.keysight.com/upload/cmc_upload/All/phase_noise_and_jitter.pdf

This is the first link encountered for "phase noise leeson equation". http://rfic.eecs.berkeley.edu/~niknejad/ee242/pdf/eecs242_lect22_phasenoise.pdf

• All I see is some random facts which do not answer the question at all. – wu yi May 16 '19 at 1:47
• You need to do some reading of the links provided. – analogsystemsrf May 16 '19 at 1:54
• Give me time to read and understand. – wu yi May 17 '19 at 11:46
• I have read the content of links provided and other materials related to them, but all of them don't refer to what I asked earlier. Lorentzian spectrum considers the entity of oscillator process, namely cos(wct+φ(t)) or sin(wct+φ(t)), rather than the φ(t).So the content of links provided can't solve this question. – wu yi May 18 '19 at 6:22
• Both the links discuss the Lorentzian equation. The wide of that spectral line (with the phase noise causing wander of the instantaneous frequency) is described by the equation. If you have "wct+φ(t)", then remove the ideal-constant-phase-rotation of the center frequency, with the residual variation being the φ(t). – analogsystemsrf May 19 '19 at 23:58