Phase noise measurements quantify the short term
stability of a frequency source. That is because phase and frequency are mathematically
related by a differential function [ω(t) = dΦ(t)/dt] so they are directly
connected. Phase noise also includes amplitude instability due to atomic scale effects
like shot noise
and flicker noise,
and possibly even voltage supply noise. When that source is used as a local oscillator
in a frequency converter (up or down), the amount of instability (jitter) is modulated
onto the transmitter or received signal. While not usually a major concern in analog
systems, in high speed digital communication systems phase noise can degrade the ability
of the receiver to correctly determine the difference between a "1" and a"0." That is
because the "decision point" at which a circuit declares the waveform to represent a
"1" or "0" can fall at a place where an incorrect decision is made. The drawing below
shows how a digital waveform can be distorted by phase noise during the up or downconversion
and modulation or demodulation process.
Phase noise is typically symmetrical about the primary signal (carrier) of a local
oscillator so frequency and power values normally references a single sideband (SSB)
in a 1 Hz bandwidth.
When the reference oscillator is
used by a phase locked loop (PLL) frequency source that produces an output frequency
higher than that of the reference, the phase noise power levels are multiplied by a factor
of 20*log (f_{out}/f_{ref}),
thereby degrading the final phase noise specifications.
Consider, as an example the
USXTA10MEXSXXB, 10 MHz ovenized crystal oscillator (OCXO)
manufactured by Bliley Technologies, right here in my hometown of Erie, Pennsylvania.
The graph below is where I plotted the advertised phase noise of the OCXO (red) and the
phase noise of a 2 GHz oscillator phase locked to the 10 MHz reference oscillator.
You will see that the phase noise of the 2 GHz oscillator is consistently 46 dB
[20*log(2*10^{9 }/ 10*10^{6})]
higher than the 10 MHz reference, per the above equation. Because of the multiplication
effect, many Sband and high oscillators use a 100 MHz reference oscillator in order
to gain a roughly 20 dB [20*log(10/1)] improvement in phase noise.
Use the following equation to calculate the phase noise of a phaselocked oscillator:
Phase Noise_{PLL}
= Phase Noise_{Ref} + 20*log (f_{PLL}/f_{Ref})
{dBc/Hz}
The following formulas are available in many textbooks and application notes. To be
honest, very few people really use these equations. Their value to most people is for
demonstrating the composition of phase noise.
Note: When using these formulas, be sure to keep dimension
units consistent; i.e., do not mix kHz with MHz, mm with inches, etc. It is safer to
use base units (e.g., Hz, m) for calculation, then convert result to desired units.
, where 
= signal amplitude
= signal frequency
= signal phase
= signal amplitude
variation = signal phase
variation


noise power density


single sideband (SSB) phase noise


SSB phase noise in dB relative to the carrier 
Posted October 9, 2018
