Please
note that the information on this page is not meant to be a comprehensive treatise on
phase noise. It is more of a general overview of the nature and resultant effects of
phase noise in communication systems based on practical experience with real components.
Many companies that produce oscillators and test equipment have excellent application
note with more specific information on phase noise.
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 FM flicker
noise (1/f^{3}),
white noise (1/f^{2}),
PM flicker noise (1/f),
and possibly even voltage supply noise (typically discrete spurs). When the frequency
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 (see drawing).
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 accompanying drawing 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.
Calculating PLL Phase Noise Based on a Reference Oscillator's Phase Noise
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 a typical 10 MHz ovenized crystal oscillator (OCXO) shown in graph to
the right where I plotted the phase noise of the OCXO in red and the phase noise of a
2 GHz oscillator phase locked to the 10 MHz reference oscillator in blue. 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 higher 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
based on the phase noise of the reference oscillator it is locked to:
Phase Noise_{PLL}
( ) = Phase Noise_{Ref} + 20*log (f_{PLL}/f_{Ref})
{dBc/Hz}
Be aware that the equation is theoretical and that a real world PLL will add some
of its own intrinsic components to the output phase noise.
Differentiating Between Continuous and Discrete Phase Noise
Phase noise is comprised of two basic
types of frequency content: continuous and discrete. The amplitude of continuous phase
noise is dependent upon the bandwidth in which it is measured, whereas the amplitude
of discrete phase noise is independent of the measurement bandwidth. In fact, continuous
phase noise is a spectral density function that is bandwidthdependent. That means on
a spectrum analyzer (SpecAn) display, the level of continuous phase noise will increase
as the Resolution Bandwidth (RBW) setting is increased and will decrease as the Resolution
Bandwidth setting is decreased. Increase the RBW by a factor of 100 and the continuous
phase noise level goes up by 20 dB [10*log(100)].
Decrease the RBW by a factor of 100 and the continuous phase noise level goes down by
20 dB. However, the discrete phase noise power level does not change as the RBW
is changed. That is how to discern between the two types of phase noise. See the diagram
to the right.
Although not an exact method, you can get a good estimate of continuous phase noise
(PN_{cont.}) in a 1 Hz bandwidth by measuring it at a wider RBW and then
subtracting the decibel difference based on the ratio of the measurement RBW (RBW_{meas.})
and the desired 1 Hz bandwidth. Use the following equation.
PN_{cont.} in 1 Hz
BW = PN_{cont.} in RBW_{meas.}  10 * log [RBW_{meas.}
(in Hz)]
Example: If you measure 100.0 dBm at a 10 kHz offset frequency when
using a RBW of 3 kHz, the continuous phase noise in a 1 Hz bandwidth will be
100.0 dBm  10 *log (3000) dB = 134.7 dBm
During my days as an engineer designing RF systems, I often needed to make phase noise
measurements on synthesizers. Back in the early 1990s while working for Comsat I wrote
a program in Visual Basic that automatically tested for mixer product spurs in a large
batch of synthesizers for use in the INMARSAT earth station transceivers. Time was of the essence, but
so was not missing discrete spurs above a prescribed level. If you are familiar with
spectrum analyzers, you know that the sweep time is inversely related to the Resolution
Bandwidth (RBW) setting, so a larger RBW resulted in a smaller sweep time (faster), and
vice versa. The time optimization method I devised started with a wide RBW and checked
across the band for violations. If none were identified, the RBW was decreased by one
notch and the band was swept again. The loop continued until the noise floor was at or
below the maximum permissible discrete spur level. That was the sweep that took the longest
(120 seconds on the HP8568B); however, the time savings came from the fact that if a
violation was detected at a wider RBW setting (shorter sweep time), the frequency and
power was noted and the test was terminated, thereby not performing the longer sweeps.
Textbook Phase Noise Composition Equations
The following formulas are available in many textbooks and manufacturers' application
notes. In reality, very few people really use the equations. Their value to most people
is for demonstrating all the components that contribute to 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 30, 2018
