Phase Noise, Harmonics and Sub-Harmonics

Phase noise may seem a bit mysterious to the uninitiated but any engineer
familiar with "ordinary" noise and "ordinary" power spectral density can be
brought up to speed rather quickly. The output of an oscillator may be
represented by a phasor diagram.

The signal is represented by a vector with a length proportional to the
signal amplitude rotating about the origin at the oscillator's frequency. At the
tip of this vector is a little, randomly directed vector which represents the
oscillator's noise. This noise vector may be represented by two orthogonal
vectors, one pointing in the direction of the signal vector and one pointing in
the direction of the rotation. The amplitude vector is the familiar amplitude
noise and the other vector is the phase noise vector. Obviously when the
amplitude vector changes, the oscillator's overall amplitude changes and when
the phase noise vector changes, the oscillator's phase changes. Although it is
intuitive to compare amplitude jitter to the overall amplitude, it may seem
arbitrary to compare the phase jitter in radians to the amplitude of the carrier
- the two quantities seem unrelated. The confusion rests at the feet of the
small angle assumption which states that the sine of a small angle is equal to
the angle. When phase noise is measured, it is small variations in the phase
angle that are measured and then the length of the phase noise vector is
inferred. The small angle assumption states that the length of the phase noise
vector is equal to the measured angle multiplied by the signal size. Or stated
differently, the measured angle is the phase noise vector divided by the signal
size. (For reasonably good oscillators the noise angle is quite small.) Notice
that if the little noise vector is independent from the oscillator level
(additive noise) then a larger oscillator level will give lower phase noise just
as the AM signal to noise level would improve. If the phase variations are a
modulation of the phase then the little vector will grow with the signal vector
keeping the angle constant just as an AM modulated noise sideband will grow with
the carrier size.

When observed on a spectrum analyzer, amplitude and phase noise will appear
as sideband noise on both sides of the carrier. Often, phase noise
specifications refer to single-sideband noise denoted by a script L (see chart
below). Most phase noise measurement schemes fold both sidebands together the
way that a simple AM detector combines both AM sidebands and, consequently, the
measured noise will be about 3 dB higher than the single-sideband noise
depending on the degree of coherency of the sidebands. (Script L(f) has been
recently redefined as equal to one half the sum of both sidebands thus avoiding
the whole issue of the coherency of the two sidebands.)

Measuring the noise angle or, more precisely, the spectral density of the
noise angle is conceptually simple. The oscillator to be measured is
phase-locked to a reference oscillator using a long time-constant (slow loop
response). Variations in the phase of the oscillator under test will cause
variations in the voltage at the output of the mixer. A conversion factor may be
determined for the mixer/ phase detector by observing the slope of the beat-note
at zero volts when the oscillators are not locked (as X volts per radian). The
spectral density of the noise voltage is then measured (with the oscillators
locked together) using ordinary techniques including FFT analyzers or Wave
analyzers. Several complications will arise, especially when measuring
oscillators exhibiting noise as good as the reference noise. Many publications
are available detailing the pitfalls of phase noise measurements including
several from NIST.

The harmonic content in the output of an oscillator is usually of little
importance and levels better than 30dB below the fundamental are readily
achieved. Much higher attenuation of harmonics may be achieved when a particular
harmonic falls on a critical frequency as in a sensitive receiver but care must
be taken to avoid the re-generation of the undesired harmonic when the
oscillator signal is processed by the designer's circuitry.

Sub-harmonics are present at some level when the output of the oscillator is
multiplied from a lower frequency crystal oscillator. The term sub-harmonic
should be clearly defined in the specification since a final output frequency
may be achieved with different crystal frequencies and multiplication factors.

Wenzel Associates manufacturers extremely low phase noise oscillators as
confirmed by NIST calibration reports which are available for viewing with the
Adobe Acrobat viewer for 5 MHz oscillators and
100MHz
oscillators.

Also see:

Low Phase Noise Systems -
Hints and Tips

Vibration-Induced
Phase Noise

Our
In-house Measurement Systems

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