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3
Phase Noise Basics
What is Phase Noise?
Frequency stability can be defined as the degree to which an oscillating source
produces the same frequency throughout a specified period of time. Every RF
and microwave source exhibits some amount of frequency instability. This
stability can be broken down into two components:
• long-term stability
• short-term stability
Long-term stability describes the frequency variations that occur over long
time periods, expressed in parts per million per hour, day, month, or year.
Short-term stability contains all elements causing frequency changes about the
nominal frequency of less than a few seconds duration. The chapter deals with
short-term stability.
Mathematically, an ideal sinewave can be described by
Where
But an actual signal is better modeled by
and
This randomly fluctuating phase term could be observed on an ideal RF
analyzer (one which has no sideband noise of its own) as in
page 49.
48
V t ( )
=
V o
sin
2πf o t
V o
= nominal amplitude,
V o
sin
2πf o t
= linearly growing phase component,
f o
and
= nominal frequency
V t ( )
ε t ( )
=
Vo
+
sin
ε t ( )
Where
= amplitude fluctuations,
∆φ t ( )
= randomly fluctuating phase term or phase noise.
∆φ t ( )
2πf o t
+
Figure 14
on
Agilent E5505A User's Guide
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