Stability Measures for Frequency Sources - Understanding GPS: Principles and Applications - page 665

APPENDIX B
Stability Measures for Frequency Sources

Lawrence F. Wiederholt
The MITRE Corporation

B.1 Introduction

The principle of employing satellite navigation systems for position and time deter-
mination requires the satellite clocks to be in synchronism to a common timebase.
High-accuracy AFS are required to meet the stringent stability and drift rate
requirements so that the common time base can be maintained. Stability is also
important for the less accurate crystal-based oscillators that are typically employed
in user equipment.
Frequency sources are subject to systemic errors, such as frequency offsets, aging,
and random frequency errors. Random frequency errors are a primary concern, espe-
cially when characterizing the performance of an AFS. There are a number of impor-
tant random frequency noise processes (i.e., frequency fluctuations): random walk
frequency modulation, flicker frequency modulation, white frequency modulation,
flicker phase modulation, and white phase modulation, as described in [1].

B.2 Frequency Standard Stability

The stability of a frequency source can be described by starting with an oscillator
whose output voltage V ( t ), is given by:

( )

( ) ( )

() () ()

Vt = V + ε t sin 2 πν t + φ t (B.1)

0 0

where V 0 and ν 0 are the nominal amplitude and frequency, respectively, with corre-

sponding errors ( t ).

The instantaneous phase is defined by

ε ( t ) and ϕ

() ()

Φ t = 2 πν t + φ t (B.2)

0

and the instantaneous frequency is defined by

()

dt
dt

φ

1
2

()

ν t =+

0

ν (B.3)

π

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