What Allan deviation does a GPS-disciplined oscillator achieve?

A GPS-disciplined oscillator (GPSDO) combines a local oscillator (typically an OCXO) with GPS timing corrections. Short-term stability (tau = 1 s) is determined by the OCXO, typically 1 to 5 times 10^-12. Long-term stability (tau = 10,000 s and beyond) is determined by GPS, reaching 1 to 5 times 10^-13. The crossover point where GPS takes over from the OCXO is typically at tau = 100 to 1,000 seconds, depending on the PLL bandwidth of the disciplining algorithm.

How does Allan deviation relate to phase noise?

They measure the same physical phenomenon (oscillator instability) in different domains. Phase noise is a frequency-domain measurement (dBc/Hz at offset frequencies), while ADEV is a time-domain measurement (fractional frequency stability vs. averaging time). They are related through an integral transform: the ADEV at averaging time tau is approximately equal to the phase noise spectral density integrated over offset frequencies near 1/(2 pi tau). Close-in phase noise (1 Hz to 100 Hz offset) corresponds to long averaging times (seconds), while far-out phase noise (kHz to MHz offset) corresponds to short averaging times (microseconds).

Active Components

Allan Deviation

Q: Why use Allan deviation instead of standard deviation?

Standard deviation diverges for noise processes with 1/f and 1/f-squared spectral density (flicker and random walk FM), which are the dominant noise types in oscillators at averaging times beyond 1 second. Allan deviation uses overlapping two-sample differences that cancel linear frequency drift and converge for all five standard noise types found in oscillators. It also directly indicates the dominant noise type through its slope on a log-log plot: white FM gives a slope of -1/2, flicker FM gives a slope of 0 (flat), and random walk FM gives +1/2.

A 10 MHz OCXO datasheet says "stability: 1 × 10⁻¹² at τ = 1 s." That single number tells you the oscillator's fractional frequency fluctuation averaged over 1-second intervals. Measure it over 100 seconds and you get a different (usually better) number. Over 10,000 seconds, aging and temperature drift start to dominate and the number gets worse. Allan deviation captures this entire story by plotting fractional stability as a function of averaging time, revealing which noise mechanism rules at each timescale and where the oscillator performs best.

Category: Active Components

Symbol: σ_y(τ)

Units: Dimensionless (fractional frequency)

Reading the Slope: What Each Line Tells You

Allan variance (two-sample variance):
σ_y²(τ) = (1/2) · ⟨(ȳ_n+1 − ȳ_n)²⟩
where ȳ_n is the average fractional frequency over the n-th interval of duration τ

Allan deviation: σ_y(τ) = √(σ_y²(τ))

ADEV Slope (log-log)	Noise Type	σ_y(τ) ∝	Physical Origin
−1	White phase noise	τ⁻¹	Broadband noise in buffer amplifiers
−1/2	White frequency noise	τ^−1/2	Thermal noise in oscillator loop
0 (flat)	Flicker frequency noise	τ⁰	1/f noise in active devices
+1/2	Random walk frequency	τ^+1/2	Environmental perturbations
+1	Frequency drift	τ⁺¹	Crystal aging, temperature ramp

Oscillator Technology Comparison

Oscillator Type	ADEV at τ=1s	ADEV at τ=100s	ADEV Floor	Typical Cost
TCXO	1×10⁻⁹	5×10⁻¹⁰	1×10⁻¹⁰	$5 to $30
OCXO	1×10⁻¹²	3×10⁻¹³	1×10⁻¹³	$200 to $2,000
Rubidium	3×10⁻¹¹	5×10⁻¹²	1×10⁻¹²	$1,000 to $5,000
Cesium beam	5×10⁻¹¹	5×10⁻¹²	2×10⁻¹⁴	$30,000+
GPSDO	2×10⁻¹² (OCXO)	5×10⁻¹³	1×10⁻¹³	$500 to $3,000

Common Questions

Frequently Asked Questions

Why use Allan deviation instead of standard deviation?

Standard deviation diverges for flicker and random-walk FM noise, the dominant oscillator noise types beyond 1 second. Allan deviation uses two-sample differences that converge for all five noise types and reveals the dominant mechanism through its slope on a log-log plot (−1/2 for white FM, 0 for flicker FM, +1/2 for random walk).

What ADEV does a GPS-disciplined oscillator achieve?

Short-term (τ=1s) is set by the internal OCXO: ~2×10⁻¹². Long-term (τ=10,000s) is governed by GPS: ~1 to 5×10⁻¹³. The crossover point is at τ=100 to 1,000s depending on the PLL bandwidth.

How does ADEV relate to phase noise?

Both measure oscillator instability in different domains. ADEV at averaging time τ corresponds approximately to phase noise at offset frequency 1/(2πτ). Close-in phase noise (1 to 100 Hz offset) maps to long averaging times; far-out noise (kHz+) maps to short averaging times.

Related Terms

← ALC Loop Allan Variance →

Frequency Standards

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