Modified Allan variance
Encyclopedia
The modified Allan variance (MAVAR) , also known as mod σy2(τ), is a variable bandwidth modified variant of Allan variance
, a measurement of frequency stability in clock
s, oscillators and amplifier
s. Its main advantage relative to Allan variance is its ability to separate white phase noise
from flicker phase noise
.
The modified Allan deviation (MADEV) , also known as mod σy(τ), is the deviation variant of the modified Allan variance.
has a drawback in that it is unable to separate the white phase modulation (WPM) from the flicker phase modulation (FPM). Looking that their response to Power-law noise it is clearly seen that WPM and FPM has almost the same response to tau, but WPM is linearly sensitive to the system bandwidth fH where as FPM is only weakly dependent on it. Thus, by varying the system bandwidth the WPM and FPM noise forms may be separated. However, it is impractical to alter the hardware of the measurement system. By post-processing the sample-series and implementing a software bandwidth a modified Allan variance measure can be given capable of resolving the noise forms.
or with average fractional frequency time series
where n is the integer number of samples averaged over.
or with average fractional frequency time series
Allan variance
The Allan variance , also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after David W. Allan. It is expressed mathematically as\sigma_y^2. \,...
, a measurement of frequency stability in clock
Clock
A clock is an instrument used to indicate, keep, and co-ordinate time. The word clock is derived ultimately from the Celtic words clagan and clocca meaning "bell". A silent instrument missing such a mechanism has traditionally been known as a timepiece...
s, oscillators and amplifier
Amplifier
Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...
s. Its main advantage relative to Allan variance is its ability to separate white phase noise
White noise
White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...
from flicker phase noise
Flicker noise
Flicker noise is a type of electronic noise with a 1/ƒ, or pink power density spectrum. It is therefore often referred to as 1/ƒ noise or pink noise, though these terms have wider definitions...
.
The modified Allan deviation (MADEV) , also known as mod σy(τ), is the deviation variant of the modified Allan variance.
Background
The Allan varianceAllan variance
The Allan variance , also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after David W. Allan. It is expressed mathematically as\sigma_y^2. \,...
has a drawback in that it is unable to separate the white phase modulation (WPM) from the flicker phase modulation (FPM). Looking that their response to Power-law noise it is clearly seen that WPM and FPM has almost the same response to tau, but WPM is linearly sensitive to the system bandwidth fH where as FPM is only weakly dependent on it. Thus, by varying the system bandwidth the WPM and FPM noise forms may be separated. However, it is impractical to alter the hardware of the measurement system. By post-processing the sample-series and implementing a software bandwidth a modified Allan variance measure can be given capable of resolving the noise forms.
Definition
The modified Allan variance is defined for using time error samples asor with average fractional frequency time series
where n is the integer number of samples averaged over.
Estimators
The modified Allan variance estimator for time error time series isor with average fractional frequency time series