# Time deviation

Time deviation (TDEV),[1] also known as $\sigma_x(\tau)$, is the time stability of phase x versus observation interval τ of the measured clock source. The time deviation thus forms a standard deviation type of measurement to indicate the time instability of the signal source. This is a scaled variant of frequency stability of Allan deviation. It is commonly defined from the modified Allan deviation, but other estimators may be used.

Time variance (TVAR) also known as $\sigma_x^2(\tau)$ is the time stability of phase versus observation interval tau. It is a scaled variant of Modified Allan variance.

TDEV is a metric often used to determine an aspect of the quality of timing signals in telecommunication applications and is a statistical analysis of the phase stability of a signal over a given period. Measurements of a reference timing signal will refer to its TDEV and maximum time interval error (MTIE) values, comparing them to specified masks or goals.

## Definition

The most common estimator uses the modified Allan variance

$\sigma_x^2(\tau) = \frac{\tau^2}{3}\operatorname{mod}\sigma_y^2(n\tau_0)$

where $\tau = n\tau_o$. The 3 in the denominator normalizes TVAR to be equal to the classical variance if the deviations in x are random and uncorrelated (white-noise).

or TDEV, which is the square-root of TVAR, may be derived from MDEV modified Allan deviation

$\sigma_x(\tau) = \frac{\tau}{\sqrt{3}}\operatorname{mod}\sigma_y(n\tau_0)$