Very-short-term frequency instability (time domain) of an oscillator disturbed by additive internal thermal noise

The frequency instability, over a period τ, of an oscillator whose internal thermal noise is its sole source of noise is defined by a standard expression [1, (16)] tending to infinity when τ → 0, and hence unsuitable to cover very-short-term instabilities. The present letter demonstrates a fuller expression applicable to any value of τ ≥ 0.