The exponential rate constant (τ) that determines how quickly the output amplitude of an electrical signal that is under automatic gain control (AGC) responds to a sudden increase or decrease in input signal amplitude. Mathematically,
Af(t) = Ai(t) + ΔAi (1 − e−t/τ)
where Af is the output signal amplitude, Ai is the input signal amplitude (Ai), ΔAi is the change in input signal amplitude and t is time. When t equals τ, the function (1 − e−t/τ) equals (1 − 1/e) equals 0.63. Therefore, the AGC time constant (τ) is the amount of time that elapses for the output signal of AGC to reflect 63% of the change in the input signal amplitude.