Pavg

Pavg, short for average power, is the mean rate at which energy is transferred or converted by a device or system over time. It is widely used in physics, electrical engineering, and related fields to quantify how much power is effectively delivered during a given interval, especially for signals that vary with time.

For a time-varying instantaneous power p(t) = v(t) i(t), where v(t) is voltage and i(t) is current, the average power over a time interval T is Pavg = (1/T) ∫0^T p(t) dt. If the signal is periodic with period T, this equals the average over one period. For a random or stochastic process, Pavg is the expected value E[p(t)].

Special cases help connect Pavg to common measurements. For a purely resistive load with resistance R, p(t) = v(t)^2 / R, so Pavg = (1/T) ∫ v(t)^2 / R dt = V_rms^2 / R, where V_rms is the root-mean-square voltage. In terms of currents, Pavg = I_rms^2 R. For sinusoidal signals with a phase difference φ between v and i, Pavg = V_rms I_rms cos(φ).

Pavg contrasts with instantaneous power, which varies in time, and with peak power, which is the maximum power at any moment. It is a key figure of merit in efficiency calculations, thermal design, and power-management strategies in devices ranging from linear amplifiers to switching power supplies. In periodic or duty-cycle-controlled systems, Pavg is often controlled by the duty cycle of the waveform.

See also: RMS power, instantaneous power, duty cycle, efficiency.