Maximum Average Power

A simple loop circuit used to illustrate the derivation of the maximum power transfer theorem as it applies to circuits operating in the sinusoidal steady state.we can determine the conditions for an AC load to absorb maximum power in an AC circuit. For an AC circuit, both the Thévenin impedance and the load can have a reactive component. Although these reactances do not absorb any average power, they will limit the circuit current unless the load reactance cancels the reactance of the Thévenin impedance. Consequently, for maximum power transfer, the Thévenin and load reactances must be equal in magnitude but opposite in sign; furthermore, the resistive parts -according to the DC maximum power theorem- must be equal. In another words the load impedance must be the conjugate of the equivalent Thévenin impedance. The same rule applies for the load and Norton admittances.

Zth = Rth + j Xth ZL = RL + j XL

ZL = Zth

* RL = Rth and XL = - Xth

This Means that for Maximum average power transfer to a purely resistive load the load impedance is equal to the magnitude of the thevenins impedance.

with Dennis James Matildo.
          2/20/16