Consider a linear AC circuit connected to a load, represented by its Thevenin equivalent.

The current flowing through the load is determined using the rectangular form of the Thevenin and load impedance.

The average power delivered to the load is obtained from the current expression.

To determine the load resistance for maximum power, the derivative of power with respect to resistance for maximum power is set as zero.

Similarly, the load reactance for maximum power is obtained.

So, for maximum average power transfer, the load impedance's reactance is the negative of the Thevenin impedance's reactance, and its resistance equals the Thevenin impedance's resistance.

By substituting these values, the maximum power is obtained.

According to the maximum average power theorem, the load impedance equals the complex conjugate of the Thevenin impedance.

For purely resistive loads, maximum average power transfer occurs when the load impedance equals the magnitude of the Thevenin impedance.

In wireless communications, the antenna's impedance is matched to the transmission line or receiver circuit's impedance, maximizing power transfer, ensuring optimal signal strength and enhancing communication quality and range.