When seeing transmission lines and antennas in class we saw that the power delivered to a load is equal to:
$$
P = \frac{1}{2}\cdot \left | I \right |^{2}\cdot Re\left \{ Z \right \}
$$
Where I is the current input of the load/antenna and Z is the impedance of the load/antenna.
What I don't understand is, where does this division by 2 come from? In other classes we've learned that P = VI = I²R but this seems to be different?
I tried to look for an answer to this online/in books but I couldn't find one. All the resources I found just threw that formula out there without an explanation of where it comes from.
Best Answer
When driving a matched load (impedance of the load is the complex conjugate of the impedance of the source), this gives maximum power transfer, and the efficiency is 50 %.
In RF applications, matched loads are usually used to a) to ensure that signal (power) reflections from the load don't create unwanted disturbances in the power amplifier, and b) actually deliver maximum power to the load.