Maximum Power Transfer

It is sometimes important to be able to transfer as much real power as possible from a source to a load, Figure 42.

**Figure 42:** Power transfer.
$\begin{figure} \begin{center} \epsfig{file=images/acimg10.eps}\end{center}\end{figure}$

Consider the (Thevenin) model of Figure 43. We wish to determine the value of the load impedance Z_L for which the real power P_L absorbed by the load is a maximum.

**Figure 43:** Power transfer.
$\begin{figure} \begin{center} \epsfig{file=images/acimg11.eps}\end{center}\end{figure}$

It can be shown that the maximum occurs when the load is matched to the source in the sense that

$\begin{displaymath}{\mathbf Z}_L = {\mathbf Z}_{source}^\ast , \end{displaymath}$

(52)

i.e. the load impedance is the complex conjugate of the source impedance.

Recall that in the DC case with source resistance R_source and load resistance R_L maximum power transfer is achieved when

R_L = R_source ;

see Computer Lab/Tutorial 1.

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