Table of contents |

2 Power transfer 3 Transmission lines 4 Impedance matching devices |

## General

Whenever a source of electicity, such as a signal source or a radio transmitter, operates into a load, optimum power is delivered to the load when the impedance of the load is equal to the internal impedance of the source. Arranging this is called **impedance matching**.

## Power transfer

Pload = I^2 * Rload (where I is the current in the circuit and ^2 means "squared")

so Pload = Vsource^2 * Rload / ((Rsource+Rload)^2)

Pload = Vsource^2 * Rload / (Rsource^2 + 2*Rsource*Rload + Rload^2)

Pload = Vsource^2 / (Rsource * (Rsource/Rload + 2 + Rload/Rsource))

Note that this function approaches zero as r becomes very small or very large - this indicates that an extreme impedance mismatch results in very little power being transferred to the load.

We are interested in knowing what value of r, and hence of Rload, we should use for maximum power transfer. We need to maximise 1/(1/r + 2 + r) which is the same as minimising 1/r + 2 + r. The derivative is 1 - 1/(r^2) which takes the following values:

- Negative for r < 1
- 0 when r = 1
- Positive for r > 1

Pload = Vsource^2 / (Rsource * (1 + 2 + 1))

Pload = 1/4 * Vsource^2 / Rsource

And this is the maximum power that can be transferred into Rload, occurring when Rload = Rsource, ie the impedances are *matched*.

## Transmission lines

## Impedance matching devices

**Impedance matching** devices include baluns, antenna tuners, acoustic horns and terminators used with 10base2 ethernet. See also impedance mismatch.