Impedance matching explained

A load takes the most power from a source when its resistance equals the source's own resistance. That's the maximum power transfer theorem, and making a load look like its source is impedance matching. It's why radio transmitters, cables, connectors and antennas are all built for the same impedance, usually 50 Ω.

Every source has resistance inside

Seen from its terminals, any source is a voltage behind a resistance, its Thevenin equivalent. A radio transmitter has 50 Ω inside, by convention. The load gets whatever that internal resistance leaves.

• A huge load gets nearly all the volts, but hardly any current: little power.
• A tiny load gets plenty of current, but almost no volts: little power again.
• In between there's a best, and it's a load equal to the source's resistance.

The sign of a match: the load gets exactly half the source's voltage. More than half and the load is too big; less and it's too small.

Live experiment

Find the load that takes the most

A 1 V generator with 50 Ω inside drives Pip's load. Step it from 5 Ω to 1 kΩ: a big load gets the volts but little current, a small one the current but no volts. The power peaks at 2.5 mW when the load is 50 Ω and gets exactly half the volts.

Try it yourself: free lesson

“Match the load” is lesson 4 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the 3 before it first.

A worked example

A 50 Ω transmitter drives a 200 Ω antenna. The antenna gets 200 ÷ 250 = 80% of the voltage, and its power compared with a matched load is:

Over a third of the power that could reach it doesn't.

Matching with an L-network

Two reactive parts can make one impedance look like another at a chosen frequency. For 200 Ω to 50 Ω, put a capacitor across the 200 Ω antenna and a coil in series towards the transmitter. The capacitor pulls the antenna's impedance down towards 50 Ω, leaving some reactance; the coil cancels it.

At 10 MHz, about 140 pF and 1.4 µH do it. From a 1 V source, the antenna now gets a full 1 V instead of 0.8 V: the network steps the voltage up as it steps the impedance. Coils and capacitors store energy rather than burning it, so the network itself wastes almost nothing. But it only works near one frequency.

Matching with reactance

When the source and load have reactance too, the best match is the complex conjugate: the same resistance, with equal and opposite reactance, so the reactances cancel. A mismatch on a long cable also reflects part of the signal back, measured as SWR (standing wave ratio). Radio uses 50 Ω throughout, and TV aerials 75 Ω, so every link in the chain matches the next.