A matching network makes a load look like a different impedance to whatever drives it, so that power flows into it instead of bouncing back. It is built from coils and capacitors (in theory lossless) or from transformers and transmission-line sections. The output of a transmitter, an antenna tuner and many antennas all rely on one.
Why match
A source delivers the most power when the load equals its own impedance. A transmitter is built for 50 Ω; an antenna rarely offers exactly that, and often has some reactance too. A matching network does two jobs: it cancels the reactance and it sets the resistance.
A matching network does two jobs: cancel the reactance, then set the resistance.
A network at the transmitter does not alter the antenna or the line, which still see their original mismatch. It only makes the radio happy. See SWR and reflections and Antenna tuners.
The L network
Low-pass L-network. The shunt part always sits on the side with the higher resistance.
Inductor1.94 µH
Capacitor194 pF
The L network is the building block: one series part and one shunt part. The rule is that the shunt part goes on the side with the higher resistance and the series part on the lower side. Then:
Q = √(R high ÷ R low − 1). It is fixed by the two resistances.
Series reactance X = Q × R low, shunt reactance X = R high ÷ Q.
Worked example, 200 Ω to 50 Ω at 7.1 MHz. Q = √(200 ÷ 50 − 1) = 1.73. The series reactance is 1.73 × 50 = 86.6 Ω, which is a 1.94 µH inductor (86.6 ÷ (2π × 7.1 MHz)). The shunt reactance is 200 ÷ 1.73 = 115.5 Ω, which is a 194 pF capacitor. Checking the result, the source sees exactly 50 Ω with no reactance.
In the low-pass form drawn, the series part is a coil and the shunt part a capacitor; swap them for a high-pass form. The greater the mismatch, the larger Q becomes: bandwidth narrows and losses and circulating currents grow.
Pi and T networks
Low-pass forms shown. Swap each inductor for a capacitor and vice versa for the high-pass form.
A Pi network is two L networks back to back, with the series coil shared; a T network is the dual. The extra part brings an extra freedom: Q can be chosen. A higher Q filters harmonics more strongly but narrows the bandwidth and adds loss, which is why the Pi network is the usual output stage of a tube amplifier; its TUNE and LOAD controls are the two variable capacitors. Pi and T circuits are also the heart of most manual antenna tuners.
Other ways to match
Transformers. Impedance changes as the square of the turns ratio: a 2 : 1 ratio changes impedance 4 : 1, so 200 Ω across the larger winding looks like 50 Ω at the smaller one. Broadband and tuning-free; see Transformers and Baluns and ununs.
Quarter-wave line section. A quarter-wavelength of line with impedance √(Z1 × Z2) matches two resistive impedances: 100 Ω line between 50 Ω and 200 Ω. See Stubs, quarter-wave sections and the gamma match.
In practice
A network is never lossless. Coil resistance heats up, increasingly so at high Q. A tuner can show a perfect match while turning much of the power into heat.
Match at the antenna if you can. A matched antenna avoids extra loss on the feed line, which a tuner at the radio cannot recover; see Feed line loss and velocity factor.
Tune at low power and adjust for minimum reflected power, to avoid arcing and stressing the transmitter.