Impedance matching and SWR

Why 50 ohms, what SWR and return loss actually tell you, how much power a mismatch really costs, and why a low SWR is not proof of a good antenna.

Why anything reflects at all

At low frequencies a wire is a wire. At radio frequencies, once the connection is a meaningful fraction of a wavelength long, it stops behaving like a connection and starts behaving like a transmission line — something a wave travels along rather than something that simply joins two points.

A wave travelling along a line meets whatever is at the far end. If the load absorbs exactly what the line is built to deliver, all the energy goes in. If it does not, part of the wave reflects and travels back towards the source. That is the whole of impedance matching: arranging for the load to look like what the line expects.

The forward and reflected waves then interfere along the line, producing a fixed pattern of voltage peaks and troughs — a standing wave. The ratio between the highest and lowest voltage on that pattern is the standing wave ratio, SWR.

Why 50 ohms

The number looks arbitrary and is not quite. For air-dielectric coaxial cable, two optimum impedances exist and they are not the same one:about 77 Ω gives the lowest loss, and about 30 Ω handles the most power before breakdown.

Fifty is close to the geometric compromise between them, and it happens to be convenient to manufacture. It stuck, and once an ecosystem of connectors, cables, instruments and chip designs settled on it, the value became self-reinforcing.

Seventy-five ohms survives in television and video distribution, where signals are small and low loss matters more than power handling — which is exactly the case 77 Ω is optimal for. Both conventions are rational; they just optimise different things.

SWR, return loss and reflection coefficient

Three ways of saying the same thing, and it helps to see them side by side because different instruments report different ones.

Γ = (SWR − 1) / (SWR + 1)  ·  Return loss (dB) = −20·log₁₀|Γ|

Γ (gamma) is the fraction of the voltage reflected. Squared, it gives the fraction of the power. Return loss expresses the same thing in decibels, and larger is better — a 20 dB return loss is an excellent match, 6 dB is poor. SWRis the ratio on the line, where 1:1 is perfect and larger is worse.

Computed at build time from Γ = (SWR−1)/(SWR+1).

A mismatch costs less than people fear

This table is worth reading carefully, because the intuition around SWR is badly calibrated in both directions.

At 2:1 — the figure often treated as a hard limit — you reflect 11.1% of the power and lose0.512 dB. Half a decibel. In a link budget where you are carrying 10 dB of margin, that is close to irrelevant, and it is certainly not the difference between working and not working.

Even 3:1 costs only about1.25 dB. You would struggle to notice that in the field.

So why does anyone care? Three reasons, none of which is the lost power:

• The reflected power goes somewhere. It returns to the power amplifier, which has to dissipate it. Small transmitters usually cope; larger ones fold back their output or fail. Datasheets often specify a maximum SWR for exactly this reason.
• A bad match usually indicates something else. An antenna that reads 5:1 is not merely inefficient — it is not resonant where you think it is, which means it is detuned by its surroundings, wrongly built, or connected through a fault. The SWR is a symptom worth chasing.
• It shifts with everything. A match measured on the bench changes when a hand, a wall or an enclosure arrives. Aiming for a good match at the centre gives you room for that drift.

A low SWR does not mean a good antenna

This is the most important thing on this page, and the one that catches experienced people out.

A 50 Ω resistor has a perfect 1:1 SWR and radiates nothing at all. It absorbs every watt you send it and turns them into heat. From the transmitter's point of view it is an ideal load.

An SWR meter measures how well power is getting into the load. It says nothing about whether the load then radiates that power or dissipates it. A lossy antenna, a wet cable, a corroded connector, or a long run of poor coax will all improve the SWR you measure at the transmitter, because the loss attenuates the reflection on its way back.

That last point deserves emphasis: cable loss flatters SWR. Measure through 3 dB of feeder and a genuinely awful antenna reads as a respectable match, because the reflected wave is attenuated twice on the round trip. If a suspiciously perfect reading appears at the end of a long cable, suspect the cable rather than congratulating the antenna.

Efficiency and match are separate properties. Only one of them is easy to measure, which is why the easy one gets over-trusted.

Matching networks

When a load is not 50 Ω, you insert a network that transforms it. Because the components are reactive rather than resistive, they do this without dissipating the power — which is the point.

The workhorse is the L network: one series and one shunt reactance, two components, capable of matching any purely resistive load to any other. Most small-antenna designs leave footprints for a pi or T arrangement — three positions, some left unpopulated — so the match can be tuned once the real board and enclosure exist. If you are laying out a product with a PCB antenna, leave that network in even if you hope not to need it; adding it later means a board spin.

Two things to keep in mind. Matching is narrowband: a network tuned at one frequency is progressively wrong away from it, and the higher the transformation ratio, the narrower the result. And componentQ matters, because real inductors and capacitors have resistance — a matching network built from lossy parts converts some of your signal to heat while it works. The reactance calculator gives the component values, andLC resonance the frequency they act at.

Measuring it honestly

Three practical habits separate a measurement you can trust from one you cannot.

Measure at the antenna, not at the radio. Anything between the two attenuates the reflection and improves the reading. If you must measure through a cable, know its loss and correct for it.

Measure across the band, not at one point. A single-frequency reading tells you nothing about whether resonance is where you intended it. A sweep shows the dip, and the position of that dip tells you which way the antenna is detuned — too long or too short.

Measure in the product. On the finished assembly, in the enclosure, with the battery fitted, near whatever it will be near. An antenna matched on an open bench and then closed into a plastic case is not the antenna you measured — the dielectric alone typically pulls resonance down by a few percent.

And when the match is good and the range is still poor, remember what SWR cannot see. The power is getting into the antenna; whether it is leaving again is a question about efficiency and pattern, not about impedance.