Hertzian
Hertzian

Transmission Lines and VSWR

beginner

Why RF cables and PCB traces have an impedance, what happens when the line and the antenna disagree, and how VSWR measures the mismatch.

The idea

At radio frequencies a cable or a circuit-board trace stops behaving like a plain wire. The signal travels along it as a wave, and the line has a characteristic impedance, written Z₀. Z₀ is set by the line's shape and materials, not by its length. Almost all RF gear is built around 50 Ω.

Think of it like a rope tied to a wall. Flick the rope and a wave runs along it. If the far end is held by something that moves exactly like more rope, the wave carries straight on and none comes back. If the far end is a solid wall, the wave bounces back towards you. An antenna or receiver at the end of a line is that far end. When its impedance matches the line, all the power goes in. When it doesn't, part of the wave reflects back down the line.

The forward and reflected waves overlap and form a standing wave: fixed spots along the line where the voltage is high and others where it is low. VSWR (voltage standing wave ratio) is the ratio of the highest voltage to the lowest. A perfect match gives 1:1. Bigger numbers mean more reflection.

For a PCB, the Transmission Line Calculator tells you how wide to make a trace so it really is 50 Ω. For a finished system, the VSWR Calculator tells you how much a measured mismatch is costing you.

The math

The reflection coefficient Γ says how much of the wave bounces back, from the load impedance Z_L and the line impedance Z₀:

Γ=ZL−Z0ZL+Z0\Gamma = \frac{Z_L - Z_0}{Z_L + Z_0}

VSWR, return loss and mismatch loss all follow from |Γ|:

VSWR=1+∣Γ∣1−∣Γ∣RL=−20log⁡10∣Γ∣Lmismatch=−10log⁡10(1−∣Γ∣2)\text{VSWR} = \frac{1 + |\Gamma|}{1 - |\Gamma|} \qquad \text{RL} = -20\log_{10}|\Gamma| \qquad L_{mismatch} = -10\log_{10}\left(1 - |\Gamma|^2\right)

Worked example: a 100 Ω antenna fed by a 50 Ω cable. Γ = (100 − 50) / (100 + 50) = 0.3333, so VSWR = 1.3333 / 0.6667 = 2:1. Enter VSWR 2 in the VSWR Calculator and it shows a return loss of 9.54 dB. 11.11% of the power reflects and 88.89% reaches the antenna, a mismatch loss of 0.51 dB. That 0.51 dB goes into a link budget just like cable loss does.

On a circuit board the line's width sets its impedance. With the Transmission Line Calculator's defaults (microstrip on 1.6 mm FR-4 at 1 GHz), a 2.9 mm trace comes out at 50.83 Ω, and asking it to synthesize 50 Ω gives a width of 2.986 mm. Narrow the trace to 1 mm and the impedance climbs to 84.15 Ω: thinner traces have higher impedance.

Common misconceptions

  • Myth: A 2:1 VSWR wastes half your power. Reality: It reflects only about 11% of the power, a 0.51 dB loss. It is a common, acceptable target for antennas.
  • Myth: The reflected power is just lost. Reality: It travels back towards the transmitter, where a bad mismatch can overheat or damage the output stage. That is why many radios cut their power when VSWR is high.
  • Myth: Impedance depends on how long the cable is. Reality: Z₀ depends on the conductor sizes and the insulation between them. A 1 m and a 30 m length of 50 Ω coax are both 50 Ω (though the longer one has more cable loss).
  • Myth: A low VSWR reading proves the antenna works well. Reality: A long, lossy cable also absorbs the reflected wave, so the VSWR measured at the radio can look better than it really is at the antenna.

Try it

Open the VSWR Calculator and type in 1.5, 2 and 3 to see how fast the reflected power grows. Then open the Transmission Line Calculator, switch to synthesis, and find the trace width for 50 Ω on FR-4. To see a mismatch as a point on a chart, move a load around in the Smith Chart Explorer: the centre of the chart is a perfect 1:1 match.