Transmission Lines, Standing Waves, and VSWR
A transmission line is a path designed to carry a wave. At RF, a cable or PCB trace is not just a connection between two points. It is a distributed structure with capacitance and inductance along its length. A signal needs time to travel through it.
Learning Objectives
By the end of this lesson, you should be able to:
- explain incident and reflected waves;
- describe how standing waves form;
- calculate VSWR from reflection coefficient magnitude;
- relate return loss to reflected power;
- identify practical causes of RF mismatch.
Incident and Reflected Waves
The forward-moving wave is called the incident wave. The wave that comes back from a mismatch is called the reflected wave.
If the load accepts all the energy, there is no reflected wave. If the load rejects part of the energy, the returning wave combines with the forward wave. At some positions the two waves add; at other positions they cancel. This creates a standing-wave pattern along the line.
title "Forward and Reflected Waves"
type cartesian
canvas width=860 height=460
axes x="Distance" y="Voltage" xunit=wavelength yunit=norm xmin=0 xmax=1 ymin=-1.8 ymax=1.8
series FWD label="forward" x=[0,1] y="sin(2*pi*x)" samples=360 color=#2563eb
series REF label="reflected" x=[0,1] y="0.45*sin(2*pi*x+pi)" samples=360 color=#dc2626
series SUM label="sum" x=[0,1] y="sin(2*pi*x)+0.45*sin(2*pi*x+pi)" samples=360 color=#0f766e
This is an explanatory normalized chart, not a measured cable trace.
Standing Waves
A standing wave does not mean energy has stopped everywhere. It means the forward and reflected waves create fixed voltage maxima and minima along the line.
The ratio of maximum voltage to minimum voltage is voltage standing wave ratio:
$$
\text{VSWR}=\frac{V_\text{max}}{V_\text{min}}
$$
Using reflection coefficient magnitude:
$$
\text{VSWR}=\frac{1+|\Gamma|}{1-|\Gamma|}
$$
Perfect match:
$$
|\Gamma|=0,\quad \text{VSWR}=1:1
$$
Severe mismatch:
$$
|\Gamma|\rightarrow1,\quad \text{VSWR}\rightarrow\infty
$$
Reflection, Return Loss, and Reflected Power
Return loss is usually expressed in dB:
$$
\text{Return Loss}=-20\log_{10}|\Gamma|
$$
Reflected power fraction is:
$$
\frac{P_\text{reflected}}{P_\text{forward}}=|\Gamma|^2
$$
| Gamma magnitude | VSWR | Return loss | Reflected power |
|---|---|---|---|
| 0.00 | 1.00:1 | infinite | 0% |
| 0.10 | 1.22:1 | 20.0 dB | 1% |
| 0.20 | 1.50:1 | 14.0 dB | 4% |
| 0.33 | 1.99:1 | 9.6 dB | 10.9% |
| 0.50 | 3.00:1 | 6.0 dB | 25% |
title "VSWR Rises Quickly Near Large Reflection"
type cartesian
canvas width=860 height=460
axes x="Reflection magnitude" y="VSWR" xmin=0 xmax=0.9 ymin=1 ymax=20
series VSWR label="VSWR" x=[0,0.9] y="(1+x)/(1-x)" samples=360 color=#7c3aed
point GOOD x=0.1 y=1.222 label="good"
point BAD x=0.5 y=3 label="3:1"
Why Mismatch Happens
Mismatch can come from many places:
- antenna impedance changes with frequency, nearby metal, enclosure plastic, hand position, and ground size;
- PCB trace width or stackup differs from the intended controlled impedance;
- connectors and adapters add discontinuities;
- filters or amplifiers are not designed for the same source and load impedance;
- component parasitics move the circuit away from the schematic value.
Transmission-Line Length Matters
A very short mismatch may be harmless at low frequency. At RF, even a short physical length can represent significant phase rotation.
Electrical length is often measured in wavelengths:
$$
\theta=360^\circ\frac{l}{\lambda}
$$
where l is physical length along the line. A lambda/4 line rotates impedance by 90 deg. This is why quarter-wave antennas, stubs, and matching sections are common in RF.
Worked Example: Reflected Power
A small antenna has measured VSWR = 2:1 at one frequency.
First solve for reflection magnitude:
$$
|\Gamma|=\frac{\text{VSWR}-1}{\text{VSWR}+1}
$$
$$
|\Gamma|=\frac{2-1}{2+1}=0.333
$$
Reflected power fraction:
$$
|\Gamma|^2=0.333^2=0.111
$$
About 11.1% of forward power reflects. The rest is accepted by the antenna system, although accepted power may still be lost as heat if the antenna is inefficient.
Practical Checks
- Use a VNA or antenna analyzer to measure return loss or VSWR.
- Sweep over the whole operating band, not one frequency only.
- Keep matching components close to the antenna feed.
- Do not tune an antenna far away from its final enclosure.
- Check cable, connector, and adapter ratings at the operating frequency.
Common Mistakes
- Thinking VSWR directly equals antenna efficiency.
- Measuring the antenna outside the product and expecting the same result inside.
- Ignoring a short open stub because it looks tiny at DC.
- Treating return loss and insertion loss as the same quantity.
- Assuming a good match at one frequency means a good match across the band.
Summary
A mismatch reflects part of an RF wave. The reflected wave combines with the incident wave and produces standing-wave maxima and minima. VSWR, return loss, and reflected power are different ways to describe the same mismatch behavior.