E1 · Published 21 October 2026 · By The Ham Desk

Transmission Lines and Impedance Matching

Everything between the transmitter and the antenna is a transmission line problem, and at Extra level the questions stop asking for rules of thumb and start asking why the numbers come out the way they do. This unit works from characteristic impedance through standing waves to the matching networks that make an antenna present the load the transmitter wants.

Band 20 m
Study time 19
Level Stretch
questions 10

Waveform and antenna diagram for Antenna Design and Transmission Lines — Antenna Design and Transmission Lines — waveform overlay and radiation pattern

Pre-flight briefing

Characteristic impedance and velocity factor

A transmission line's characteristic impedance is set entirely by its construction - the ratio of the conductor diameters, the spacing between them, and the dielectric material between them. It does not depend on the line's length, and it does not change when a different load is connected. A coaxial cable with a solid polyethylene dielectric settles near 50 ohms; air-dielectric parallel line usually lands between 300 and 600 ohms. Those two families behave very differently, and most of the matching questions come down to which one is in use.

A wave travels along a line more slowly than it does in free space, because the dielectric loads the electric field. The velocity factor is the ratio of the propagation velocity in the line to the speed of light, and it is what turns an electrical length into a physical one. A quarter wavelength at 14.2 MHz is about 5.28 metres in free space, but a coax with a velocity factor of 0.66 gives a physical quarter wave of only about 3.48 metres. Every stub and matching section has to be cut using the velocity factor, not the free-space figure.

Standing waves and what they cost

When the load impedance does not equal the line's characteristic impedance, part of the forward wave reflects back toward the transmitter. The two travelling waves add and subtract along the line to produce a standing wave, and the ratio of the maximum to minimum voltage is the standing wave ratio. A perfect match gives 1:1; anything else means some of the power the transmitter produced is on its way back rather than out of the antenna.

A common but incomplete belief is that the reflected power is simply lost. In fact a mismatch does not by itself dissipate power in a lossless line - the reflection sends energy back, and a matching network at the transmitter can re-reflect it toward the antenna. What a mismatch really costs is loss: the higher currents and voltages associated with standing waves increase resistive loss in the line, and the effect grows with the line's attenuation and its length. That is why open-wire line, whose loss is very low, tolerates a large mismatch on a multiband doublet, while a long run of small coax does not.

The same reasoning explains the standard advice about antenna tuners. A tuner installed at the transmitter makes the transmitter happy, because it presents 50 ohms at the radio, and it lowers the loss on the line between the tuner and the radio. But the line between the tuner and the antenna still carries the standing wave, and if that line is lossy the energy is spent as heat before it ever reaches the antenna.

Matching sections and baluns

The quarter-wave matching section is the classic transformer for a single band. A quarter wave of line whose characteristic impedance is the geometric mean of the two impedances to be joined - the square root of the source impedance times the load impedance - transforms one to the other. Joining a 50 ohm transmitter to a 200 ohm load, for instance, calls for a quarter wave of 100 ohm line. The same mathematics makes a shorted or open stub useful: a section of line shorter than a quarter wave looks capacitive or inductive depending on which end is shorted, so a stub can cancel a reactance without any coil or capacitor.

The stub length is set by the operating frequency and the velocity factor, which is why stub matching is a single-band technique unless the stub is switched. On the higher HF bands a shorted stub is often used across the feed point to notch a single interfering frequency, since a shorted quarter wave presents a very high impedance at its resonant frequency and little effect anywhere else.

A balun solves a different problem. A balun - from balanced to unbalanced - couples a balanced load such as a dipole or a parallel feed line to an unbalanced source such as a coaxial cable or a transmitter output that is grounded on one side. Without it, current can flow on the outside of the coaxial shield, turning the feed line itself into part of the antenna. That causes pattern distortion, radio frequency interference in the shack, and unpredictable impedances. A choke balun made of several turns of coax achieves the same suppression without a transformer core's losses.

Terms you must be able to define
Term	What the examiner wants to hear
Characteristic impedance	The impedance a line presents to a travelling wave, set by conductor geometry and dielectric, not by length.
Velocity factor	The ratio of propagation velocity in a line to the velocity in free space.
Standing wave ratio	The ratio of maximum to minimum voltage along a mismatched line.
Quarter-wave matching section	A quarter wave of line whose impedance is the geometric mean of the impedances being joined.
Balun	A balanced-to-unbalanced transformer, or a choke, that stops current flowing on the outside of a coaxial shield.

Question deck 10 questions

E4A01 Core

What determines the characteristic impedance of a transmission line?

E4A02 Core

Why must the velocity factor be used when cutting a quarter-wave matching section?

E4A03 Core

What is the standing wave ratio on a transmission line?

E4A04 Stretch

What does an antenna tuner at the transmitter actually accomplish?

E4A05 Stretch

What characteristic impedance should a quarter-wave matching section have to join a 50 ohm transmitter to a 200 ohm load?

E4A06 Core

What problem does a balun solve?

E4A07 Stretch

Why does open-wire feed line tolerate a large mismatch better than small coaxial cable?

E4A08 Stretch

What does a shorted quarter-wave stub present at its resonant frequency?

E4A09 Core

What happens to a wave reaching a load whose impedance does not match the line?

E4A10 Stretch

Approximately what physical length is a quarter-wave section of coaxial cable with a velocity factor of 0.66 at 14.2 MHz?

Reference sheet

The explanations for all ten questions sit on this sheet. Pick an answer on the left and the matching card lights up.

E4A01 Explanation 1

Key B — The conductor diameters or spacing and the dielectric material between the conductors

Characteristic impedance is a property of the line's cross-section alone. Cutting a piece of coax shorter does not change its 50 ohm rating, and connecting a 200 ohm load does not either - what changes is the standing wave the mismatch creates, not the line itself.

Rule Fundamentals - transmission lines

E4A02 Explanation 2

Key A — Because the wave travels more slowly in the line than in free space, so the physical length is shorter than the free-space quarter wavelength

The dielectric slows the wave, so an electrically quarter-wave section is physically shorter than the free-space figure. At 14.2 MHz a free-space quarter wave is about 5.28 metres, while coax with a 0.66 velocity factor needs only about 3.48 metres.

Rule Fundamentals - velocity factor

E4A03 Explanation 3

Key D — The ratio of the maximum to the minimum voltage along the line

A mismatch sets up a standing wave whose envelope peaks and nulls along the line, and SWR is the ratio of those extremes. It runs from 1:1 for a perfect match upward without limit as the reflection grows.

Rule Fundamentals - standing waves

E4A04 Explanation 4

Key C — It presents 50 ohms to the transmitter and reduces loss on the line between the tuner and the radio, but the line to the antenna still carries the standing wave

The tuner cancels the reactance and transforms the impedance so the transmitter sees its design load, which reduces stress on the radio and on the short length of line to it. Energy still reflects between tuner and antenna, so if that span is lossy the mismatch is paid for as heat.

Rule Fundamentals - matching networks

E4A05 Explanation 5

Key B — 100 ohms, the geometric mean of the two impedances

A quarter-wave section transforms impedance by the square of its own characteristic impedance, so the required value is the square root of the product of the two impedances: 50 times 200 is 10,000, whose square root is 100 ohms.

Rule Fundamentals - quarter-wave transformer

E4A06 Explanation 6

Key A — It couples a balanced load to an unbalanced source and prevents current from flowing on the outside of the coaxial shield

Without a balun the outside of the coax becomes a radiating element, distorting the pattern and bringing radio frequency energy back into the operating position. A choke balun made of coiled coax suppresses that current without the losses of a transformer core.

Rule Fundamentals - baluns

E4A07 Explanation 7

Key D — Its inherent loss is very low, so the extra loss caused by standing waves is small

The penalty for a mismatch is additional loss, and that penalty scales with the line's own attenuation. Air-dielectric parallel line has very little loss to begin with, so even a 5:1 standing wave adds little, while the same SWR on a long thin coax run converts a large fraction of the power into heat.

Rule Fundamentals - feed line loss

E4A08 Explanation 8

Key C — A very high impedance, so it can notch a single interfering frequency

A short at the far end of a quarter-wave section is transformed to an open circuit at the near end. Placed across the feed point it therefore blocks only the frequency it is cut for, leaving the rest of the band essentially untouched - which is why stubs are popular for removing a single strong local signal.

Rule Fundamentals - stub matching

E4A09 Explanation 9

Key B — Part of the wave is reflected back toward the source and part is delivered to the load

A discontinuity in impedance acts like a partial mirror. The proportion reflected grows as the load departs from the line impedance, and that reflected wave is what travels back to form the standing wave and the SWR reading at the transmitter.

Rule Fundamentals - reflections

E4A10 Explanation 10

Key B — About 3.5 metres

A free-space quarter wave at 14.2 MHz is 300 divided by 14.2, divided by four, or about 5.28 metres. Multiplying by the 0.66 velocity factor gives roughly 3.5 metres, and that is the length that must actually be cut.

Rule Fundamentals - electrical length

How to use this unit

Work the ten questions in one sitting with the reference sheet covered, then uncover it and read every explanation - including the ones you got right. The wording of the real exam is different, so learn the reasoning rather than the answer letters.