Coax Stub & Electrical Length Calculator

Velocity factor

A signal travels more slowly in coaxial cable than in free space, because the dielectric between the conductors slows it. The velocity factor, VF, is the ratio: about 0.66 for solid polyethylene, as in RG-58 and RG-213; about 0.78 to 0.80 for foam polyethylene, as in many RG-8X; about 0.85 for LMR-400’s foam; and close to 0.95 for air-dielectric hardline. A wavelength in the cable is the free-space wavelength times VF. At 14.2 MHz, the free-space wavelength is 21.11 m, so a quarter wavelength of solid-dielectric coax is 0.25 × 21.11 × 0.66 = 3.48 m, 11.43 ft, a third shorter than a quarter wavelength of wire.

What stubs do

A section of line an exact fraction of a wavelength long transforms the impedance at its far end in a predictable way. A quarter-wave section inverts it: shorted at the far end, it looks like an open circuit at the input at that frequency, and open at the far end, it looks like a short. An open quarter-wave stub teed across a feed-line therefore acts as a notch filter, shorting out one frequency while passing others; amateurs use them to reduce harmonics or to stop a nearby station on another band from overloading a receiver in a contest. A half-wave section repeats its termination, so the impedance at the far end appears again at the input. A quarter-wave section of 75 Ω cable transforms 100 Ω to 56 Ω, which is how a full-wave loop, around 100 Ω, is matched to 50 Ω coax: Z = √(Z₁ × Z₂).

Electrical length of your feed-line

The same arithmetic tells you how long a cable is in wavelengths. That matters for phasing harnesses, where two antennas must be fed through lines of exactly equal electrical length or of a specified difference, and for diagnosing feed-lines whose length happens to transform a mismatch into an impedance the radio cannot handle. A common mistake is to measure the cable physically and assume it is the right electrical length; connectors add a little, and VF varies between manufacturers and even production batches by a few per cent.

Measuring and trimming

Cut stubs slightly long and trim while measuring. An antenna analyser connected to an open quarter-wave stub shows a near-zero impedance, a dip, at the frequency where the stub is exactly a quarter wave; cut a little at a time until the dip lands on your target. You can also find the actual VF of a cable this way: measure the dip frequency of a known length, and VF = 4 × length in metres × frequency in MHz ÷ 299.79 for a quarter-wave stub.

How to use it

1. Enter the frequency the stub or section must work at.
2. Choose the electrical length: a quarter, half, three-quarters or a full wavelength.
3. Enter the velocity factor from the cable’s datasheet.
4. Read the physical length, and optionally enter a cable you have to see its electrical length.