measuring velocity factor

last updated 25 March 2025.

Velocity factor is something we don’t usually need to keep track of for transmission lines, unless we are trying to cut them to a specific electrical length, such as for phasing lines or impedance matching.

But sometimes we might want to do that. For example, using 1/2 wavelength (or integer multiple) of 75 ohm coax with 50 ohm antennas, or a quarter wavelength of 100 ohm line to match a 200 ohm loop to 50 ohms.

The velocity factor is a measure of how much slower RF propagates through the cable compared to the speed of light in a vacuum. An electrical wavelength in the cable is the distance the wave travels in one cycle of RF. We use the term “electrical” length of a cable to differentiate from the physical length.

Common 50 ohm coax cables with solid polyethylene insulation will typically have velocity factors around 0.67. That is, the electrical length is about 2/3 of that we would calculate using the standard formula for wavelength in a vacuum of 300 / MHz in meters ( or 984 / MHz in feet). So for a wavelength of 80 meters, such a cable would only be 80 * 0.67 = 53.6 meters long. The same ratio applies to 1/2 or 1/4 wavelength cables, or any other electrical length.

The velocity factor depends type of insulation between the feedline conductors. Types with air insulation (such as open wire line) have velocity factors very close to 1.0 (typically 0.93 – 0.97) because most of the insulation is air (usually there are some spreaders involved that lower it a bit). Foamed insulation gives a higher velocity factor than solid, because some of the plastic is replaced by air bubbles, so many low-loss cables with foam dielectric may have velocity factors around 0.8 or so.

measuring velocity factor

In concept, measurement is relatively simple. You find the resonant frequency of a length of line, and divide the physical length by the expected length in a vacuum.

Methods of determining the resonant length usually rely on the impedance transformation properties, with an appropriate termination on the far end of the cable, and either the frequency or the cable length adjusted as needed.

method #1 : quarter wave open circuit

This is often the easiest method using an antenna analyzer. It relies on the fact that a quarter wavelength of line with the far end open will look like a short circuit (or close to it, when we account for losses) at the near end. If we look at a plot of R and X on an analyzer, at very low frequencies X will be negative, then as the frequency increases the value will approach 0 ohms, where R should still be quite low. That is the 1/4 wave resonant point. Measure the physical length of the line, and divide it by the free-space value of 75 / MHz in meters ( 246 / MHz in feet ) to get the velocity factor.

This approach can be used if the far end of line is shorted, in which case the reactance will be positive at low frequencies, decreasing to zero at the quarter wave resonant point (where the impedance will be high). But I find that my analyzer gives more reliable results when measuring low impedances.

method #2 : half wave short circuit

This uses the same principle as method #1, except that the line is 1/2 wavelength and the termination is a short circuit. (Again, an open circuit will also work in theory, but my analyzer works better with lower impedances.) With a shorted half-wavelength line, if you sweep R and X over frequency you will see the impedance bump up to a high value at the 1/4 wave mark, then come back to a low value of R and X = 0 at the half wave resonance. In this case, the expected free-space length is 150 / MHz in meters ( 492 / MHz in feet ).

method #3 : known termination impedance

When a feedline is terminated in a mis-matched load, the impedance will vary along the line in a predictable manner. We can use this approach to perform the same sorts of tests as we did with open and shorted lines, but over a range of impedances that may be easier for our devices to measure.

For example, to measure a 300 ohm transmission line, I can terminate it with a 100 ohm resistor. This gives similar results to a shorted line (because the termination is lower than the characteristic impedance), but the minimum impedance is 100 ohms (or a bit larger to account for losses, with a half wave line) and the maximum is 900 ohms (or a bit less, with a quarter wave line), rather than the very small and very large numbers that may be encountered with open/shorted lines. That may make it easier to find the dips and peaks on the analyzer display. Similarly, terminating the line with a 1800 ohm resistor would result in ( 300 * 300 / 1800 = ) 50 ohms when the line is 1/4 wavelength, and an SWR plot would easily show the frequency where the line is 1/4 electrical wavelength. We’ll discuss this further with regards to measuring characteristic impedance. Terminating a line in 50 ohms will give a low SWR at half wave resonance, regardless of the line impedance (but won’t provide any variation to determine the length of a 50 ohm line). Even for lines with unknown impedances, a pair of small 100 ohm non-inductive resistors will often provide enough options ( 50 ohms in parallel, 200 ohms in series, or 100 ohms using a single resistor) to evaluate most cables.

method #4 : measurements using SWR

When we don’t have an analyzer available, we may need to measure using a transmitter and SWR meter instead. Note that many ham SWR meters are not very accurate at high SWR values, so we will try to keep the values with a reasonable range.

When the feedline is NOT 50 ohms, we can put a 50 ohm termination on the far end and look for a frequency where the SWR dips to a low value. That will be a multiple of 1/2 electrical wavelength. Because hams only have small frequency bands, we may need to measure at a fixed frequency and vary the feedline length rather than varying the frequency for a fixed line length. So if we cut the line a bit longer than a half wavelength, we can trim back the line until we see the SWR get as low as possible.

We can also terminate the cable in a load that will be transformed down to 50 ohms by 1/4 wavelength of cable and search for low SWR that way, but such load resistors that will tolerate the required transmitter power to get an accurate SWR reading are not as common.

When the feedline and dummy load are designed for the same impedance as our SWR meter, that causes an issue with this approach, as the SWR will always be low when the line is terminated. In that case, use a T connector to connect the coax under test in parallel with the dummy load: the SWR will be lowest when the test cable presents a HIGH impedance. That means minimum SWR will be when the test cable is 1/4 wavelength (or odd multiple) when the far end is shorted, or 1/2 wavelength (or multiple) when the far end is open. Using an open end is easier when trimming the cable, as it doesn’t require stripping the cable to make a short circuit after each adjustment. But either method will work.

The minimum SWR point may be rather broad in some of these cases, leading to more uncertainty in the measurement. Sometimes using longer cables (more quarter or half wavelengths) will help make more accurate measurements.

example

So let’s take an example. I found a piece of AC power cord (“zip cord”) 1.75m (5.75 feet) long in the garage with two 0.8mm (AWG #20) conductors, and decided to characterize it for HF use. The first step was to measure the velocity factor.

To use method #1, I connected to my antenna analyzer, with the far end of the line open. (Usually I would use a longer piece, which reduces the variation due to any adaptors that may be required. I finally had to connect the wire ends directly to the coax jack to get reliable readings.)

First I estimated the frequency at which this line would be 1/4 wave resonant. Simply multiplying the length by 4 gave me 7 meters for a full wave, and guessing an approximate velocity factor suggested somewhere around 10m would be close, so I started my search at 30 MHz. If I wasn’t so lazy, and used the formula 75 / length instead, it puts the quarter wave resonance at 42.8 MHz. If I guess a velocity factor around 0.67, that would be about 28 MHz. (In imperial units, using 246 / 5.75 feet gives a similar result – again with a guess for the velocity factor.)

In this case, you only need an initial guess for velocity factor to know what range on the analyzer. It works just as well if you simply scan from, say, 1 to 50 MHz, for a line of this length.

In this case, I had the analyzer plot the R and X from 20 to 40 MHz. (Or whatever range you expect to include the expected resonant frequency.) Look at the curve for X: it will start negative (capacitive) at low frequencies, and rise until it passes 0 ohms – that is the quarter wave resonance point. On my scan, it crossed the axis a little below 30 MHz. Let’s try 28 MHz instead. Here I simply looked at the reactance value: +1 ohm. Positive in this case means the frequency is too high. What about 27.8 MHz? -1.0 ohm. Reactance is zero at 27.9 MHz. (Less than 1 ohm of reactance is usually close enough.) Some analyzers have features that require less manual steps to find the resonant frequency. What length would we expect at this frequency without the velocity factor correction? 75 / 27.9 MHz = 2.69m. (In imperial units 246 / 27.9 MHz = 8.8 feet.)

Then the velocity factor is the actual length divided by the expected length, or 1.75m / 2.69m = 0.65 ( 5.75 feet / 8.8 feet gives the same result ).

I’ll use the results of this example in the other articles where we calculate characteristic impedance and matched line loss.