# Velocity factor measurement

A frequently asked question is how to measure transmission line velocity factor. The wide adoption of the NanoVNA has spurred these questions.

So, it is good that ownership of a NanoVNA stimulates thinking and search for applications of the instrument.

I note that when these questions are asked online, early responses include recommendation of using the VNA to perform a TDR transform to measure the electrical length of the cable and calculate the velocity factor as $$vf=\frac{\text{PhysicalLength}}{\text{ElectricalLength}}$$. The resolution of the NanoVNA swept from 1 to 1500MHz with 401 steps is around 60mm, so you can only measure to about 0.25% resolution if you have a test cable 20m long. So this method might not be very practical in a lot of situations for that reason alone. More later…

It is practical to measure the quarter wave resonance of a shorter section of test cable to better than 0.1% resolution.

A significant problem measuring short cables is the contribution of the test fixture, the reference plane is usually not at the very beginning of the uniform cable, if you know where that is anyway (it may be inside a connector).

Let’s look at an example, a measurement of some ordinary nominally 300Ω TV windowed ribbon line.

Above is the test fixture, the VNA and 1:1 transformer board have been OSL calibrated to a point very close to the pins of the grey terminal block. The transformer module is described at Conversion of NOELEC style balun board to 1:1.

A section of line that measured 0.303m from the grey terminal block to the end of the line was measured observing phase of s11, and the frequency where phase switched from -180° to 180° noted as 209.000MHz, see above. We can calculate the electrical length as c0/fo/4=0.3586m and vf=0.845.

That went well, let’s try a longer section.

A section of line that measured 1.750m from the grey terminal block to the end of the line was measured observing phase of s11, and the frequency where phase switched from -180° to 180° noted as 37.115MHz, see above. We can calculate the electrical length as c0/fo/4=2.019m and vf=0.867.

## Why do they disagree?

The problem is that the length measurements made are not from the reference plane, it is somewhere towards the VNA, and in fact both sections are physically a little longer.

We can use Velocity factor solver.

Above is the solution, the distance measurement zero point (the outer edge of the grey terminal block) is in fact 36.18ps (9.45mm) from the reference plane.

The final solution is good to 0.1% of velocity factor (pu).

## What about the nanoVNA ‘measure cable’ facility?

From this and the measured length of 1.750m we can calculate VF=1.75/2.073=0.844. The 3% error is attributable to the error in length measurement datum and reference plane. The error will be worse for a short cable section, less for a long cable section.

## What about the nanoVNA TDR (FDR) facility?

Above is a sweep 1-1500MHz with 401 steps and VF set to 100%.

Range resolution is about 100mm for VF=1, more like 87mm for this cable for maximum cable length of 40 for VF=1, more like 35m for this cable. The NanoVNA zooms to approximately 80% of this range.

So, we measure the first impulse peak at 2.109m. From this and the measured length of 1.750m we can calculate VF=1.75/2.109=0.829. The 5% error is attributable to range resolution and the error in length measurement datum and reference plane. The error will be worse for a short cable section, less for a long cable section.

## Parting thoughts

Some parting thoughts:

• popular alternatives are not as accurate as often believed;
• velocity factor is not independent of frequency, though it is approximately so for most good RF cables above about 10MHz;
• most applications are not as phase critical as believed;
• many if not most measurements I see described online give questionable results;
• solid dielectric coax cables are usually very close to datasheet, and results otherwise are questionable;
• foam dielectric coax cables do have significant variation (due to variation in gas content) and warrant accurate measurement for phase critical applications; and
• two wire lines pose a challenge with used with an ‘unbalanced’ instrument, and workarounds proposed are often troublesome.