# Finding velocity factor of coaxial transmission line using the velocity factor solver

## Example 1: Youkits FG-01

we have two lengths of H&S RG223 terminated in identical BNC connectors at both ends. Let’s connect each in turn to a Youkits FG-01 antenna analyser and find the quarter wave resonance of each (ie the lowest frequency at which measured X passes through zero). Above, the line sections are connected to the Youkits, and the length overall is measured from the case of the analyser to the of the cable.

We need not worry that the actual cable length is a little less than measured (due to connectors), that will null out in the calculations. It is vital though that the measurements are made consistently and accurately.

Resonances are observed by middling the interval where Z is minimum.

The two cable lengths and resonances are:

• 1.919m: 25.025MHz; and
• 6.374m: 7.665MHz.

Entering those into Velocity factor solver we obtain: The key result is the calculated velocity factor is 65.68%. It can be used to calculate the physical length of a given electrical length at a given frequency. for example, if we wanted 180° of cable alone at 144.1MHz (and vf=0.6568), we could calculate using RF Arbitrary Transmission Line Loss Calculator that the physical length would be 683.2mm. Of course adjustment is necessary for any pigtails, connectors and adapters used.

The offset figure is the propagation time from the reference plane to the zero on the measuring tape (located against the FG-01 case), 243.8ps means that the tape zero in the picture is right of the reference plane by 243.861ps, the reference plane is well inside the box. This demonstrates that even with an analyser where the reference plane is not known, the measurement procedure discovers the true offset of the measurement plane from the zero reference for length measurement.

## Example 2: Rigexpert AA-600

I have two lengths of RG6 Dual Shield terminated in identical F connectors at one end, the other end cut cleanly square. I will connect each in turn via a N(M)-BNC(F) and BNC(M)-F(F) adapters to a Rigexpert AA-600 antenna analyser and find the quarter wave resonance of each (ie the lowest frequency at which measured X passes through zero). Above, the line sections are connected to the Rigexpert via adapters, and the length overall is measured from the case of the AA-600 to the of the cable.

We need not worry that the actual cable length is a little less than measured (due to adapters and connectors), that will null out in the calculations. It is vital though that the measurements are made consistently and accurately. Above, the quarter wave resonance measurement of the short cable. The analyser is adjusted to the mid point of the interval between X=-0.1Ω and X=0.1Ω. Above, the quarter wave resonance measurement of the long cable.

The two cable lengths and resonances are:

• 1.077m: 57.352MHz; and
• 3.083m: 19.857MHz.

Now the most common practice would be to simply calculate velocity factor from only one of these observations, but making some adjustment for the ‘actual’ end of the cable. Look back at the picture, should we deduct 60mm? Some other value? Make your own judgement (guess) and calculate the velocity factor from that observation alone and compare it with that found below.

Entering those observations into Velocity factor solver we obtain: The key result is the calculated velocity factor is 81.29%. It can be used to calculate the physical length of a given electrical length at a given frequency. for example, if we wanted 90° of cable alone at 50.1MHz (and vf=0.8129), we could calculate using RF Arbitrary Transmission Line Loss Calculator that the physical length would be 1216.1mm. Of course adjustment is necessary for any connectors and adapters used.

The offset figure is the propagation time from the reference plane to the zero on the measuring tape (located against the AA-600 case), -60.08ps means that the tape zero in the picture is left of the reference plane by 61ps. This demonstrates that even with an analyser where the reference plane is not known, the measurement procedure discovers the true offset of the measurement plane from the zero reference for length measurement (rather than a guess as is commonly done with single observation measurements).

## Practical tips

### Velocity factor tolerance

Velocity factor is a fairly well controlled parameter for solid dielectric cables, but less so for foamed dielectric. In critical applications, it is worth measuring velocity factor of foam cables, but measuring it inaccurately is of little use.

### Pigtails

It is well and good to measure velocity factor of cable, but be aware that gross errors in both the measurement exercise and application can accrue for untidy long pigtails.

### Resonance target

Choose to measure either the series resonance or parallel resonance considering the capabilities of the instrument. Low end instruments tend to be more accurate in locating the series (ie low impedance) resonance of a stub.

### Cable loss

It is often stated somewhat loosely that the input impedance of a 90° open circuit stub includes zero reactance. That is true for Distortionless Lines, and the departure for lossy lines may become significant in this test. for example, the electrical length of a quarter wave open circuit resonant section at 1MHz is ~90.26°, an error of 0.3%. Make the measurements at frequencies where Zo is close to purely real.

### Connector security

Tighten all connectors properly for consistent and accurate results

### Loose shield end

In the second example, the distant end of the cable is cut clean, which is fine. In the first example, the distant end is a BNC(M) connector which is fine as the centre contact and shield are rigidly associated.

If the far end was a connector like UHF(M) or SMA(M), the loose nut is the shield terminal and it needs to be secured for best results. That could simply comprise a F-F adapter (use the same adapter for both cable lengths).

## References

https://owenduffy.net/tx/concept/TappedCoil/index.htm

Velocity factor solver