Coax Velocity Factor in Baluns, Does it Matter? Part 2

In the previous post I discuss various attributes concerning the use of Baluns especially in the VHF/UHF bands. I point out other web sites with excellent tutorials on why and where to use Baluns in VHF work. Two particular Balun styles come up strong: 1:1 Coaxial Cable Balun and the Pawsey Stub otherwise known as 1:1 Folded Balun. Each Balun’s topologies are shown in Figures 1 and 2. I highlight the mistaken, I believe, assertion one should adjust the Pawsey Stub’s length by the amount of the coaxial cable velocity factor. Figure 3 shows why I think the Pawsey Stub length does not need as drastic a reduction in length as you might do for stubs that contain the electric and magnetic fields within their structure. Finally, I say I will prove my assertion the Pawsey Stub is electrically a 1/4 wave in free space or close.

What follows is the experiment which provides proof Velocity Factor of Coaxial Cables does not apply to cables used simply as a wire in parallel with another wire.

The Experiment

The two Baluns are an excellent pair to compare. The Coaxial Cable Balun is just two transmission lines tied together one 1/4 wavelength long, the other 3/4 wavelength long. In this case the electric and magnetic fields are entirely within the dielectric material. Thus the velocity factor adjustment should apply. The Pawsey Stub relies entirely on becoming a parallel transmission line with the feedline coax. Its fields are entirely outside the structure of the coax.

I built the two baluns using some RG316 coax. My target frequency for both is 300 MHz. I cut pieces with no corrections applied to see how the frequency changes.

The Coaxial Cable Balun has the following dimensions based on calculations…

• 1/4 wave section = 300m/s / 300 MHz * .25 = 25cm ~ 9.8 inches
• 3/4 wave section = 300m/s / 300 MHz * .75 = 75cm ~ 29.5 inches

I simply cut two pieces of coax to the above lengths and added a third with an SMA connector for the feed line.

Figure 4 shows the Coaxial Cable Balun with a 50 ohm resistance at the balanced feed point.

With the resistance at the feedpoint, the Balun should show some very obvious frequency dependence on a Return Loss or SWR plot. Because this is the case where Velocity factor does apply, the target frequency of 300 MHz should be lowered by .695 or about 208 MHz. Given that I flayed the coax shield and center, thereby reducing some of the coaxial cable length, the actual frequency should be a little higher.

Figure 5 shows what happens when I connect the Coaxial Cable Balun to the VNA…

Wow the 214 MHz pretty much confirms that Velocity Factor is well in play for this style of Balun.

Now let’s try the Pawsey Stub. The only critical dimension is the stub length.

• 1/4 wave section = 300m/s / 300 MHz * .25 = 25cm ~ 9.8 inches

Once again, my trimming slightly shortens the actual electrical length to about 9.2 inches which raises the frequency just a bit. Figure 6 shows my test unit with 50 ohms at the feed point.

What’s the prediction here? If you listen to the web sites which suggest coax cable VF applies, the frequency will be between 210 and 230 MHz. If I am right and this is free space, or very close to free space, then the frequency should be about 300 MHz, or since the connection points on the stub are a little closer together, something a bit higher. Let’s see the Return Loss plot…

Bulls Eye!!!!

This strongly suggests the lengths of external stubs, like the Pawsey Stub (or any Folded Balun variant), should be calculated using free space wavelengths without corrections for Velocity Factor.

The funny thing is, this has been the case in the ARRL Antenna book for many many years. The later editions never suggest to apply velocity factor to external stub calculations and the 13th edition specifically says VF does not apply.

Interference from Nearby Objects – an Additional Observation
Testing of the above two Baluns revealed an interesting behavior. The 1:1 Coaxial Cable Balun was immune to effects from handling during the test. The Pawsey Stub was very sensitive to touch or even being close to the stub portion. This evidence correlates well with the measurements suggesting the Pawsey Stub’s electric and magnetic fields are, at least some if not entirely, outside the realm of any dielectric material.

Conclusion
It is a good thing Amateur Radio Operators know about transmission line Velocity Factor specifications. Without this knowledge you would be cutting stubs incorrectly. However, some Amateurs assume that just because a piece of coax is used for a stub, Velocity Factor applies. The key to understanding when it does and when it doesn’t is found by following the electric and magnetic fields. Where are they? Are they inside the coax or outside between pieces of coax? If inside, apply VF. If outside assume freespace.

Measure, but verify…
This experiment relies on some crude cutting of cable lengths and assumed values of Velocity Factor. Potential sources of error include:

• Cable End Trimming – Source for my slight errors above
• Coax Velocity Factor not what the manufacturer says – When you do need to know VF, it might be a bit off especially with lower quality coax
• Freespace not quite freespace – Even the best air gap transmission line has some dielectric material in the fields – VF values of 0.95 are common even with parallel transmission ladder line.

So what does this suggest? If you are going to the trouble to make something as critical as a Balun for your Yagi antenna, electrically measure each cable with your SWR meter or VNA to ensure you are spot on the frequency of choice.

This was an interesting test. I am now so interested in Baluns, I will focus on posts for each type in the near future.

Thanks for reading.

John

Tags: Baluns, Pawsey Stub, Split Coax Stub