Impedance effect of using 75 ohm coax between transmitter and an EFHW antenna

Question

I have been given several hundred feet of very high quality 75 ohm coax. I need a run of about 36' from my QRP transmitter (FT-817 with elecraft T1 tuner) to an EFHW antenna (about 75' long). Running the coax will be a difficult task so I am curious about the effect of using this 75 ohm coax instead of 50 ohm. Frequencies will be 3-54mhz. I have been using this antenna but with a temporary piece of 50 ohm coax and need to relocate the feed end of the antenna which results in a much longer run (was about 10').

I have a limited understanding of the issues involved but I think the 25 ohm difference would not cause much of a problem. However I request advice and guidance before I install the coax because of the difficulty of the install.

Answer 1

It won't make much of a difference. In fact, if the feedpoint impedance of the antenna is closer to 75 ohms than 50 ohms, it may be better. And if this is much higher quality coax (thus, lower loss) than the alternative, it will certainly be better.

If the coax impedance does not match the load (antenna) impedance, two things happen, which may or may not be a significant problem:

1. The VSWR is higher than 1:1, and thus there will be additional losses, and
2. the impedance seen by the transmitter will be the load impedance, centered around a constant-VSWR circle centered on 75 ohms.

It's easy to see what this "constant-VSWR circle" on a Smith chart.

Or to put it mathematically, VSWR is defined by:

$$ \left(\text{load impedance} \over \text{coax impedance}\right)^{\pm 1} $$

±1 is selected to give whichever provides a value greater than 1. So let's say the load impedance is 50 ohms, and you are using 75 ohm coax. That's an SWR of 1.5, because $75/50 = 1.5$. Then depending on the feedline length, the transmitter might see any impedance that satisfies:

$$ \left(\text{impedance seen by transmitter} \over 75\right)^{\pm 1} = 1.5 $$

So it might be 50 ohms, or 112.5 ohms, or any number of complex impedances in between.

Is this a problem?

Well, was your load matched to 50 ohms in the first place? End-fed antennas are notoriously difficult to predict, so probably not. So the impedance gets rotated about whether you use 50 ohm or 75 ohm coax, but you probably have a tuner which will be adjusted so the transmitter sees 50 ohms regardless.

Even if you don't have a tuner, a 112.5 ohm load isn't that bad for most transmitters. You'd have to consult the transmitter specifications to see the range of permissible impedances for it to deliver its rated power, but in many cases you'll be fine.

Answer 2

When considering atypical coax cable for ham applications, there are a few things that can come into play.

Shielding Material

Check that the shielding material is capable of being properly terminated in a PL-259 style connector. If the shield consists of braid plus foil, a crimped style connector may be the best choice.

Suitable Connector

The dimensions of 75 coaxial cable are different than those of 50 ohm cable. The result is that a standard 50 ohm coax cable connector may not properly fit over the dielectric and the braid of the 75 ohm cable. Check in advance to make sure you have a good fit.

Jack Material

Not all jackets are suitable for outdoor use. For example, the PVC jacket on Belden 9116 75 ohm cable is not rated for outdoor use.

Voltage Rating

Most coax cables carry a maximum RMS voltage rating. This will either be influenced by safety agency ratings or the maximum voltage that will not perforate the dielectric material of the coax.

The maximum RMS voltage on the coax is calculated as:

$$V_\text{RMS}=\sqrt{P_\text{xmtr}*Z_o*SWR} \tag 1$$

So with a 75 ohm coax, a transmitter power of 100 watts, and a 1:1 SWR the maximum RMS voltage on the line will be ~87 volts. But when the SWR is 25:1 as it could be on a wide coverage antenna, the maximum RMS voltage rises to ~433 volts. This would be well above the 300 volt RMS maximum voltage rating of Belden 9116 75 ohm cable, for example but well below the 2700 RMS voltage rating of Belden 8215 75 ohm cable. Check the manufacturer's datasheet for the specifications of the cable you will be using.

Tuner Connections

If you use a 50 ohm patch cord between your transmitter and the tuner, the transmitter will be able to develop its maximum rated output. The tuner will convert the 50 ohm impedance to match the impedance seen at the tuner end of the coax cable going to the antenna. This is the optimum configuration.

Coax Loss

The wide frequency range implies a potentially large SWR range. This can cause significant losses in the coax as the SWR increases. The tuner may match the transmitter to the coax but the SWR is still present. Depending on the coax, the majority of your transmit power could go up as heat in the coax.

Using low loss coax and placing the tuner closer to the antenna will help to minimize these losses.