Fundamentals of coax 2

You can not simply connect a piece of coax to a wire and expect it to work. We can simplify it somewhat if we think of the coax as simply two wires. We have a center conductor and a braid, also called a shield. If we take a wire, let’s say it’s 66 feet long, and connect the coax right at the center. We do that by cutting the wire in the center and connecting the center conductor to one side and the braid to the other. We have just made a dipole fed with coax. Will it present a 50 ohm pure resistive load to the coax that we want? The answer is maybe. 

A 66 foot of wire is resonant at about 7.1 MHz on the 40 meter amateur band. Resonant only means that there is no reactance. The wire will appear as a pure resistance anywhere we break the wire and connect the coax. If we connect the coax at the center we have a point where the resistance will be low. If we move off center we have a point where the resistance will be higher. Near either end the resistance will be maybe 2000 ohms. We will not discuss how to connect the cable at the very end as in the common EFHW antenna right now.

So we see the resistance that will be presented to the coax can vary from “low” to “very high” depending on exactly where we connect the coax. 

We can usually connect the coax at the center and if we operate around 7.1 MHz we will probably have a close match to coax. The resistance at the center of a resonant wire varies with the height above ground. The resistance starts out much lower than 50 ohms when very low and increases to 50 ohms at some height near 1/8 wavelength and continuous up to near 100 near 3/8 wavelength then drops again to below 60 ohms near 5/8 wavelength where it increases again to just above 80 ohms  and continues to oscillate above and below 73 ohms  until at a very great height it essentially stabilizes at about 73 ohms. 

As long as the antenna is resonant, or very nearly so, we can expect the impedance at the center to be in this range unless the antenna is less than 1/8 wave above the ground or in close proximity to some other conductor that may be of such a critical length as to adversely affect the antenna impedance.

The resulting SWR with 50 ohm coax connected at the center should be 2:1 or less as long as the antenna is 1/8 wave or higher. This will occur on the fundamental frequency for which the wire is half wave resonant and should also occur at approximately three times the fundamental frequency. Such a wire will actually be resonant just a bit higher than three times the fundamental. 

Feeding such an antenna that is one wavelength long instead of a half wavelength long will present the coax with an extremely high impedance. However since some of our bands are harmonically related one length of wire can be resonant on several frequencies such as 3.5, 7, 14, 21 and 28 MHz. As long as the antenna is resonant we will have a pure resistance with very little reactance near the resonant frequency regardless of where we connect the coax. 

By connecting the coax at some point not in the exact center we can find a point that has a resistance near 200 ohms on several bands. That makes it possible to use 50 ohm coax with a 4:1 impedance transformer. As long as the impedance is less than 400 ohms a SWR less than 2:1 should be possible on several bands. 

When using a 4:1 transformer any time 50 ohm coax is connected at a 200 ohm point the SWR should be perfect. The 200 ohm antenna is transformed down to 50. ( 200/4=50)

At the upper limit, if the coax is connected at a 400 ohm point the SWR should be 2:1. The antenna impedance is transformed to 100. (400/4=100).

This works for wires that are resonant or close to resonant and the reactance involved will be small. Trying to operate too far off resonance will cause the impedance to be no longer resistive and the reactance / complex impedance raises the SWR higher than 2:1. This causes additional power loss in the coax. If the losses can be tolerated then either the built in antenna tuner or an external antenna tuner can be used. Although we use the term “antenna tuner” these devices do not tune the antenna, they simply transform an impedance at the input to the coax to something that will allow the transmitter to handle.