Re: Technical Puzzle #25 - Linear Loading

Thankyou to everyone who took part again!

1. Resonant lengthWe can quickly rule out the 34ft option - that would make the linear-loaded vertical no shorter than a full-sized quarter-wave vertical, so there would be no point ever using linear-loading!

Nor can we simply say the total amount of wire, including the folds, must equal a quarter-wave - there are complex interactions taking place between the elements of the folded section, and it certainly isn't behaving like one continuous straight piece of wire. I know of no way to predict accurately the loading effect of the folded section other than to use a modelling programme. EZNEC predicts resonance when the height is 25ft -

making #3 the correct answer.

2. Resonant ImpedanceWe might well expect that the impedance of the linear-loaded vertical will be different from the 35 ohms of the full quarter-wave vertical - after all they are different heights and different construction. Many of you opted for the "higher than 35 ohms option". Let's look carefully at the currents flowing around that folded section in this magnified drawing:

Notice the currents at the top of the 10ft folded section - we have 1A in wire A and 0.65A in wire C flowing in one direction, and 1A in wire B flowing in the opposite direction. Those wires are so close together that the radiation from each wire will either cancel or reinforce the radiation in the others. So the net radiation will be proportional to 1A+0.65A-1A=0.65A. Similarly at the bottom of the folded section the radiation will be proportional to 1A+0.9A-0.9A=1A.

What we have here is a quite high current flowing through 3x10ft of wire, but because of the cancellation much less RF is being radiated than if the same current was flowing through a 30ft straight piece of wire.

That doesn't mean the antenna can't radiate effectively - it simply means we will have to supply more current to get the same power radiated than we would have had to supply into the quarter-wave.That gives us our answer: If Power=Current*Current*Resistance, and we know that with the linear-loaded vertical we have to provide more current to get the same power radiated, then its resistance must be lower;

that makes Answer #5 correct.

Don't be misled by the fact that this antenna is made up of 45ft of wire - it still behaves like an electrically short antenna that is 25ft tall. When we make verticals shorter than a quarter-wave their radiation resistance is always lower, no matter how we load them. To emphasise the point, if we looked at a vertical for 40m that was 6ft long with a large base loading coil, we wouldn't expect the length of wire making up the loading coil to cause the radiation resistance to be high; rather, experience tells us that a 6ft vertical will have a very low radiation resistance on 40m.

EZNEC predicts the radiation resistance of our linear-loaded vertical will be 15 ohms compared to 35 ohms for a full-size quarter-wave. That means we have to flow 50% more current into it than into a full-sized quarter-wave to radiate the same power. In turn that makes it potentially less efficient if we have a poor ground system; for example 50% efficient compared to 70% if the ground losses were 15 ohms. We could have achieved at least the same performance by base-loading a simple 25ft vertical with an inductor, and we could certainly have done better with a 25ft vertical mid-loaded with an inductor.

In summary: linear-loading is one way of making an antenna shorter, but it can't be treated as if it were simply a full-sized antenna with part of the wire folded up; it may be a convenient way to load a short antenna, but it's not the most efficient way. 73,

Steve G3TXQ