Some of the FCC pool questions may lure you into making a mistake if you don’t pay attention. A good example of this is question E9C01 from the Extra Class section. You might be thinking that 180 degrees is the same as 0 degrees. This is absolutely true for anything that the Smith Chart will solve for you.

This may seem like no-brainer stuff and I am wasting your time. However, I maintain that if you understand the distinction between the electromagnetics presented by the Smith Chart and the electromagnetic energy that results from phase differences, you will suddenly become the one that other amateurs in your sphere of influence will migrate to with their questions.

## Loads and Cancelations

The nature of the Smith Chart is relational to the mechanical analogy of work. In the mechanical domain, work is defined as the application of a force to move a mass. A mass is just sitting there occupying space. But then a force acts on it moving it a distance. Work has now been performed which can be measured and quantified.

Moving to the electrical and thermal domains, a mass (such as a copper wire) is sitting there minding his own business when a force (a Voltage) acts upon him causing a current flow. Energy has been spent which can be measured and quantified.

In the above paragraphs, direction is not relevant. The direction of the mass movement does not participate in how much work was performed. When electrical energy is spent, it is always positive or at least without direction. You could define things a little differently where there is such a thing as negative energy but then you would have to explain why you no longer have loads.

The Smith Chart can be used for a variety of applications, but as a generalization, it is safe to say that it is solving for loading (impedances) and those elements contributing to impedances. Therefore, zero (0) degrees phase for the Smith Chart is the exact same as its 180 degrees of phase. If you had a 360 degree Smith Chart, then 5 degrees would be the same as 185 degrees. You would have a lot of unnecessary duplication. Simpler is better and thus the Smith Chart only has up to 180 degrees of phase and a half-wavlength.

But now consider something that the Smith Chart does not address. What happens when you add two signals together? We know that given a fundamental frequency and an infinite set of its odd harmonics (each A/n in magnitude), when you sum them together you get a perfect square wave. A square wave is in fact a whole bunch of sine waves. Further, it takes a full wave of the fundamental to make the square wave (360 degrees). Therefore, when it comes to adding signals (there is no subtraction, only addition of negatives) 234 degrees from 43 degrees means something.

## FCC Pool Questions:

**What is the radiation pattern of two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed 180 degrees out of phase?**

- A. Cardioid
- B. Omni-directional
- C. A figure-8 broadside to the axis of the array
- D. A figure-8 oriented along the axis of the array

The correct answer is D, a figure-8 pattern along the axis as if there were a north-and-south path. But when I originally looked at this, I though it was a trickster question designed to lure in the unaware. But we are talking about summing together signals. We have a signal that is 180 degrees out of phase from what is given to the other antenna.

Many thanks to our own Don Winsor who pointed out difficulties in what I had written.

## Consider the J-Pole Antenna and its Nature

The J-Pole antenna is a good example of wave cancelations.

The “U” part of the J-Pole is a classic dipole antenna when considered all by itself. It has two quarter-wave wires and is fed at its middle. But the “U” part of the J-Pole antenna does not radiate into the atmosphere with efficacy. Note our careful choice of words with “radiate” and “efficacy.” It does in fact radiate but without efficacy. The observed effect is as if it is not radiating into the atmosphere at all.

So, here’s the story: If you were to cut off the upper straight-wire half-wave section of the J-Pole and un-bend the lower U-section, the un-folded U-section would become a center-fed classic dipole antenna and would radiate like crazy WITH efficacy to the four corners of the globe. But bent up into a U-shape, the two quarter-wave radiators cancel each other…because they are EXACTLY out of phase. Think of them as mirror images of each other. When you add them together, you get zero.

## Transition Back to the Semi-Tractor Trailer

In another blog post, we wrote of antenna phasing, as is common with semi-tractor trailer rigs. In that post we noted antenna RF phasing that truckers would like their rigs to exhibit. Suppose the two antennas were mounted next to each other at the center of the cab instead of at the cab broadside extremities on the mirrors. From the explanation above we know that the antennas would be fully loaded and radiate but without efficacy yielding NOTHING into the atmosphere.

But now we have started moving the antennas apart from each other. This changes the configuration so that there is no longer a single standalone feed point but two feed points with transmission lines between them. It takes time for signals to travel these two transmission paths. Therefore, assume that the lengths are exactly equal. Thus there is no phase difference between them, and the two quarter-wave antennas are therefore fed IN PHASE or 180 degrees out of phase (your choice). 0 (zero) phase and 180 degrees phase are identical for this discussion.

With an undefined distance between the two quarter-wave antennas, there is less cancelation. Some RF energy will therefore escape into the atmosphere. But its nature is undefined. But it should be understood at this point that there is a distance and phase where the trucker’s dream of finding the Holy Grail comes true of full efficacy forward and rear and nulls broadside.

## Finding the Holy Grail

Recall that zero degrees (zero wavelength) and 180 degrees (a half-wavelength) are identical for this discussion. Let’s move the two quarter-wave antennas a half-wavelength apart while maintaining equal transmission line lengths. Equal transmission line lengths mean zero phase difference on the antenna inputs. We know that the two antennas will radiate as before, but what difference should we expect in efficacy?

## Two Planes, Four Directions

Let’s think it through, once again, throwing away the cookbook. There are two planes (or directions) applicable. On one plane (which has two directions), the two antennas look at each other in one direction and see no obstructions in the other direction. On the other plane, the two antennas see no obstruction in either direction.

**The Plane Where the Two Look at Each Other**

We can expect 100% cancelation where the antennas send energy to each other in exact phase. That is, from horizon to horizon. On that same plane, horizon to horizon, but exactly in the other direction, the energy has been nullified so a perfect null results.

But what should we expect from those waves looking slightly off the horizon? There will be a vector cancelation. This is where the magnitude of cancelation will depend on how far from the horizon is being considered. Almost on the horizon, the cancelation will be nearly complete. Considerably away from the horizon the cancelation will be minimal.

But that brings up the next question. What happens to that portion of the energy that is not canceled? Answer: It radiates to the four corners of the globe.

But recall that there is another exact replica antenna only a half-wavelength away being fed with the exact same signal. What effect is there from the interaction of the two? The answer to this lies in consideration of the other plane with its two directions.

**The Plane Where they See No Obstruction in Either Direction**

For this plane, much of the above discussion can be repeated. But what becomes the subject of discussion now becomes in the interaction of the two planes.

We already saw that there was a vector cancelation between these two. But if there is a vector cancellation, the natural result to expect in consideration of a vector cancelation is a vector addition with what is left. So, yet, it is true. There is a vector addition such that radiation is minimal for a broadside vehicle perspective and a doubling of radiation for a forward/reverse vehicle perspective.

Thus, we can see that if the two antennas are spaces one half-wavelength from each other with transmission lines of equal length from the transmitter, the Holy Grail is realized.

## Attaining the Holy Grail

Truckers are operating CB rigs which the FCC allocates frequencies of 11 meters. What is a half-wavelength of 11.0355 meters? It is 5.51775 meters (channel 19) which equals 18 feet and 3/32 inches. It is impossible to place the quarter-wavelength antennas that far apart so the trucker is simply out of luck. Or is he? No, not by a long shot. He can place the antennas as far apart as possible and then add a calculated distance of feedline length to one of the antennas creating a *phase difference*. It is simple to do but beyond the discussion of this blog post.

The important thing to take home from this discussion is that you should hate cookbooks. ðŸ™‚