# ANTENNAS FROM THE GROUND UP

### L. B. Cebik, W4RNL

In our last episode, we looked (all too briefly) at some of the basic concepts underlying the operation of parasitic or Yagi beams. We noted the importance of near and far fields, as well as examining what mutual coupling was all about. Finally, we peeked at the idea of relative current magnitude and phase between 2 elements, one fed with a signal, and the other energized by mutual coupling. Although very far from the whole story of Yagi antennas, it is a start from comparatively basic ideas.

Let's continue our look at the relative current magnitude and phasing among elements. By keeping an eye on these quantities, we can get an insight into some alternative antenna designs and perhaps also see how the whole family of 2-element beams is interrelated. The kinship may remove some of the mystery surrounding antenna names like "ZL-Special," "HB9CV," and "Moxon Rectangle."

Fig. 1 will be one key to keeping track of current magnitudes and phase angles. In the typical 2-element array in which one element is fed and the other is energized via mutual coupling, we track the current magnitude and phase at the center of each element (the circles in the figure). Even if we fed both elements separately or if we energized the 2 elements from a third source, we would normally use the element center as our point of reference. For this little excursion, we shall not worry about the exceptions to our rule of thumb.

Last time, we saw that, for any given spacing, there was a limit as to how much we could change the relative current magnitude and phase just by adjusting the 2 element lengths. This action alone would not yield much more than 11 dB of front-to-back ratio with the elements 1/8 wl apart.

There is a technique we can use to obtain a better front-to-back ratio. We can feed both elements. In fact, we can by a number of means feed each element with a specific value for either the magnitude or the phase or both. To see how this might work, let's perform a small experiment.

Fig. 2 shows two 10-meter arrays. We shall not be concerned with how well they perform. Our interest in them begins with the fact that if we feed only one element, each array is resonant. What is also interesting to us is the fact that one array uses equal-length elements, while the other uses unequal- length elements. This difference gives us two (of an endless number of) possibilities for arrangements.

Now let's feed both elements. We shall arbitrarily set the current magnitude on the forward (upper) element in each case to a magnitude of 1.0 and a phase angle of 0.0 degrees. Then, we shall feed the rear (lower) element of each array with a current that is variable in both magnitude and phase angle.

The goal of the experiment is to find the exact current and magnitude that produces the maximum front-to-back ratio for each array. Actually, we can perform each maneuver with greater and greater precision at least in theory so that we end up with an indefinitely large ratio. When I performed this task on antenna modeling software, I stopped when the front-to-back ratio exceeded 50 dB. This is well beyond what we would need in practice, but it helped me create some interesting graphs.

Now let's add one more variable into the mix. We shall vary the spacing between the elements for each array. Since most 2-element arrays or beams are well under « wl from front to back, I chose to vary the spacing in 0.05 wl increments from 0.05 wl up to 0.40 wl.

What I wanted to find out for these two slightly different arrays is how the current magnitude and phase angle on the rear element (relative to the preset value on the forward element) might vary as we changed the spacing. These (and a number of similar) exercises proved to be very instructive.

One discovery is that for any combination of element lengths and spacings, there will be a specific value of relative current magnitude and phase angle on the rear element that will produce the deep rear null. That set of values will vary if we change the spacing or if we change the length of one or both elements. In other words, there is no general magic number for either how much current, or at what phase angle it is, on the rear element, relative to the forward element.

Each antenna configuration will have a specific pair of values that yields the maximum front-to-back ratio. If we look at Fig. 3, we can see how the values vary with spacing for our two sample antenna arrays. Let's start on the right axis with the current phase. Notice that as we change spacing, the required phase of the rear element current changes. Since both of our antennas are near resonance, the two phase curves overlap each other. Had one of them been well off resonance, the lines would have been further apart.

Since the two arrays have different element lengths, we should expect at least the current magnitude required for a maximum front-to-back ratio to be different and we can see the difference. The two curves track each other as we change the spacing, but at quite different current magnitudes.

Very often, phased arrays are set up to produce the maximum front-to-back ratio. This applies often to phased arrays of vertical antennas. But it also applies to some horizontal designs, such as the ZL-Special. This antenna uses a length of transmission line between elements. Among its other properties, a transmission line is a continuous transformer of voltage, current, and impedance. When we construct "phased" arrays, we are most interested in the transformation of the current magnitude and phase, relative to the forward element, where the phase line, the forward element, and the feedline join.

By choosing the right kind of line considering its characteristic impedance and its velocity factor and by choosing the right length, we can often get close to the best level of transformation to feed the rear element with the right current magnitude and phase angle. Here "right" means the best values to maximize front-to-back ratio, given the element spacing and lengths. Transmission lines come in only a small range of characteristic impedances. So if a certain element arrangement will not yield the deep rear null, we can change element lengths or the spacing until some useable line length does the job.

Of course, the absolute maximum front- to-back ratio occurs over only a tiny frequency range, and away from the test frequency, the value drops into the ordinary range say about 20 dB. In addition, maximum front-to-back ratios do not tend to coincide with maximum gain that the antenna might give. Some antenna designers look for a balance of properties.

Before we can look for the balance, we should find out how the rear element current magnitude and phase angle affect the maximum antenna gain for our small arrays So let's do a second experiment: find the rear element current and phase angle that will give us the highest gain from the element lengths we originally set up, but let's vary the spacing along the way.

Fig. 4 gives us an initial look at how the current magnitudes and phase angles change as we increase the spacing from 0.05 wl up to 0.40 wl. Once more, the phase angle changes considerably as we change the amount of spacing between the two elements. Yet, because the two antennas are near resonance, the curves for the required phase angle closely match each other.

In contrast to the phasing situation, the relative current magnitude required by the rear elements on each of the antennas for maximum gain differs for the two configurations. There is an average of more than 10% difference between the two levels.

However, what is interesting is that both magnitude curves are almost flat. Changing the spacing of either array does not change the ideal current magnitude by much, but the required phase angle will change.

There is no need to memorize any of this. Instead, simply develop an appreciation for the fact that the relative current magnitude and phase on the elements of a beam largely account for its performance. These values are affected by element lengths and spacing, and every configuration requires a careful study to find the values that give the best results.

Sometimes, those results are a compromise between maximum gain and maximum front-to-back. The HB9CV is an phased array that purposely uses intermediate values to obtain good 2-element gain with a good front-to-back ratio across most of any ham band for which it is designed. Like the ZL-Special, it uses a phasing system , but it consists of separate lines to the forward and rear elements, joined in the center.

Last time, we noted that there is a limit to how closely we can approach our ideal front-to-back phasing requirements just by adjusting antenna element lengths while avoiding the use of a phasing system. There is an antenna design that can do much better in the front-to-back department than the common Yagi with its linear elements.

In Fig. 5 we find the general outline of the Moxon rectangle. It is capable of better than 30 dB front-to-back ratio at its design frequency, whether we are talking about a wire version for 80 meters, a tubing version for 20 or 10, or one made from rods for 2 meters or higher. Let's see how the Moxon is able to improve on the Yagi without losing more than a couple of tenths of a dB in gain.

Like our Yagis, the Moxon has parallel wires, one forming the driver and the other forming a reflector. We would take our current magnitude readings at the centers of these element sections. Like any other antenna where wires are parallel (or nearly so), there is a great deal of mutual coupling. Hence, a good part of the radiation from the Moxon is produced by standard parastic means (meaning just like a Yagi).

However, the Moxon's parallel wires are only about 3/4ths full Yagi length, with the ends bent around. The driver ends point at the corresponding reflector ends. The driver length consists of length A plus twice the length of B, and usually, we choose the length to be resonant. The reflector overall length is length A plus twice length D. We choose this length to place maximum front-to-back ratio on the desired frequency.

"C" is the critical dimension. It sets the amount of the second kind of coupling involved in the antenna. The "tip" coupling (sometimes called "capacitive" to distinguish it from the mutual or "inductive" coupling between parallel wires) is set to get maximum front-to- back ratio. We then juggle the various dimensions to get a rectangle with the desired feedpoint impedance.

The combination of couplings allows the rear element to reach a set of current magnitude and phase angle values that comes close to the ideal for maximum front-to-back ratio. It does so without using a second (or phased) feed to the rear element. Magnitude values near to 1.0, phased at about 140 degrees, are common. If you look back at Fig. 3, you will see that these are close to ideal front-to-back values for a resonant array of element that differ in length. A most interesting array, indeed!

Updated 06-21-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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