# A GAP in Our Understanding of Feedpoints

### L. B. Cebik, W4RNL

One enduring cluster of questions often raised by newer antenna builders involves the gap at the center of an element at the feedpoint connection. Apparently a number of misconceptions have arisen to create concerns, especially if a person who writes an article about an antenna does not specify how wide the gap should be for that antenna. These notes hope to at least partially dispel some of the misconceptions.

You may note that I am placing this set of notes in the section of the index concerned with transmission lines. There are 2 reasons for this placement, one a matter of convenience, the other a matter of fundamentals. Because the subject does not strictly belong in any of the other sections--which I have divided according to antenna types and frequency ranges, it is convenient to place it here. The general principles apply to any antenna for any frequency whatsoever. More important, newer antenna builders tend to think of the feedpoint gap as a function of the antenna element. As we shall see, the feedpoint gap is a function of the transmission line. More specifically, it is a function of the feedpoint-antenna connection point as a remote source for the antenna.

Let's begin by clearing the air in terms of the two most common questions that newer antenna builders pose about the feedpoint gap.

#### Considering the Gap, How Long Is an Antenna Element?

Let's consider 2 antenna elements, each one composed of wires, rods, or tubes on each side of the feedpoint gap. Lengths L1 and L2, as shown in Fig. 1 can be equal, but need not be. The considerations that apply to center-fed elements also apply to off-center-fed elements.

The only difference between the 2 elements in the figure is the size of the feedpoint gap. So the question transforms it self into this one: Is the element length L1 + L2 or is it L1 + L2 + Gap?

The general answer that applies in almost all cases appears in Fig. 2. The element length is the total tip-to-tip length of the element, regardless of the size of the gap. There are some practical building constraints that we should observe, but for almost all cases where the gap represents an opening for connecting the feedline, the answer in Fig. 2 applies.

#### What Really is the Feedpoint Gap?

Since feedpoint gaps may vary in size, even for antennas of similar design for the same frequency, the general answer we have just given sometimes causes confusion. Individuals sometimes have a difficult time trying to formulate what the confusion is, but it usually boils into this question: what precisely is a feedpoint gap. The answer to this question involves an understanding of what goes into building an antenna element with a feedpoint.

Ordinarily, we have 2 element halves or sections plus a center insulator or cable connector. This description omits one set of critical elements--the wires that connect the element sections to the feedline or connector. In many amplifier and similar circuits, we tend to think of connecting wires as conveniences to ensure that all of the components meet all other relevant components. Most of our concerns are focused on eliminating stray effects by keeping the leads or connecting wires as short as possible or routed where they can neither emit nor receive anything harmful to the circuit's operation.

Antenna-to-feedline connecting wires, however, have a very different place in life. Most often, they are part of the antenna. Sometimes--by accident or by intention--they may be part of the feedline as well. But let's start by looking at them as part of the antenna element. Fig. 3 illustrates the basic case.

The "real" or "actual" gap is simply the distance between the wires of the feedline. (Now we know why I have placed this note among the transmission line notes.) The connecting wires are parts of the antenna elements. For a parallel transmission line, the gap is simple to see and appreciate. When using coaxial cables, the use of a connector at the feedpoint can obscure the fact that the real gap is the distance between the center conductor and the braid that make up the feedline. Note that in both cases, I have created an ideal situation in which the connecting wires are in the same plane as the antenna element. I even created a small gap in the braid oval so that you can see that the center conductor connecting wire does not touch the braid.

Ideally, then, the connecting wires are a part of the antenna element. So we may think of those wires as an extension inward of the antenna element section until it reaches the proper side of the feedline. Since the feedline transfers energy from the source or transmitter to the antenna (and conversely from the antenna to a receiver), we may think of the gap as the energy source. Fig. 4 provides this picture for the transmitting situation. We may replace the source symbol with a load symbol to capture the receiving condition.

Let's look at Fig. 4 from 2 perspectives. First, from the point of view of the antenna builder, the gap disappears electrically, even if it is required physically for the feedline connection. The source is in series with the element regardless of whether we make a direct connection to the antenna or use a transmission line. Since a source has no dimension of its own, outside of the physical requirements for connection, the antenna element is continuous from tip-to-tip.

Second, let's take another look at the source point of the antenna element. Making connections of any sort requires that we interrupt the continuity of the element to insert the source. Hence, we necessarily have a gap. There will be element material ends that face each other across the gap, and these ends will exhibit a capacitance relative to each other. For HF antennas using normal materials, we tend--as practical builders--to ignore the very small gap effects. However, those who design antennas for UHF frequencies and those who experiment withh very fat elements become very much aware of the capacitance. In fact, antenna modeling software calculates gap properties using the source segment as the gap. The software then factors these calculations into the overall model of the antenna, just as it does the special calculations for effects that occur at the outer ends of the element.

#### Does the Second Look at the Gap Have Any Effect on How We Treat the Feedpoint Connection?

If you are copying a design from an article in a journal or a handbook, then following the construction instructions ensures that you will take any gap effects into account, since the prototype antenna did so. However, let's look at construction practices a little more closely to see what these notes imply for a practical antenna. We may begin with a coaxial cable as our feedpoint connector. Fig. 5 shows the outlines of a UHF connector, but the same general rules of thumb apply to BNCs, SMAs, Ns, and any other coaxial-cable connector.

We can divide the connecting wires into 2 segments for each one. Segments A and A' are the ones that are inward extensions of the antenna element. Ideally, they should be the same length. This requirement is not critical if both sections are very short and we are using an HF frequency. In addition, the current of a half wavelength element does not change rapidly at the element center. Hence, a very small amount of off-center placement makes no difference to antenna performance. However, ideally, we should keep the amount as low as permitted by the connector type that we are using.

Practical building constraints often dicate that we must use the connecting-wire sections labeled B and B'. Keeping these segments as short as possible is the ideal. Also ideal is making them the same length. However, connectors tend not to cooperate fully, since most coax connectors have a projecting center pin and a shell below it. As well, the only convenient place to make a connection between the shell and the element section is at a point lower than the upper lip of the shell. Once more, at HF, these slight differences between B and B' make little difference.

In fact, we often have occasion to stretch the ideal situation. We can do so with no harm at HF, since a wavelength is so long and the actual leads are only a tiny fraction of a wavelength. Fig. 6 illustrates a few variations on the ideal theme.

On the left is a simplified representation of a feedpoint with a beta match hairpin at the feedpoint. The hairpin or shorted transmission-line stub has a width and length calculated to provide a certain inductive reactance across the feedpoint. For very practical reasons we may wish to use a common connection point on each element half for both the hairpin and the feedline connector. The fewer connections we create, the fewer connections we have to worry about in terms of degradation by weathering.

Some builders use a plastic housing to provide some weatherproofing for the pin-side of the connector. This treatment lets us avoid slathering waterproofing goop over this vulnerable side of the connector. (The cable side also needs waterproofing, but allows us to install it in a more orderly fashion with an eye toward periodic removal and renewing.) Adding a waterproof housing to the connection may require us to use longer than normal leads for our connections, even if they are inside a plastic or RF-transparent box.

From an idealistic perspective, the relatively thin leads do not distribute current in the same pattern as the fatter main element halves. However, at HF, these leads are only a very tiny fraction of a wavelength. Hence, they do not disturb the current distribution on the element in any measurable way.

At UHF, we may become concerned with the cumulative effects of the leads. In such cases, we have an alternative shown on the right in Fig. 6. We may directly connect the coax to the element using as close to zero-length leads as feasible. As well, we may take great care in dressing and soldering the connections so that we do not have solder lumps and other construction anomalies.

Let's pause here to reconsider the effects of the connecting wires labeled B and B' in Fig. 5. We have noted that the length of B and B' were not critical in the HF range, but might be so in the UHF range. Consider the fact the B and B' form a parallel transmission line section that runs from the coax connector to the antenna element. Now let's specify that we have so arranged the antenna element that it has a feedpoint impedance of 50 +/- j0 Ohms at the gap point where the horizontal wires (A and A') turn downward into the parallel transmission line formed by B and B'. We may ask what the impedance is at the other end of the line B-B' where the actual 50-Ohm coax line begins.

The answer to that question depends on 4 factors: 1) the diameter of the connecting wires; 2) the spacing between the wires; 3) the length of the wires B and B'; and 4) the frequency of operation. The characteristic impedance of the transmission line B-B' is a function of the first 2 factors. Let's use #12 wire (0.0808" diameter) and set the wires 0.111" apart center-to-center. These specifications set the characteristic impedance at 100 Ohms. The actual spacing is likely to be wider, with a resulting higher characteristic impedance, but these values will do for a simple example.

Next, let's choose 14 MHz as a mid-range HF frequency and 432 MHz as a UHF frequency. Finally, we shall evaluate the transformation of our 50-Ohm antenna feedpoint impedance with the length of B-B' set at 1", 2", and 3". The following small table gives us the results.

```Sample Impedance Transformation for Parallel Leads at 2 Frequencies

Lead Length       14 MHz                 432 MHz
(Inches)          (R +/- jX Ohms)        (R +/- jX Ohms)
0               50.0 +/- j0            50.0 +/- j0
1               50.0 + j0.6            52.0 + j17.3
2               50.0 + j1.1            58.7 + j35.0
3               50.0 + j1.7            71.8 + j52.9
```

Clearly, lead length in the form taken by B-B' as a short section of parallel transmission line makes virtually no difference in the HF region. However, even 1" leads at the improbably close spacing of the leads in the example produces a significant impedance transformation, especially in terms of the inductive reactance, at the beginning of the true coaxial cable run. As a result, the higher the operating frequency, the more important it becomes the keep the leads designated as B and B' as short as possible. The scheme on the right in Fig. 6 represents one way to approach the desired UHF goal of zero-length leads.

#### What About Wire Element Connections?

Fig. 7 shows a typical wire-antenna center set-up. The sketch omits refinements that will add mechanical strength to the feed-line-antenna junction. The actual connection fixture can be as simple as an insulator with end loops for connecting the wires. Alternatively, it may be a fancy fixture with the feedline compressed inside to relieve the wire connections of bending stresses that eventually result in a broken connection. For open construction, we often solder the wrap region to preserve and protect the electrical continuity between the 3 pieces of wire that we have wrapped into a single line.

Essentially, we have a nearly ideal situation where there are no leads to be labeled B-B'. The only discontinuities along the antenna element are the slight changes in diameters at the soldered section, the loop through the insulator, and the short wire lengths from the end of the transmission line to the insulator loop openings. At HF, these small variations make no practical differences in the operation of the antenna element.

There is a variation of the system that deserves a quick look. It is possible to have an antenna element at some higher impedance (let's say 800 Ohms) and to effect a match to a lower-impedance transmission line (perhaps 600 Ohms) by a simple technique. We simply spread the 600-Ohm line gradually as we approach the antenna feedpoint. The left side of Fig. 8 shows the general scheme.

The system works best under 2 conditions. First, the impedance change is not too great. Second, the length B is considerably longer than the ultimate gap length A. The right side of Fig. 8 gives us an equivalent circuit in arbitrary step sizes. The actual analysis would use step sizes that are each infinitesimal. However, a useful sketch would not then be possible. Along the spreading line length designated as B, each change of spacing between the line introduces a new line segment with a slightly higher characteristic impedance. Hence, the spreading line has the form of a large cluster of transmission line segments, each with a slightly different characteristic impedance.

However, each step introduces a small but definite length of wire that is parallel to the antenna wire itself. Therefore, each step yields some radiation. I have not given any particular dimensions for the lines, and certainly not the dimensions that we might physically calculate as yielding an 800-Ohm parallel transmission line. The mixed function of the spreading line will change the required dimensions with respect to the overall A length necessary for an 800-Ohm impedance at that end of the line. Experiment and experience are generally the best guides to setting the dimensions for a spreading line.

We should not confuse the type of impedance conversion in Fig. 8 with some others. In the case that we have been examining, the antenna impedance is higher than the characteristic impedance of the line before spreading, and the element has the normal source gap at its center. There are some other related schemes that work in the other direction, matching a lower antenna impedance to a higher feedline impedance. Fig. 9 provides some samples that rarely appear in the same drawing. However, the Delta, Tee, and Gamma match systems are members of the same family.

The oldest of the sibling matching systems is the Delta, although we do not find many practical uses for it today. In earlier radio days, home-made parallel transmission lines ruled most amateur antenna installations. Suppose that we have a 70-Ohm resonant 1/2 wavelength dipole, but a 600-Ohm transmission line. How do we effect a match?

Let's start by not opening the antenna element center. Instead, let's attach a spreading transmission line to points on the antenna so that we achieve a matched condition. The length of the spreading line (that forms an inverted Greek Delta) and the spread interact so that experimentation becomes the most reliable guide to finding the right attachment points. As well, just like the earlier case, the angled wires have vectors that are parallel to and at right angles to the transmission line. The right-angle vector, of course, is parallel to the antenna wire and represents a source of radiation in addition to the antenna wire. Since we use coaxial cable for virtually all monoband resonant dipoles these days, the Delta match has mostly historical interest.

However, if we bring the transmission line close to the antenna wire and run a wire on each side and parallel to the antenna, we transform the Delta match into a Tee match. The wires or tubes of the Tee section are parallel to and radiate just like the main radiating element. Note that just like the Delta match situation, the main element has no gap because we are not inserting the source (transmission line) at that point.

The Tee match system has many practical complexities outside the scope of this particular set of notes. The parallel Tee rods or tubes are normally thinner than the antenna element itself. In fact, the Tee match finds its most general use with Yagi antennas where the feedpoint impedance (if we opened the element at the center) would be considerably lower than 50 Ohms, the standard value for the most used coaxial cables. We find a number of commercially made UHF Yagis still using the Tee-match system. In the HF range, some builders use a Tee match to elevate low element impedances up to 200 Ohms. At that point, they insert a 4:1 balun at the element, thus bringing the impedance down to 50 Ohms and effecting a change from a balanced feed system to a single-ended coaxial cable feed system.

For many choices of length and diameter for the Tee-bars/tubes, the impedance at the feedline terminals will show some inductive reactance. So a number of installations will use series capacitors so that the terminals shows a purely resistive impedance. However, with judicious calculation, planning, and experimentation, we can usually find Tee-bar length and spacing values that will allow capacitor-less connections.

An added advantage of the Tee match system is that it allows the Yagi element to be continuous. In that condition, we may pass it through the boom in the same way that we pass the parasitic elements. In most cases today, only HF antennas make direct connections between the boom and the element. VHF and UHF Yagis tend to use insulated bushings at the boom pass-through points. Direct element connections with the boom have ways of weathering and aging, with a resultant increase in self-generated noise. However, even with an insulating plate to separate the element from the boom, a Tee-match system is still serviceable.

A variant of the Tee is the Gamma match, shown on the right in Fig. 9. It also functions to match a low element impedance to a higher feedline impedance, and the most common use is with low-impedance Yagi drivers and coaxial cable feedlines. The Gamma match is designed for driven elements that directly connect to the boom. However, the Gamma match is inherently single-ended, with the coax braid connected directly to the element center, which is also the boom. For the range of materials used to make a Gamma match, a series capacitor is a normal part of the system at the junction of the feedline center conductor and the Gamma rod.

In the present context, the only reason for looking briefly at the Tee and Gamma matches is to note their kinship to the older Delta match. All three use a continuous, that is, no-gap element and find connections that will raise a lower impedance antenna center to a higher value at the feedline junction.

When we began these few notes on the gap at the center of driven antenna elements, we thought of the gap as simply a break of the antenna element. In the end, the gap is a function of the feedline, which supplies energy to the antenna. Any gap in the element itself has some effect on the feedpoint impedance, but with normal materials at HF, these effect is negligible for practical installations. Gap effects become noticeable with outsized materials or very high frequencies. The actual gap is the distance between the conductors of a feedline, viewed as the energy source for the antenna element. We examined a few of the complexities that typical installations encounter, some of which are unintentional and others of which are intentional.

For most cases, changing the way we look at the feedpoint gap in an antenna element removes most of the questions about standard installations. As well, understanding the role of the connecting wires may allow us to construct antennas that present fewer problems during the field tune-up phase. We can then place our questions and concerns at the point where they will do the most good for the final product.

Updated 01-16-2005. © 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.