Shortened Dipoles and Capacity Hat Yagis

There is one seeming exception to these principles: the shortened Yagi "loaded" at the element ends with capacity hats. The exception is an illusion, because the hatted dipole is not loaded in the conventional sense. Rather, the main linear element section is shortened and the remaining lengths is composed of a symmetrical array of wires which is at right angles to the linear section and whose net radiation is at or near zero. Current along the linear wire at the point where the hat begins is the same as it would be on a full-size linear element. It divides among the wires of the hat array, and the array must be large enough to permit the element to reach resonance at the same frequency as the full-size element.

Under these conditions, the performance of a full-size Yagi and a shortened, hatted version will be very similar, at least with shortening no greater than about 70% of full size. Since the distribution of current along the dipole element is roughly sinusoidal, most of the current contributing to the antenna radiation pattern occurs in the linear section of the elements and very little in the hat arrays.

Modeling an element-end hat is not so problematical in NEC as modeling closely spaced wires of complex geometries. Because the net radiation from a hat is zero, interactions with the main element that might make results unreliable when adjacent segments differ in diameter are minimized. NEC hat models correspond very closely with those created with MININEC. The potential slight differences are minimized in this exercise by making the hat wires of the same diameter as the main element: 0.375 inch.

Antenna Frequency F-S Gain Feedpoint Z SWR MHz dBi Ohms Full 28 2.10 64.54 - j36.09 1.706 Hat 2.01 52.80 - j30.23 1.727 Full 28.5 2.11 68.19 - j18.07 1.301 Hat 2.02 55.80 - j15.09 1.307 Full 29 2.13 72.04 - j 0.08 1.001 Hat 2.03 58.98 + j 0.05 1.001 Full 29.5 2.14 76.19 + j17.90 1.280 Hat 2.04 62.33 + j15.21 1.292 Full 30 2.16 80.40 + j35.90 1.616 Hat 2.05 65.87 + j30.38 1.640

Although the hatted dipole at 70% of full size has a lower feedpoint impedance and a 0.1 dB lower gain, in practice, no difference in performance could be detected by any station using the two antennas side- by-side. A similar situation accrues to 2-element Yagis shortened to 70% full size and hatted. The comparison here is between a full-size Yagis and a hatted Yagi of 70% full-size in free space, both with a spacing of 0.12 wl (4.1')

Antenna Frequency Gain F-B Feedpoint Z SWR MHz dBi dB Ohms Full 28 6.98 5.46 15.32 - j48.24 7.12 Hat 6.73 3.30 11.99 - j51.30 10.0 Full 28.5 6.74 9.79 23.34 - j22.22 2.33 Hat 6.88 9.93 19.94 - j23.43 2.72 Full 29 6.25 11.19 32.47 + j 0.01 1.01 Hat 6.28 13.49 30.67 - j 0.61 1.02 Full 29.5 5.82 10.37 41.18 + j20.24 1.81 Hat 5.73 11.83 40.70 + j18.40 1.79 Full 30 5.48 9.18 49.11 + j38.92 2.76 Hat 5.31 9.78 49.16 + j35.62 2.70

Although the SWR of the hatted Yagi is higher than that of the full-size Yagi, the operating bandwidth (2:1 SWR) is actually a bit wider for the hatted beam. Peak front-to-back ratio is a little over 2 dB better for the hatted array, and it holds up better in the upper half of the frequency range investigated. Except at the lowest edge of the band, where the hatted beam passes peak gain and is on the descent of the gain curve, the feedpoint impedances are similar enough to be interchangeable. Had the design center of either beam been between 28.5 and 28.75 MHz, the beams would have provided respectable coverage of the entire 10-meter band.

The construction of hatted Yagis permits an additional construction variable: the effective diameter of the hat. The models shown here used simple hats of 4 spikes. Performance does not change with differences of hat construction, although different hat designs will require different sizes for given element lengths. For the Yagi demonstrated here, both elements used spikes of identical lengths and varied the element lengths to achieve the final results. Modeling suggests that this procedure yields higher performance peaks, possibly at the cost of slight reductions in operating bandwidth.

As will be evident later, hatted Yagis perform like what they are: virtually full size beams. The slight performance differences are due to two variables: the shorter elements and the revised geometric relationships between elements offered by those shorter elements.

Wherever an inductive load is placed, there is a current gradient representing the missing linear length for which the loading element substitutes. Because such loads are only effective where antenna current is high, the missing lengths of linear element represent radiation that for all practical purposes does not occur. Moreover, inductive loads, whatever their form, have losses associated with their resistance. Even high Q inductors introduce losses into the antenna element.

Both of these phenomena may be demonstrated by reference to shortened dipoles relative to full-size counterparts. Some loads are more difficult to model than others, but simple solenoid inductors may be modeled well within the limits of variables affecting any model's transfer to fabricated reality. Models treat solenoid inductances as wholly nonradiating elements, which is largely but not absolutely true. Coils do radiate a bit. However, the model also assigns the coil an effective zero space by distributing its loss along the element segment to which it assigned. That segment functions like a linear element, which in a real antenna is missing and replaced by the coil. The results remain as accurate to real antennas as any other aspect of antenna modeling. The more significant keys to accurate modeling lie in the realm of using adequate load values, placing them precisely, and using the proper technique of load assignment for the modeling task at hand.

To see effects of shortening antenna lengths alone, however, requires no load, but only an examination of short dipoles. For any model, the capacitive reactance at the feedpoint can be canceled by a lossless center inductance without any change of antenna characteristics. Notice the reduction of gain of the following antennas gradually shortened from full size to 40% of full size. All antennas at 29 MHz in free space, with the same 0.375" diameter aluminum element.

% of Full Gain Feed R Feed Xc 100 2.13 72.04 0.79 90 2.05 52.41 102.3 80 1.98 37.76 205.0 70 1.92 26.71 312.5 60 1.87 18.33 430.8 50 1.83 12.01 568.6 40 1.79 7.31 741.6

These gain reductions are equivalent to using lossless center inductors as loading elements, each sized exactly to compensate the capacitive reactance remaining at the feedpoint. Although the loss of gain is modest per step, it adds up quickly as we shorten the antenna. Missing gain in the individual dipoles of a 2-element Yagi cannot be restored for any given design. Notice also the reduction of feedpoint impedance at resonance down to values where basic efficiency may become a concern.

If we use real inductors having a finite Q, the losses grow even faster with shortening. The following table gives free space gain figures for coil Qs ranging from 300 to 50. A Q of 300 may be about the best obtainable before weathering effects reduce it. A Q of 50 represents a worst case scenario where maintenance is lax and acid rain is heavy.

% of full Gain with Q = 300 200 100 50 90 2.02 2.00 1.96 1.88 80 1.90 1.86 1.75 1.53 70 1.75 1.67 1.44 1.01 60 1.54 1.39 0.95 0.20 50 1.19 0.90 0.14 -1.07 40 0.52 -0.01 -1.25 -3.03

A dipole 50% of full size with a loading coil Q of 300 has lost nearly a full dB of gain, while the loss at 70% of full length is less 0.4 dB. Obviously, loss of gain increases faster than the rate of shortening. The rate of loss for lower Qs increases proportionately.

A center-loaded dipole can present the user with an illusion of well-being. The feedpoint impedance at resonance will be roughly the sum of the feedpoint impedance with no losses plus the resistive component of the coil's Q. With time, weathering, and lowering Q, a short, loaded dipole may seem to show an improvement in SWR relative to a 50-ohm feedline. In actuality, it is more likely that coil losses are increasing, and the additional resistance is simply converting power to heat.

An alternative to center loading is mid-element loading, that is, the placement of loading inductors somewhere along each element away from the feedpoint. Claims for significantly increased efficiency unfortunately do not materialize from this arrangement, although the arrangement does show a slightly lower rate of gain decline.

As the loading coil is split and moved outward from the antenna center, the required value of inductive reactance necessary to achieve resonance increases. By the time the coils are midway between the center and the element ends, each coil must have an inductive reactance of about 93% of what a single center-loading inductor would require. For equivalent coil Q, the nearly doubled resistance tends to wash out most of the gain increase occasioned by letting full current exist at and near the feedpoint.

As the following table shows, gain improvements are marginal. The chief benefit of mid-element loading is that the feedpoint impedance remains higher than with center-loading. As with the previous table, dipoles are 3/8" diameter aluminum in free space.

% full Load coil Feed R Gain (dBi) for Q = reactance Ohms inf. 300 200 100 50 per coil 90 93.0 @ 63.16 2.06 2.03 2.02 1.98 1.90 80 188.0 53.66 2.00 1.93 1.89 1.78 1.57 70 288.0 43.86 1.94 1.80 1.71 1.50 1.09 60 399.0 34.20 1.89 1.59 1.45 1.05 0.35 50 528.0 25.02 1.84 1.27 1.01 0.32 -0.8 40 690.0 16.78 1.80 0.68 0.21 -0.9 -2.6

Mid-element feedpoint impedance figures average about 10 ohms higher than center-loaded dipole feedpoint impedances for equivalent shortening. However, even with this improvement, illusions of well-being are possible. If one ends up with loading coils with a Q of 50 in a dipole only 40% of full size, the antenna will seem to match a coax cable very well--because the RF resistances in the coils will roughly add to the natural resonant impedance of the antenna. In that extreme case, the loss resistance would double the antenna resistance and occupy corresponding amounts of power.

In the end, there is little to choose between center and mid-element loading except feedpoint impedance and such mechanical considerations as may apply to the antenna structure. Center loads are more easily supported, but in some case a problem to feed. Mid-element loading coils often require one or two step-ups in element diameter to support the coil. Gains for the two systems, with coils of equivalent Q, would be indistinguishable in practice.

If both lines are equidistant from the main element, then straightforward shorted transmission line stub calculations are sufficient to calculate the required length of each stub. Each stub will require 1/2 of the reactance required for center loading. If the stub lines are not equidistant from the main element, unequal currents will be induced by the field from the main element, resulting in a longer linear load line. (For more on this subject, see "Modeling and Understanding Small Beams: Part 4: Linear- Loaded Yagis." Communications Quarterly, Summer, 1996, pp. 85-106.)

In some commercial beams, the linear load is made to appear to be placed farther out along the element. The main element is fed and, on each side, breaks at some distance from center. Smaller lines are run back toward the feedpoint, make a turn and return to the break, to be connected beyond the break point. Despite appearances, these antennas have center-loading linear loads composed of one fat wire and one thin wire. The main element is actually the return thin wire back to the break point where it attaches to the tubing used to finish the element. Although the system has much in the way of mechanical soundness to recommend it, and although the difficulty of calculating the precise length of needed linear load makes empirical experimentation more efficient in antenna development, the system is electrically quite normal.

To gain a sense of the advantages of linear loading, let's look at a dipole 70% of full length (11.4') and try to model linear loads of varying proportions upon it. For consistency and comparability of results, all models were done in NEC-4. Due to constraints within NEC, this procedure restricted the construction of linear loads using that same diameter material as the main element: 3/8" diameter aluminum.

Two types of linear loads were modeled: those placing both load lines equidistant from the main element and those lining up the lines vertically beneath the element. For these rough samples, variations were limited to changing the spacing from the main element and from line to line. The spacings were equalized: that is, if the space between lines was 3", then the space from the main element was also 3" for both types of loads. Where E = equidistant load lines and V = vertically suspended load lines, the sample models are these:

Antenna Specification E3 Equidistant lines 3" apart and 3" from the main element E6 Equidistant lines 6" apart and 6" from the main element V1 Vertically suspended lines with 1.5" spacing V3 Vertically suspended lines with 3" spacing V6 Vertically suspended lines with 6" spacing

In the table below, the meaning of all values is obvious, except perhaps equivalent Q. The value of equivalent Q is derived by replacing the linear load with an inductor of sufficient size to resonate the antenna and then adding resistive losses until the element gain equaled the gain of the linear-loaded element. Although these values are useful markers with respect to gain, they will be less useful with respect to operating bandwidth. "Length" indicates the total length of the linear load from tip to tip.

Antenna Length Gain dBi Feed Z Equiv. Q (R +/- jX Ohms) E3 4.46' 1.88 24.1 + j0.12 1150 E6 3.14' 1.89 21.3 + j0.32 1400 V1 7.50' 1.71 25.7 - j0.37 230 V3 5.36' 1.83 22.9 + j0.16 500 V6 3.64' 1.90 20.2 + j0.31 2000

From these few samples, some trends (verified by a large number of file samples) are evident:

1. The wider the spacing among elements, the higher the element gain and equivalent Q.

2. Vertically suspended linear loads vary more widely in length, gain, and equivalent Q than equidistant linear loads.

3. The wider the spacing, the lower the feedpoint impedance of the element.

Most notable is the lack of significant variation in the gain of the two equidistant linear load models. The spacing is doubled between the two, but the gain varies by almost nothing. These models correspond most closely to a pair of series connected transmission line stubs. Independent calculation of required stub lengths produces values for each side of center that are longer than the modeled stubs by about the length of the vertical connectors. The connecting lines are not the entire story here, since stub line calculations presume that the shorting connection at the stub end is insignificant. However, 3" and 6" connecting rods are likely of some significance here.

Vertically suspended linear loads vary more widely in part due to the unequal induced currents from the proximity of the main element. For these loads, the designer is faced with a trade-off: load spacing and element gain on the one hand and feedpoint impedance on the other. Equidistant load lines may be placed close to the main element to increase the feedpoint impedance without significant loss of element gain.

For a final comparison, we may look at the operating bandwidths of all the loaded elements, including those with a center-loading inductor, mid- element-loading inductors, and linear loads. As before, the table will show calculated SWRs for 28 through 30 MHz at 0.5 MHz intervals. Linear loaded antennas will be designated as given in this section. Center-loaded and mid-element-loaded antennas will be called CL and ML, respectively, and followed by a number representing a value of Q used in earlier comparisons. The inductor-loaded antennas will be restricted to those 70% of full size to correspond to the linear loaded models. A full-size dipole for 29 MHZ is included for comparison.

Figures for inductor-loaded models were developed by introducing the load(s) as inductors with the requisite reactance for resonance at the design center frequency. Since reactance varies with frequency, using a constant reactance would have produced too optimistic a set of SWR figures. All models retain the 3/8" diameter aluminum construction, and figures are for free space.

Antenna SWR at 28 28.5 29 29.5 30 MHz Full size dipole 1.71 1.30 1.00 1.28 1.62 CL-300 4.06 2.06 1.00 1.99 3.57 CL-200 3.96 2.03 1.00 1.96 3.50 CL-100 3.72 1.96 1.00 1.90 3.31 CL-50 3.32 1.84 1.00 1.79 3.00 ML-300 3.77 2.00 1.02 1.89 3.32 ML-200 3.70 1.98 1.02 1.86 3.28 ML-100 3.51 1.92 1.02 1.81 3.11 ML-50 3.20 1.83 1.02 1.71 2.82 E3 4.35 2.14 1.01 2.08 3.87 E6 4.34 2.12 1.02 2.10 3.88 V1 4.53 2.22 1.01 2.10 4.03 V3 4.30 2.12 1.01 2.08 3.85 V6 4.35 2.12 1.02 2.10 3.88

Carrying out SWR to 2 decimal figures is largely spurious in terms of practical operation. However, adding the final decimal place makes the trends clearer and also clarifies the lowest SWR on which the other figures are based.

All forms of element loading narrow the operating bandwidth and are roughly related to the Q of the loading element(s). For inductor loading, the 2:1 SWR bandwidth increases as Q decreases, but the differences are small. The differences between comparable Q-values for center and mid-element loading are smaller yet.

The operating bandwidth for a linear loaded element shows the inherently higher Q of the system, but the actual figures are not directly related to an assignable value of Q. Among the vertically suspended linear loads, V1 had the lowest assignable Q in terms of gain equivalence, but also displays the narrowest bandwidth of the entire group. Once a certain lower limit of element spacing is exceeded, operating bandwidth tends to be the same for all practical purposes.

In the end, the use of linear loading trades higher gain for a narrower operating bandwidth than inductor loading. Mid-element loading provides a higher feedpoint impedance than either form of center-loading.

The next question is how these characteristics of loaded elements will show
up in 2-element Yagis.

*Updated 5-6-97. © 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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