What Can We Expect From a 2-Element Beam?

Part 4
Loaded Yagis

L. B. Cebik, W4RNL





Loaded Yagis

One poorly appreciated fact about shortened Yagis is to what degree the antenna geometry plays a role in optimizing performance. When looking at shortened Yagis with hatted elements, we found a set of dimensions for the driven element and the reflector which provided close to the best obtainable performance for a 2-element beam designed to maximize front-to- back ratio and to resonate the beam. Interestingly, if we retain a driven element that is about 70% full size, we may use virtually the same main element dimensions with all forms of loading and achieve close to the best performance obtainable.

In essence, all methods of loading (center inductor, mid-element inductors, or linear loading) are doing the same job in the same manner: replacing a linear section of antenna element with inductive reactance. A beam with elements about 70% of full size will have the same optimal geometry, whichever loading method is used.

Because maximum gain at the design center frequency results in poor, if not unusable, performance below the center frequency, the models we shall examine will by optimized for maximum front-to-back ratio and resonance. For some models, the maximum gain frequency will lie very close to (and below) the front-to-back peak frequency, and the beam reversal point for a few samples will fall inside the 2 MHz 10-meter span we have chosen as our test bed. In fact, for loaded Yagis, the performance below the center frequency drops off much more rapidly than performance above the center frequency, especially when compared to the rates of degradation for a full size beam.

We may begin with 3 models: 1 each of the center inductor, mid-element inductors, and linear loaded variety. Each antenna will be spaced 0.12 wavelength (4.1' at 29 MHz). The driven element will be 5.7' long, with a reflector 5.93' long. Elements, as in all the models in this refresher, will be 3/8" diameter aluminum.

The center-inductor loaded model called for an inductive reactance for each element of 288 Ohms. This translates into a solenoid with an inductance of 1.5806 microH to achieve resonance and very close to peak front-to-back ratio.

The mid-element loading coils needed to yield the same result had 280 Ohms reactance or an inductance for each of the 4 coils of 1.5367 microH. The gain, front-to-back ratio, and feedpoint impedance of these antennas are listed in the table. A series load resistance is also listed to produce coil Qs of 300, 200, and 100, in order to investigate the effects of Q on performance. Models are in free space for this initial design test. A full-size Yagi of the same (0.12 wavelength) spacing is included for comparison.

Antenna   Resistance     Gain (dBi)     F-B (dB)  Feed Z (R +/- jX)

Full-size       --       6.25           11.19     32.47 + j0.23

Center-load
Infinite Q       0       6.18           20.22     16.69 + j0.02
Q=300           .96      5.76           18.40     17.74 - j0.66
Q=200          1.44      5.55           17.63     18.26 - j0.98
Q=100          2.88      4.98           15.70     19.84 - j1.90

Mid-element-load
Infinite Q       0       6.28           17.04     24.31 + j0.31
Q=300           .93      5.84           15.79     25.97 - j0.67
Q=200          1.40      5.64           15.25     26.80 - j1.15
Q=100          2.80      5.05           13.80     29.29 - j2.51

Let's look at the patterns, one factor at a time.

Gain: Theoretically, the loaded Yagis can attain the gain of a full size beam, IF Q could be increased without limit. However, once a finite Q is introduced, the gain drops rapidly. With an optimistic Q of 300, the gain of either load model approaches a half dB less than a full size Yagi with the same design goals. Another 3/4 dB disappears in the transition from a Q of 300 to a Q of 100. Most coils cited in commercial designs have had values below 300 and above 100, so the actual gain of such antennas will be between 5 and 5.75 dBi (or around 3 to 3.5 dB better than a dipole in free space). Gain expectations for a beam 70% full size and spaced 0.12 wl that are higher than this are unwarranted.

Front-to-back ratio: Shortened Yagis are capable of much higher front-to- back ratios than full size 2-element Yagis. The center-loaded model has a theoretic 3 dB advantage over the mid-element model, although that quickly decreases with finite Qs. Nonetheless, one true advantage of a loaded Yagi over a full-size model is the superior front-to-back ratio.

Feedpoint impedance: The center-loaded model exhibits the lowest feedpoint impedance of any of the loaded 2-element Yagis. Although it can be used with Coax with a beta match, the low impedance raises questions of basic efficiency in terms of power consumed by resistive losses throughout any practical assembly. Note that as Q decreases, the feedpoint impedance increases proportionally to the total series resistance in the driven element.

It is also significant to examine the operating bandwidth of loaded 2- element Yagis. We would expect something narrower than a full-size Yagi, and figures do not disappoint us. Models for obtaining operating bandwidth and other figures across a span of frequencies must enter the resistance and inductance of the loading coils (rather than resistance and reactance) and allow NEC to calculate the reactances for each frequency selected. Again, the full-size Yagi is presented for comparison with only the Q=300 models of loaded Yagis.

Antenna   SWR at    28        28.5      29        29.5      30   MHz
0.12 wl full-size    7.12     2.33      1.01      1.81      2.76
Center-ld, Q=300    18.65     5.30      1.04      1.99      3.05
Mid-el-ld, Q=300    18.03     5.24      1.03      2.12      3.38

The operating bandwidth of the loaded Yagis is so narrow that the 2 MHz spread is too wide to be informative. It is clear that the SWR climbs very much more slowly above the design center frequency than below it. Whether the antenna has worthwhile characteristics in that region requires that we look at most of the antenna's properties over a narrower spread of frequencies--perhaps a half MHz either side of center.

Frequency      28.5      28.75     29        29.25     29.5 MHz

Full size Yagi
Gain (dBi)     6.74      6.49      6.25      6.02      5.82
F-B (dB)       9.79      10.90     11.19     10.91     10.37
SWR            2.33      1.47      1.01      1.39      1.81

Center-loaded Yagi, Q=300
Gain (dBi)     6.02      6.14      5.76      5.33      4.95
F-B (dB)       5.80      12.62     18.40     14.59     11.24
SWR            5.30      2.06      1.04      1.49      1.99

Mid-element-loaded Yagi, Q=300
Gain (dBi)     6.04      6.19      5.84      5.43      5.07
F-B (dB)       5.42      11.35     15.80     13.94     11.22
SWR            5.24      2.07      1.03      1.54      2.12

If the design center frequency is shifted downward by about 150 kHz, the full size Yagi would provide a 2:1 SWR operating bandwidth over the full 1 MHz spread. Gain and front-to-back ratio would be respectable throughout the range (for an antenna of this type).

The operating bandwidth for the loaded Yagis is less than 700 kHz. The maximum gain frequency occurs within this spread and marks the limit of the lower frequency excursion for a 2:1 SWR. Above the design center frequency, the SWR climbs at half the rate as below it. Gain and front-to- back ratio fall off much more rapidly than with a full size model. Indeed, the higher front-to-back ratio obtainable with shortened and loaded elements now shows itself for what it is: a fairly narrow peak with extended values closer to those of the full size antenna. At the upper frequency limit, gain is less than 3 dB better than a dipole.

The same pattern shows up when the antennas are modeled over real ground at various heights.

0.12 wl spaced full-size Yagi
Height    TO Angle  Gain dBi  Gain dBdr F-B dB    Feed Z Ohms
FS        --         6.25      4.12     11.19     32.47 + j0.24
1/8 wl    55         5.10      1.44      6.08     25.67 - j5.28
1/4       43         8.58      3.34      9.79     27.79 + j4.15
3/8       33         9.84      3.89     13.34     34.40 + j4.35
1/2       27        10.80      3.58     13.37     36.14 - j1.18
5/8       21        11.23      3.50     10.22     21.21 - j2.56
3/4       18        11.27      3.98     10.08     30.29 + j1.04
7/8       16        11.37      4.22     11.81     32.96 - j0.20
1         14        11.61      3.98     12.51     34.30 + j0.24

Center-loaded Yagi, Q=300
Height    TO Angle  Gain dBi  Gain dBdr F-B dB    Feed Z Ohms
FS        --         5.76      3.63     18.40     17.74 - j0.66
1/8 wl    56         4.69      0.96      7.05     15.06 - j3.77
1/4       44         8.05      2.75     13.11     15.07 + j0.39
3/8       34         9.33      3.33     20.96     17.81 + j1.39
1/2       26        10.33      3.14     22.74     19.54 - j0.46
5/8       22        10.81      3.05     16.26     17.77 - j2.16
3/4       18        10.78      3.49     15.77     16.61 - j0.72
7/8       16        10.86      3.71     18.71     17.57 + j0.27
1         14        11.13      3.50     21.71     18.60 - j0.45

Mid-element-loaded Yagi, Q=300
Height    TO Angle  Gain dBi  Gain dBdr F-B dB    Feed Z Ohms
FS        --         5.84      3.71     15.79     25.97 - j0.67
1/8 wl    55         4.66      1.00      7.24     21.93 - j5.01
1/4       43         8.10      2.86     12.51     22.18 + j1.18
3/8       34         9.40      3.40     18.30     26.37 + j2.31
1/2       26        10.41      3.22     20.78     28.60 - j0.67
5/8       21        10.87      3.14     14.95     25.81 - j2.84
3/4       18        10.86      3.57     13.91     24.35 - j0.62
7/8       16        10.95      3.80     16.04     25.86 + j0.68
1         14        11.21      3.58     18.35     27.24 - j0.51

Because for any height, the model is compared with a dipole at the same height, similar values of gain in dBi for different antenna heights yield different valuers of gain in dBdr. Overall, the differences between the performance of the two loaded models are academic. In general, the center- loaded model yields higher peak front-to-back ratios, while the mid- element-loaded model has higher feedpoint impedances for lower losses for loss sources other than the loading coils.

I have purposely excluded the linear-loaded 2-element Yagi of 70% full size from the comparison so far because it has some interesting properties. Linear-loading, especially when executed using loading elements the same size as the main element, is inherently high Q, with all the advantages and disadvantages. Let's scan one of the linear-loaded models, choosing the one with load lines equidistant form the main element by 3" and 3" apart. with the 3/8" diameter aluminum elements 5.7' and 5.93' for the driven element and reflector, respectively, the load lines were 2.095' either side of center (4.19' overall) for resonance and maximum front-to-back ratio. Because the linear-loading elements are directly modeled as physical entities, there are no mathematical loads in the model.

Frequency      28.5      28.75     29        29.25     29.5 MHz
Linear-loaded Yagi
Gain (dBi)     5.83      6.86      6.17      5.43      4.87
F-B (dB)       1.33      9.47      20.44     13.63     9.64
R +/- jX       5.2-27    8.4-12    14.8-.2   20.6+8    24.6+15
SWR            12.69     3.20      1.01      1.77      2.49

The operating bandwidth for this high-Q model is under 400 kHz at 29 MHz (and proportionately less for lower band models). Peak values are superior to anything obtainable from inductor-loading, but very short-lived as one changes frequency. Can anything be done to increase the operating bandwidth of this antenna?

One strategy that is open to all three forms of loading is to increase the spacing between elements. If we select 0.16 wl (5.4' at 29 MHz), we can expect not only a wider operating bandwidth, but somewhat higher feedpoint impedances, along with reductions in gain and front-to-back ratio.

Frequency      28.5      28.75     29        29.25     29.5 MHz

Full size Yagi
Gain (dBi)     6.55      6.33      6.12      5.92      5.74
F-B (dB)       9.84      10.63     10.86     10.68     10.29
R +/- jX       36.7-20   41.8-10   46.7-.3   51.2+9    55.5+17
SWR            1.74      1.32      1.07      1.19      1.41

Center-loaded Yagi, Q=300
Gain (dBi)     6.29      6.15      5.75      5.34      4.98
F-B (dB)       6.78      11.35     13.98     12.86     10.87
R +/- jX       13.5-19   17.9-9    22.4-1    26.0+5    28.7+11
SWR            3.12      1.66      1.06      1.28      1.62

Mid-element-loaded Yagi, Q=300
Gain (dBi)     6.17      6.11      5.72      5.32      4.97
F-B (dB)       6.97      13.05     15.84     13.12     10.62
R +/- jX       14.3-30   20.5-14   27.7-.4   34.1+10   39.4+20
SWR            4.51      1.89      1.02      1.50      2.02

Linear-loaded Yagi
Gain (dBi)     6.62      6.59      5.91      5.28      4.79
F-B (dB)       4.30      10.84     14.87     11.95     9.26
R +/- jX       9.3-22    14.3-9    20.1+.4   24.3+8    26.9+15
SWR            4.96      1.85      1.02      1.49      2.08

At a spacing of 0.16 wl, a full-size 2-element Yagi is a good match (with a 1:1 balun or choke) for 50-ohm coaxial cable. The other beams require a beta match. However, note the table carefully: the center-loaded models-- both inductor and linear--improved their operating bandwidths and increased their feedpoint impedances by a greater amount than the mid-element-loaded model. At the closer (0.12 wl) spacing, the center and mid-element inductor loaded models were very similar in operating bandwidth, with the linear-loaded version much narrower. With the wider (0.16 wl) spacing, the mid-element and linear loaded models are on a par (with the linear-loaded model showing a slightly narrower bandwidth), while the center-loaded model shows at least 100 kHz wider operating bandwidth.

At the same time, the wider mid-element-loaded model has lost less of its gain and front-to-back ratio relative to the closer-spaced model than either of the other two antennas. The advantage of one method of loading over another is marginal and may be secondary to structural and other design concerns. The general effect of wider spacing to decrease the overall Q of a 2-element Yagi is most effective on the center-loaded models and least effective on the mid-element-loaded model.

Before drawing this refresher to a close, let's briefly look at a pair of beams that have been shortened even further: to the 50% of full size point. At 29 MHz, the driven element would be about 4' long, with the reflector 4.095' long with a spacing of 0.12 wl. We shall compare a center inductor with mid-element inductors as loads with a Q of 300. By now, we know not to expect wide differences between the two types of loading. More interesting are expectations of operating bandwidth, gain, and front-to- back ratio. As always, the elements are 3/8" diameter aluminum, and these models are once more in free space. R means that the pattern shows gain in the reverse direction.

Frequency      28.5      28.75     29        29.25     29.5 MHz

Center-loaded Yagi, Q=300
Gain (dBi)     2.06 R    3.73      4.46      3.97      3.46
F-B (dB)       1.09      6.07      27.15     11.07     7.11
R +/- jX       5.5-27    6.6-14    12.8-3    19.2+2    20.7+5
SWR            12.7      4.56      1.23      1.52      1.76

Mid-element-loaded Yagi, Q=300
Gain (dBi)     6.32 R    4.16      4.59      4.07      3.57
F-B (dB)       0.98      7.18      31.15     11.04     7.27
R +/- jX       10.6-47   13.4-24   25.0-.4   35.3+6    38.9+15
SWR            11.1      3.79      1.16      1.50      1.90

As elements are radically shortened, it is possible to achieve for very narrow frequency limits indeed exceptional front-to-back rations with a 2- element Yagi. However, the front-to-back ratio quickly diminishes off the design frequency to ordinary levels associated with an antenna with a quite narrow operating bandwidth.

There is one more design illusion we can create with this beam. Note that the SWR increases above the design frequency at a slow rate. The antenna is capable, in strictly SWR terms, of an operating bandwidth of over 0.5 MHz. However, in the upper half of the range, gain exceeds a dipole by about 1.5 dB or so, and the front-to-back ratio is on a constantly descending curve. Citing the design frequency performance figures and then, without further explanation, providing a figure for operating bandwidth, might easily mislead a potential builder with respects to performance anticipation.

It would be interesting to see to what degree the problems associated with half-size 2-element Yagis might be overcome by increasing the spacing. Therefore, let's look at these same antennas reoptimized for front-to-back ratio and resonance with a spacing of 0.16 wl (5.4' at 29 MHz).

Frequency      28.5      28.75     29        29.25     29.5 MHz

Center-loaded Yagi, Q=300
Gain (dBi)     2.75      4.83      4.61      3.92      3.40
F-B (dB)       0.34      8.56      17.16     9.99      7.90
R +/- jX       6.7-22    9.1-11    14.2-3    16.6+2    17.2+8
SWR            7.78      2.72      1.22      1.25      1.71

Mid-element-loaded Yagi, Q=300
Gain (dBi)     2.89      4.95      4.78      4.13      3.61
F-B (dB)       0.15      7.78      15.94     10.55     7.40
R +/- jX       13.3-41   17.7-19   27.2-2    33.1+8    35.3+20
SWR            7.00      2.50      1.10      1.40      1.96

Interestingly, the wider spaced versions of the half-size Yagi achieve marginally more gain than the closer spaced versions, although the front- to-back ratio peak is much smaller for these Q=300 models. As a reminder, the fact that the SWR does not go to 1.0 is due to the modeling process used: the antennas were resonated with lossless coils and then losses were added to achieve the desired Q.

Clearly, the SWR curve is also flatter for these antennas than for the closer models, and operation over a 600 kHz span of 10 meters should be possible (with proportionately smaller bandwidths on lower bands to which the antennas might be scaled). Although the resistive component of the feedpoint impedance of the center-loaded model is low enough to cause concern, the impedance of the mid-element model is high enough for an efficient beta match to coaxial cable.

As a parting shot, let's place the mid-element-loaded version of the half- size 2-element Yagi, with its 3/8" diameter aluminum elements, over real ground and see what we get.

Mid-element-loaded Yagi, Q=300
Height    TO Angle  Gain dBi  Gain dBdr F-B dB    Feed Z Ohms
FS        --         4.78      2.65     15.94     27.23 - j2.46
1/8 wl    58         3.92      0.08      5.82     22.13 - j4.73
1/4       45         7.17      1.82     11.40     23.94 + j0.08
3/8       34         8.46      2.46     17.41     28.24 + j0.36
1/2       26         9.47      2.28     19.13     29.74 - j3.01
5/8       21         9.89      2.13     14.38     26.65 - j4.49
3/4       18         9.81      2.52     13.85     25.69 - j2.09
7/8       16         9.91      2.76     16.20     27.41 - j1.13
1         14        10.19      2.56     18.14     28.49 - j2.58

Compared to a dipole, the half-size Yagi suffers at low heights (below 3/8 wl) due to its high elevation (or take-off) angle of maximum radiation angle. Above that height, it provides a consistent gain over a dipole in the 2.5 dB ballpark. Front-to-back ratio and feedpoint impedance are stable with height increases, making the antenna quite predictable. The one limiting factor in these figures is that they are peak figures. Performance in one or another way will be less off the design frequency.

This and the other models should make usable antennas, especially when scaled for lower frequencies--so long as we do not expect of them or claim for them more than they can do.

A word about the models: although every effort has been made to optimize them in accord with the expressed design goals of maximum front-to-back ratio at antenna resonance, there is no guarantee that another few hundredths or even a tenth of a dB might not be garnered by even more painstaking modeling. However, do not expect NEC or MININEC to yield much more than these models. If a model seems to deliver a lot more than the ones in this refresher, it is likely that the model has a problem or in one or another way presses one or more of the limits of the modeling program.

Two-element Yagis, in either full-size or shortened versions, have an important place in amateur radio. Understanding what they can and cannot do is critical to station and operation planning. I hope this refresher on 2-element performance contributes something to that cause.



Updated 5-7-97. 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.



Go to Part 5: Strategies for Improving Forward and Rearward Performance

Return to Index
Go to Amateur Radio Page