SM 5 BSZ - The Optimum 6 Element Yagi Antenna (UKW Berichte 3/81, VHF Communications 1/82)
(Sept 15 1997)
Leif Åsbrink, SM 5 BSZ

The Optimum 6 Element Yagi-Antenna

In an article in the IEEE Transactions on Antennas and Propagation (Vol. AP 23, 1975, page 8 ff.), two authors C.A.Chen and D.K.Cheng described a method of designing optimized Yagi antennas using computer calculations. The article also included a numerical example for an optimum 6 element Yagi antenna. In this case, optimum means the highest possible gain, independent of boom length and bandwidth.

This article is now to give the data for constructing a 70 cm and 2 m version of this antenna, however, it is not meant to be a fool-proof method of constructing antennas, but is to describe a method of constructing an antenna that really works.

THE CHEN/CHENG ANTENNA

Over the years, many radio amateurs have tried to construct an antenna according to the theoretical calculations of Chen/Cheng. The results were usually unsatisfactory. Such an antenna has been described in Ham Radio Magazine.

The reason that this antenna does not usually operate correctly is partly due to the fact that it is very critical, and partly due to the calculation method. It is necessary for the antenna to be measured and optimized after construction.

A signal generator and receiver are required for this measurement that can be tuned over a frequency range of ±5% of the required center frequency. Furthermore a site must be found and be prepared where the radiation pattern can be measured in this frequency range. The angular resolution should be in the order of 0.5°. For the level measurements, either a precision attenuator will be required, or the receiver must be linear (AGC off, maximum AF gain, CW or SSB mode, and decrease the RF-gain as required), so that the level can be measured at AF-level using a normal AF-voltmeter.

The radiation pattern can be measured by rotating the antenna in an axis that runs parallel to the elements. A suitable arrangement is shown in Figure 1. It is also possible to measure between the roofs of two houses having a suitable spacing from another. The most important point is that one avoids ground reflections and any other reflections from neighbouring objects.

If the measuring path is satisfactory, the radiation diagram is now measured at various frequencies, and the frequency is selected at which the pattern corresponds as close as possible to the theoretical values given in Table 1.

```Angle  Level  Note
(°)    (dB)
0      0
19     -3
25.5   -6
30     -9
38.5   -20    First dip
53     -11    First sidelobe
71.5   <-30   Second dip
83     -17.5  Second sidelobe
96     <-30   Third dip
108    -18.5  Third sidelobe
120    -28    Fourth dip
138    -13    Fourth sidelobe
156    -25    Fifth dip
180    -10    Back lobe
```
Table 1. The radiation pattern values of the Chen/Cheng antenna

This is followed by calculating how far this frequency is from the design center frequency in per cent and by changing the lengths of the elements by twice this percentage. The positions of the elements remain unchanged.

If the radiation patterns are now measured again at various frequencies, it will be found that a pattern will be present which is much more similar to the tabular values, and far nearer to the design frequency than before.

After carrying out one or two further corrections according to the given example, one will obtain the final (theoretical) radiation pattern at the design frequency. The gain will then amount to 11.5 dB over a dipole, which is approximately 1 dB more than can be obtained with other antennas having a comparable length.

An antenna optimized according to the described procedure participated at the Ånnaboda antenna measurement contest in 1980. The gain measured was 11.8 dB, however, it seems that the 70 cm measurements indicated gain values that are too high by 2 to 3 tenths of a dB. A direct integration of the radiation pattern will give a gain of 11.6 dB. Chen and Cheng give a theoretical gain value of 11.25 dB, which is probably incorrect for some unknown reason.

However, the exact gain value down to a tenth of a dB is only of theoretical interest; it is more important that this antenna is able to provide noticeably more gain than any other antenna of similar length. The measured values at Ånnaboda, which are very accurate for the 2 m antennas, can be used for comparison. These were published in the Swedish Amateur Radio Magazine QTC. The results for 144 MHz were given in edition 4/81, and the 432 MHz results in edition 5/81.

PROVED CONSTRUCTIONS

For those readers that do not wish to optimize the antennas according to the described measuring and optimizing procedure, a description is now to be made of an optimized Chen/ Cheng antenna for the 144 MHz and 432 MHz band.

The 432 MHz antenna is constructed using a tubular PVC boom of 19 mm outer diameter and 1.5 mm wall thickness. All elements are constructed from 5.0 mm diameter solid aluminium rods. They are pressed into holes in the boom.

The dimensions are given in Table 2.

```
Element   Spacing from
length    reflector
(mm)      (mm)
324.5     0
308.5     173.5
297.0     374.5
293 0     656.0
296.0     880.5
293.0     1173.5
```
Table 2. Dimensions of the 70 cm antenna

The 144 MHz antenna is designed for a center frequency of 144.4 MHz. The boom is constructed from aluminium tubing with an outer diameter of 25 mm. All elements are constructed from aluminium tubing with an outer diameter of 10 mm. boom using special element clamps which will possibly have an effect on the resonant length of the elements. The element clamps can be obtained from SM5ERW, Pl 8820, S-64300 VINGÅKER, Sweden.

If the elements are to be mounted onto the boom in a different manner, or when the boom diameter is changed considerably, it will be necessary for the antenna to be measured and realigned. When using the dimensions given in Table 3, the antenna will operate satisfactorily between 144.0 and 144.6 MHz.

```
Element   Spacing from
length    reflector
(mm)      (mm)
1004      0
954       519
922       1120
907       1963
917       2634
907       3511
```
Table 3. Dimensions of the 144 MHz antenna

DESIGN OF A SUITABLE GAMMA MATCH

Although the "gamma match" should be part of the fundamental knowledge of any person interested in antennas, a high-quality version of such a match is to be briefly described. The main feature is that the capacitor is made in a coaxial manner using a PTFE tube as dielectric. This construction ensures that it is impossible for water to run to a position where strong electrical fields are present. As can be seen in Figure 2, the PTFE-tube also protrudes by approximately 10 mm on both sides of the capacitor, which means that the path is very long for leakage currents when the antenna is dirty and wet. Of course, the surfaces of the two copper parts, and the end of the coaxial cable must be protected against corrosion. The result is a gamma match that is suitable for the high efficiency of this antenna. By the way, the dimensions of the gamma match are not critical; a tolerance of ±5% is permissible.

The matching should be constructed similarly for the 432 MHz band; however, no proven version is available for publication. However, SM5ERW hopes that the 144 MHz antenna can be offered in the near future complete with 50 ohm matching.

STACKING DISTANCES

Due to the very high gain of the described antenna, it is not possible for normal rule-of-thumb methods to be used for estimating the stacking distances. According to experience, a spacing of 1.8 wavelengths should be maintained when several of these antennas are to be stacked.

APPENDIX

Before publishing this article, DL3WR carried out an extensive correspondence with DL 6 WU and SM 5 BSZ. In this correspondence, the latter was able to give several details regarding the described antenna, which are not important for construction, but of such general interest that they are to be brought in the form of an appendix.

STANDING WAVE RATIO

Nearly ten years ago, SM 5 LE and SM 5 BSZ carried out a series of highly accurate radiation pattern measurements. They found that many antennas possessed a good matching (low SWR) at one frequency, whereas their maximum gain appeared at a different frequency. Typically, they had their best match at 144 MHz, whereas the maximum gain was outside of the amateur band. The in-band gain was usually 1 to 2 dB lower than the maximum gain.

Based on this experience, the Ånnaboda gain measurements were not made at 50 ohm matching, but at the actual antenna impedance, and were so published. As long as the attenuation of the feeder is known, the additional loss caused by mismatch can be easily calculated. If it is unacceptably high, it can be eliminated using a stub in the vicinity of the antenna.

The author hopes that radio amateurs will forget "the resonant frequency of an antenna", since such a concept is confusing! The only thing that is in resonance is the match, and any antenna can be matched impedance-wise at any frequency - even when the frequency of optimum gain is far away. Radio amateurs should understand that

Antenna gain = Good radiation pattern !

IS A SINGLE dB IMPORTANT?

Good, normal Yagi antennas such as the Tonna 9-element, HyGain 8-element, Cushcraft 11-element, Wisi 10-element, or Jaybeam 10-element, are all on a straight line in a diagram giving the gain as a function of boom length (such diagrams should be drawn in a linear scale, and not in dB). This line crosses a gain value of 11.5 dB at a boom length that is 25% greater than that of the Chen/Cheng antenna. Furthermore, normal Yagi antennas require at least 50% more elements.

This means, that the described antenna is thus 25% better than conventional Yagi antennas - corresponding to 0.97 dB. The gain differences between conventional Yagis of equal length and the Chen/Cheng antenna amounts to approximately 1 dB.

Normally, it is assumed that a signal difference of 1 dB will not be audible. This is, how- ever, only (approximately) true when the signal is well out of the noise. This is also valid for a very weak continuous carrier. However, it is not commonly known that the "probability of detection" Morse signals is affected by small differences of the signal-to-noise ratio.

Experiments have shown that a good telegraphist can usually copy Morse signals at a certain speed without error, however, the errors will increase considerably when the signal approaches the noise level. If the signal-to-noise ratio is selected so that 85% of the letters can be copied correctly, a deterioration of the signal-to-noise ratio by only 1 dB will decrease the number of correctly copied letters to 60%!

For those radio amateurs that wish to carry out communication at the technological limits (e.g. EME), this represents a considerable difference. The price of this 1 dB more antenna gain is a reduced bandwidth, however, such low-signal communication is always made within the first 500 kHz of the amateur band.

