Are gamma matches as bad as all that

Seeing the comment recent online comment about a gamma match as I have noted from research online, NEC does not support modelling of the match component reminds one of the unreliability of online sources. This appeal to non-authority is fallacious, this writer writes as if it is fact that NEC does not support modelling a gamma match, and that is quite wrong.

NEC has limitations on geometry elements relative to each other and to wavelength, and those apply not just to the gamma match, but the entire model. It is the modeller’s challenge to stay within those limitations.

This article documents an NEC model of a real antenna and the model reconciles with the real antenna.

An example

The example antenna is a 4 element design which I naively built from an ARRL article quite early in my ham radio development. I did modify the design to use a gamma match and devised a novel construction to overcome some of the many practical problems of most gamma match implementations (Duffy 1998).

gamma02

Above, the physical implementation of the example gamma match. It was designed to be waterproof and resistance to corrosion, proven by 45 years of exposure to the weather.

GammaCurrents

Since the two tubes of the gamma match are the same diameter, the common mode current component in each at the middle of the dipole will be approximately half the current that would flow in the centre of a plain dipole, so there is a 4:1 impedance step up. This 4:1 feed point is shunted by the s/c stub formed by the gamma arm and parallel dipole conductor. In this implementation, a short o/c coaxial transmission line stub located inside the end of the gamma arm allows the series reactance to be tuned to zero (though this component is not essential to a gamma matched antenna).

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Above, the geometry of an NEC model of the structure showing current and phase under excitation. Though the two parallel conductors of the gamma section are spaced a little, it can be seen that the resultant current moment is approximated by resolution of the phasors for each conductor, and the resultant is the common mode current which follows the amplitude and phase of the current in the rest of the dipole. Note that the model properly includes a TL model of the series ‘capacitor’.

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Above, the VSWR plot in blue.

Though it is popularly held that gamma matches seriously reduce VSWR bandwidth, this is a very broad antenna and the gamma match has not unduly limited VSWR bandwidth in this case.

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Above is the vertical and horizontal radiation pattern.

Though it is popularly held that the gamma match skews the pattern, the pattern error at 15° in both vertical and horizontal planes is around 0.05dB, insignificant in this case.

Disadvantages

Hams popularly recite a list of disadvantages of gamma matches, most of which are not supported by fact, simply prejudice.

I will concede that most hams cannot explain how the gamma match works using a model that allows quantitative design of the match, and where that is the case, it is not surprising that they may find them difficult to optimise because they operate entirely in a “suck it and see’ mode… luck and persistence determine the outcome. You might describe this approach as empirical, but that is just a grand name for guessing your way to a possible solution.

Many of the design tools are flawed, and even many of the respected works are wrong… apparently based only on theoretical analysis which was not verified by experiment.

Another very real problem is that of physical implementation, they are often prone to water ingress and corrosion which makes those implementations unreliable.

Do you need to model the gamma match

A simpler approach is to design the Yagi with a plain dipole DE for the purpose at hand, and that might include optimisation for some parameters other than feed point impedance. Then design the gamma match to transform the expected feed point impedance (which may well be reactive) to the requirement (often 50Ω) (Duffy 2013).

Conclusions

  • Gamma match can be modelled in NEC paying due regard to geometry limitations of NEC.
  • Some of the folk-lore claims of gamma match are not soundly based.
  • Gamma match is probably best avoided unless the implementor properly understands how it works, and produces a weather resistant implementation that will be reliable in the longer term.

References

  • Balanis, C. 1997. Antenna theory – analysis and design 2nd ed. John Wiley & sons New York.
  • Cebik, L. Oct 2006. Some Preliminary Notes on the Gamma Match. Restricted.
  • Duffy, O. Apr 1998. Novel Gamma Match Construction. VK1OD.net (offline).
  • ———. Oct 2013. Designing a Gamma match using a Smith chart. VK1OD.net (offline).
  • Healey, D. Apr 1969. An examination of the gamma match In QST Apr 1969.
  • Smith, P. 1995. Electronic applications of the Smith chart 2nd ed. Noble Publishing Tucker.
  • Tolles, H. 1973. How to design gamma matching networks In 73 Magazine May 1973.
  • Folded dipole step up ratio calculator

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