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Re: [TowerTalk] Fwd: Adjusting a Gamma Match on a Yagi with an Antenna A

To: towertalk@contesting.com
Subject: Re: [TowerTalk] Fwd: Adjusting a Gamma Match on a Yagi with an Antenna Analyzer
From: Steve Hunt <steve@karinya.net>
Date: Thu, 11 Nov 2010 20:30:50 +0000
List-post: <towertalk@contesting.com">mailto:towertalk@contesting.com>
I quite often come across explanations of the Gamma Match (or Tee Match) 
which suggest that a "tap" is being made along the dipole at a point 
where the "feedpoint" Resistance is higher, and that the inductance 
inherent in the Gamma rod is then being cancelled by the series 
capacitor. That way of viewing it seems seriously flawed and can quickly 
lead to some false conclusions.

Instead, picture a folded dipole as being the limiting case of a Gamma 
Match (or Tee Match). We know that the feedpoint impedance does not 
approach infinity - as you might expect from that flawed description - 
when the Gamma Rod extends to the very tip of the dipole, nor does it 
require a very high capacitive reactance to cancel what you might expect 
to be a very high Gamma Rod inductive reactance.

We know that in the case of the folded dipole the impedance 
transformation is determined solely by the relative diameters of the 
wires and their spacing; for equal diameter wires we know that the 
transformation will be a factor 4. Now, if we halve the length of one 
side of the folded dipole - in other words halve the length of the Gamma 
Rod - nothing changes: we still get an impedance transformation of 4 !!!

Seen from that perspective it is the Gamma Rod / Antenna diameter ratio 
and spacing which determines the impedance transformation ratio, not 
the  length of the Rod.

The inductive element appears because by adding the Gamma components we 
have introduced in parallel a short-circuit transmission line, the input 
impedance of which is inductive if it's less than a quarter-wave long. 
This becomes obvious when you look at the currents in the Gamma Rod and 
realise they are out of phase with those in the parallel Antenna 
element, which in turn are out of phase with those in the outer section 
of the Antenna element.

To illustrate the change in thinking, here are a couple of series-form 
input impedances taken from an EZNEC simulation of a Gamma Match (no 
capacitor used) where I doubled the length of the Gamma Rod:

Gamma Rod = 1ft, Z = 17.5 +j53
Gamma Rod = 2ft, Z = 72 + j95.5

The "traditional" explanation would say that we have increased the 
Resistance by a factor of about four, from 17.5 Ohms to 72 Ohms, by 
"tapping" further along the antenna, and at the same time the longer 
Gamma Rod has increased the series inductive reactance.

However, now convert those impedances to their parallel form:

Gamma Rod = 1ft, Z = 178 // +j58.8
Gamma Rod = 2ft, Z = 198 // +j149.8

Now our interpretation is quite different: doubling the Rod length has 
change the resistance very little - it has simply increased the 
**parallel** inductive reactance.

I hope that is useful. At the very least, transforming measured 
impedances to their parallel form might give a better insight into what 
adjustments to make.

One of the better papers on the topic is here:  
n6mw.ehpes.com/N6MWGamma4.doc

73,
Steve G3TXQ
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