Topband: In search of resonance

[Don Johnson]

When using a gamma match you are usually going up on the tower beyond the 50 ohm point. From that point down the gamma rod and the tower is acting like a parallel wire transmission rod, transforming that impedance down to a lower value, hopefully near 50. You will see the 50 ohm R plus inductive reactance at the feed point. The series gamma capacitor tunes out the inductive reactance leaving just the R.  The way to change the R is with a shunt capacitor (as in an Omega match) the series capacitor only compensates for the series inductance.
I do not think taking a reading at the bottom of the gamma wire with the MFJ is giving a valid R value, especially since adding a series capacitor seems to " change the R".

Matching a tower with a gamma match is just like matching a Yagi with a gamma rod. 
If the bottom of the tower (center of the Yagi element) has an impedance of Z then a point up the tower or out on the Yagi element X degrees will be  Z divided by (cosine X) squared. ( plus a factor due to unequal diameters of the element and gamma rod must also be considered)
For example if the base of the tower is 35 ohms, moving up 30 degrees (40 some feet) will give a Z at that point of about 45 ohms.  But the gamma rod and the tower act like a step up transformer. Remember how a folded dipole works. Two same size wires will give a step up of 4 times what a single wire has. Single wire dipole 75 ohms and folded dipole 300 ohms. If the wires are not the same the ratio is different. In the case of the tower being larger than the gamma wire, the ratio is much higher. So the Z at the top end of the gamma will be several times higher. I usually guess this number and plot on a Smith chart. Then move around x degrees. This brings me to some value of R and inductive X. Then the gamma Capacitor tunes out the inductive reactance.  Measuring this with the MFJ 259 should give good results. If the reading is like 100 ohms you can make the gamma rod shorter, bringing down the R. If low, make the gamma rod longer. (I may have this just reversed, again, I like to use a Smith chart because it is easy to see what happens when one parameter is changed. It can be very confusing otherwise and I am relying on only my old memory as I write this)
I know some of the old ARRL antenna books have good info on designing gamma matches. For all my towers I have gotten close enough with a #12 wire about 20 to 30 foot long about 18 inches off the tower.  
One other easy method that seems to always work is to come down to an L network. I have used a slant feed wire running from an L network on the ground up at a 30 to 45 degree angle to a tap on the tower.  That particular installation was a Rohn 45 tower at 70 ft top loaded with a full size 4 element 20 meter monobander. The shunt C on the output of the L network changes the R and the coil compensates for the reactance. Remember shunt element changes the R and the series element does not change the real R. Sometimes you have to turn the L network around because you want the shunt C on the high impedance side. 

73,
Don
N4DJ

 

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