The Smith chart is a tool used a lot by professional RF engineers for solving transmission line stub matching problems and all sorts of quick calculations.
The Smith chart can also be used for quick back of the envelope L and T antenna tuner engineering calculations.
I have on the picture above plotted a T configuration antenna tuner with the first capacitor set to a so big value that it is shorted as seen by the RF voltage (large C – low |Z|). Then the configuration becomes a L tuner in practice with a shunt L followed by a series C when seen from the load in towards the generator.
I measured the Z in the shack end of the ladder line feeding my doublet antenna to be Z = (24.1 – j35) ohms at 14.200 MHz by a Vector Network analyzer. That can be plotted as a point in the lower part of the Smith chart (capacitive Z).
(1) Since we have now first an inductor (in the tuner to ground) as observed from the load towards the generator, we can use this inductance to move along a constant Conductance curve in the Y plane (upwards in the Z plane). The conductance is constant but the Susceptance varies. (We remember from the RF engineering classes at engineering school that Y = 1/Z – of course).
(2) Then we use a series capacitor to move down inside the 1.25:1 SWR circle. We dont have to hit the center because anything inside the inner 1.25:1 circle is good enough. (We move while the R part of R + jX is constant, while the X part is changing to become more negative. This means we move on a constant resistance circle in the Z plane).
Determination of component values can be done easily by hand in a tool like this while still retaining an intuitive understanding of what is going on.
Black magic! Especially with a digital smith Chart tool.
K6JCA has analyzed the needed components values for matching a load while moving on a constant reflection coefficient circle. The plot below shows that in case you select the high-pass configuration for your tuner, certain angles of the reflection coefficient will give you skyrocketing component values.
Component values for the highpass and lowpass configurations
Above you can see that the LsCp &CpLs configuration keeps the max component values quite flat. LsCp and CpLS are therefore the best engineering choices based on cost and realistic component values.
I blasted my LDG antennatuner some time ago. Or …. I thought I blasted it….. It appeared that it was only the resistor in the SWR detector circuit that got burned out. I replaced that resistor and now its ok again.It was easy to repair. However these small LDG tuners dont take more than 100W max. The designers have used ferrite cores, whereas it would have been a much better idea to use carbonyl cores or air core inductors. The latter doesnt get so easily saturated.
However I must say that the design of the LDG equipment I have seen so far is not very impressive. Why use that BIG chasis when you dont need it? Why use DB9 style connectors on a chassis that is supposed to be watertight? Look at that coax termination there. Both on the board and on the PL259 chassis connector. Why use RG174 teflon coax when you have such crappy terminaions? Perhaps it would be better with no coax at all 🙂 However when the tuner works it works fairly OK. Just dont trust this kind of equipment in a contest or on a dx expedition.
I just got myself a new roller inductor. This one is designed on the principle of a silver foil that is rolled away from and onto a ceramic form with guides for the silver form. The ceramic coil forms the coil. There is a large shorting cylinder that the unused silver foil is rolled onto. The effect of this is to significantly increase the Q of the inductor. For high power QRO applications there may either be arcing from the end of the unused part of the coil or heat loss in this part of the coil. How the unused coil is completely shorted with an inner conducting cylinder and the unused part of the coil has no flux thru it.
I recently started to have problems with AAT.EXE from ARRL under XP. AAT.EXE is a DOS program used for calculating efficiencies of antenna tuners of L and T types. The user specifies QU of the inductor and capacitors, capacitor capacitance range, max voltage that the capacitor can tolerate, and some other parameters. AAT.EXE then makes two nice tables identifying where the tuner is most effective, where the tuner has a high loss, where the tuner will see a too high voltage values over the capacitor etc. The tables are generated in a .SUM file and a .LOG file. The problem is that the keyboard suddenly ddid not work in the XP dos box that is opened. I think this happened after upgrading to SP3 or after some security upgrade. I am not sure. What I did to solve it was to make a .BAT file containing this text:
mode con: cp select=865
This selects the codepage that is Norwegian. This solved the problem! If you have another keyboard layout you can find the codepage you will have to try here: http://www.kostis.net/charsets/
Here is an example of the output from AAT: