Lets consider my original proposal, a parallel tuned circuit.
Working Q is given by (let's assume an infinite component Q for the moment)
XL/RL. That value of XL can therefore be made anything we want.
The simplest approach is now to tune the inductor to resonance with a shunt
capacitor, and we can link couple in. Vary the link (i.e.the effective leakage
inductance) and voila!
The link could be substituted by a suitable large value of inductance between
the input and the top of the tuned circuit. The value of the inductance depends
on the impedance of the step up ratio that we want: we'll have to readjust the
tuning capacitor, but we will still have the Q fixed by the ratio of the
inductance to load impedance. Or we can even tap the tx at the bottom of the
tuned circuit, and adjust the tap point for a match  and then we have a tuned
auto transformer. The higher the amount of capacitance, the higher the Q.
When the load is complex, we have to adjust the values to compensate for that.
The principles of duality make this work with a low resistance and series
tuning, too.
Now you can use the equivalent circuits to turn this into an equivalent T.
A complication occurs in an antenna tuner if the antenna itself has a high Q,
i.e. a rapid change in impedance with frequency. Although the tuner itself may
have a low working Q, it may have to be retuned for quite small frequency
excursions, and especially if the antenna is resonant in the middle of wide
band (percentage wise) this means a reversal in sign of the imaginary part as
you go through the band. I have that problem with my vertical, where its
resonance is at 3.72MHz. This leads to having to vary both L and C in the L
network: as the real part varies a lot over the band, tuned circuit would need
variable L too, to keep a constant Q.
The correct point about the L network is that for any 2 element approach, it
offers the lowest Q. Add a third element, and you have a different situation.
Add more elements and you can go further, getting a wide band match. I have an
article somewhere, translated from the Russian in the early 60's. about
designing wideband Tchebysheff networks: From memory, they could get wide band
matches across an HF BC band without retuning. The pay off point comes when
you have so many components that the losses in them get too high. Like the
wideband dipole antennas that get a match by using a load resistor. Somewhere
in all this, my aging memory recalls something about Foster's Reactance Theorem
and Hurwitz polynomials, but I can't remember why.........
So while I agree with Rich wholeheartedly about using a centre fed dipole
rather than burning up traps (and accept that the pattern gets a bit weird when
you get to the stage where it's several wavelengths long), I don't agree with
him about using an L network, especially where the feeder length is such that
the impedance gets very high or low. That can also lead to Marconi effect,
which is undesirable, but that's another matter.
73
Peter G3RZP
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