I'm planning on building an Army Loop tuner to allow experimenting with various medium-sized transmitting loops (~0.25 lambda). The schematic is as follows:

http://homepage.ntlworld.com/g4kki.william/army_loop_tuner.htmI've been trying, unsuccessfully, to figure out exactly how to compute the required value of the matching capacitor C1.

I tried following the math at the following page under the section titled "2.5.1 Reactive Capacitive Match Using Impedance 'Transformation QT' Procedure":

http://ian.r.scott.tripod.com/antenna.htmOn the above page, the author presents a similar-looking capacitive matching circuit, using two matching capacitors in a balanced arrangement instead of one matching capacitor. The author also presents a strategy for computing the required matching capacitors Cs1 and Cs2. I simulated this in LTspice and got a vaguely-correct-looking result (almost zero reactance and ~80 ohms resistance at somewhere around 31 MHz), but the result was not exactly the same as the article's computations (which should give zero reactance and exactly 50 ohms at exactly 30 MHz).

Anyway, I'm not interested in the above balanced capacitive matching scheme using two matching capacitors, but am instead interested in the unbalanced (and more common) capacitive matching scheme, using only one matching capacitor, as shown in the first schematic at the top of this post. I attempted to apply the same analysis techniques but again am getting only vaguely-plausible results. I'm not sure I'm analyzing/modeling/interpreting the problem correctly, or what the expected X-vs-f and R-vs-f graphs of the matched loop should look like around the resonant frequency.

Rather than continue along what might be a blind alley, I thought I'd ask for help on how correctly to model the unbalanced single-matching-capacitor scheme in LTspice, in particular how properly to observe in LTspice the feedpoint X and R and what the expected shape should be. Then, I'd like to know how properly to compute analytically the required single matching capacitor in the unbalanced case (similar to the above derivation for the related case of using 2 matching capacitors).

I want to simulate this before building the physical tuner because I want to understand exactly what range of loop inductances can be matched for a given tuning capacitor and matching capacitor, which will have limited tuning ranges.

I realize this is a rather complex question, but would appreciate any advice. Thanks in advance.