A reader of A common scheme for narrow band match of an end fed high Z antenna commented:
…if the coil is tapped at 1/3, surely then the coil is a 1:3^2 or 1:9 transformer and the capacitor simply ‘tunes out’ the coil reactance, what is the input impedance when it has a 450+j0Ω load?
That is very easy to calculate in the existing Simsmith model.
Above, with load of 450+j0Ω, the input impedance at 50MHz is 8.78+j34.36Ω (VSWR(50)=8.4), nothing like 50+j0Ω.
As for tuning out the reactance…
Somewhat more capacitance does result in a lower VSWR(50), but at 1.6, you could not claim it is matched.
This is not simply a 1:9 transformer by any stretch of the imagination.
As mentioned in the referenced article, solution of these circuits is not intuitive, the amount of flux leakage is critical to behavior, and that depends greatly on the geometry of the coil.