I re-scanned the antenna with the tuning Cap (4-47pF) at Maximum and again at Minimum. The both results are shown on the following graph.
Scan with Tuning Cap at Max and Min
Scale: 2 to 18mHz
The tuning Cap can vary the Resonant Frequency between 7 and 16mHz, just right for a 30m loop. This is very close to resonate frequencies as computed via a online calculator by Bruce Carter Loop Antenna Page.
All of the above was found experimental, now I an trying to justify it with math.
I know the impedance as seen at the feed point can be set by changing the turns ratios of the input toroid, The input impedance value is not critical for just looking at resonates, but it will be corrected before obtaining the final results. Currently the match is:
75 ohm input * (2 T Sec / 4 T Pri )^2 = 18.75 ohms output
According to what I have read on the Internet, the input impedance for a loop antenna is closer to 5 ohms. I should need a high turns ratio, like:
75 ohm input * (2 T Sec / 8 T Pri )^2 = 4.65 ohms output
With the tuning cap set to minimum, I would think the antenna would look like a dipole and resonate at:
22.88mHz = ( 300m / (5.7m * 2 * 1.15)
But, I measured 16.43mHz, maybe this is because the ends of the dipole are folded back in a circle and provide capacitance between the ends. Also, there is probably more self inductance due to the coil shape?
Note: I know that using a 12 AWG wire for the element is not the best for performance, but for design investigation it works just fine. Later it maybe replaced with stand alone copper pipe.
I need to do more experiments and investigate this further.