I started writing an ERP calculator for low and medium frequency, though it would cover any electrically short antenna. The calculator can be found here: LF/MF ERP Calculator. More information and notes on the theory can be found here on the Electrically Small Antenna ERP page.
I firstly measured the impedance of the unmatched inverted-L wire and found it to be . Using these values, it is possible to calculate a matching circuit – you may find a calculator, such as this website helpful. Using the linked website, I settled on a high-pass (because the components worked out nicer) low-to-high matching LC-network. From the matching circuit on the right, I found the values L=133uH and C=437pF worked ideally. We tried with some low power components to check that the values were correct, before winding a big inductor from plastic insulated wire around a 4 inch drainpipe. Mini Ring Core Calculator was used to calculate the number of turns of the given wire for a given pipe diameter. Once that was tested, we lashed up a frame to hold the capacitor and inductor from the ground and inside a box to give a slight amount of cover. The box has a waterproof seal.
Once the matching network was built, the antenna was remeasured. From the plot we can see the VSWR is 1.18:1, with a matched feed impedance of on 475 kHz. As you can see, the real part of the antenna impedance is close to while the complex (reactance) part is almost , which indicates a good match. This is, of course, confirmed with the low SWR. I decided this was close enough to start off with!
Below is an awful depiction of the antenna set up. I shall try to make a better one soon; sorry.
The lower two pictures are a view up the tree where the inverted L runs. At the top the inverted L meets the end of the G5RV, both of which run back to opposite corners of the house.
Finally, the radiation pattern as forecast by MMANA-Gal: