This was the first loop that I built, and I have learned (and continue to learn) a lot since then!
The simplest way to describe a small transmitting loop, aka the magnetic loop, is to describe it as a tuned LC circuit. The radiating loop, even at one turn, is a coil (L), IE: an inductor. On it's own, the loop will have a resonant frequency. We make this loop to be self-resonant at a frequency that is slightly above the highest frequency we intend to use the antenna on, then tune the loop to a given frequency with the variable capacitor.
The length (or circumference) of the radiating loop (big loop) is carefully selected to be no longer than 1/4 wavelength of the highest frequency of operation desired, and no shorter than 1/8 wavelength. In the case of a loop built to be the most efficient on 20 meters, the total circumference of the loop would be just under 17' at it's longest, and right around 8.5' at it's shortest. The closer to 1/4 wavelength the loop is cut to, the more efficient it will be.
The antenna is tuned to our desired frequency by means of a variable capacitor (C). The capacitor can be one of many different varieties: air variable, vacuum variable, coaxial, plates, trombone, etc. Each has their pluses and minuses in categories like maximum power handling ability, maximum voltage rating, capacitance range high/low, each of construction or mounting, and ohmic loss through the chosen capacitor. Air variable caps are very common and are easy to find, but generally limit you to QRP power. Vacuum variable caps such as Russian surplus or domestic manufacturers like Jennings are highly sought after for their power handling ability and very low loss, but come with a higher price tag. Most vacuum caps will easily allow 100 watts, and some of the larger Russian caps will allow up to 400-500 watts and more.
This antenna was originally built to tune on 30, 20, and 17 meters. I wanted to see how it would perform on 40 meters, but would need more capacitance in order to do that. What I did was to add in a 150pF doorknob capacitor in parallel to the air variable cap, and inserted a switch to enable or disable the use of the doorknob cap. This way, when I want to work on 40m, I flip the switch, then retune the capacitor to my desired frequency.
Matching the antenna to the 50 Ohm transceiver can be accomplished in a number of ways too. The quickest and easiest is the unshielded coupling loop like I am using on this antenna. The loop is simply a loop of wire or copper tubing that is approximately 20% of the diameter of the radiating loop. One end is connected to the center of the coax, the other end to the braid. I use a BNC to banana post adapter for this connection. The feed loop can be attached to the mast and slid up or down to find the best SWR and impedance match. Other methods include shielded coupling loops, gamma match, hairpin coupling, and transformer coupling, among others.
It is constructed from a 10' piece of 1/2" Type M copper pipe. The pipe was cut into eight equal length sections of 15", then soldered together with 45° elbows into an octagon shape. A section was cut out at the top, then about 4 " of each end was hammered flat, than a 3/8" hole drilled close to the ends. This enclosure for the capacitor is fitted with two 3/8-24" stainless steel bolts to act as studs to not only allow the enclosure to be attached to the loop, but provide connection points for the capacitor.
I chose to use a simple unshielded coupling loop made from 10 ga stranded copper wire, mainly because I had a lot of it. :) I started with a circumference slightly longer than 20% of that of the radiating loop. The loop was trimmed down slightly until I had a very good Z 50 Ohm match measured at the antenna.
The antenna is affected by most anything is close proximity, especially anything metal, so be sure to make the final tuning adjustments in the location where the antenna will eventually be used if possible.
There is a lot I could say about these antennas, but for the most part I would just be repeating a lot of what others that are far more intelligent than myself have already written. I would highly recommend anyone interested in learning more about these antennas to take the time to read Leigh Turners technical paper entitled "An Overview of the Underestimated Magnetic Loop HF Antenna". A PDF copy of the document can be found by clicking HERE.