Loop Antennas are considered to be `samall` when their diameter drops below about 1/10 of the wavelength they are intended to be used at. In this case, I use the term `Tiny` because the antenna's diameter is about 1/30,000 the wavelength, and at 5.5 cm in diameter, they are quite small in human terms. Coils are one of the few components experimenters can easily do a good job of making for themselves, and the coil, with or without the core, is the major component in a resonant loop antenna. The resonant loop antenna is fundamentally a parallel resonant LC circuit tuned to the carrier frequency.
A coil, or in some cases coils, of wire form the antenna, which is usually mostly inductive, and a parallel capacitance is used to make the antenna resonant at the desired frequency. Time varying magnetic fields from the signal source that cross the coils of wire induce current in the loop, which results in a voltage across the output. The closer the incoming signal is to the loop's resonant frequency, the higher the output voltage.
There are several formulae available for calculating the number of turns to use in a coil once you decide how much space you have for it, but I haven't found one that seems to get close enough to use without trimming. To get a loop of the desired inductance, I wind a coil of about the number of turns I expect to need, and then measure it. Since inductance is proportional to the square of the number of turns in a coil, I calculate an inductance factor for that size coil, and then I use that inductance factor to calculate the number of turns I will need. If I am careful, this goes pretty quickly with only a couple of iterations before the inductance is close enough to work with.
The antenna's operation in transmit mode is analogous to its operation in the receive mode, so let's take the receive mode first. The better the receiving antenna, the larger the signal appearing across it, and a lot of factors affect the amplitude. Looking at how these factors relate to one another (See Formula 1)...