Loop Antenna Calculator
Small loops are tiny, quiet and efficient only when the conductor is thick. See the radiation resistance, the conductor loss, the resulting efficiency and the tuning capacitor for an air-core loop of any size or a ferrite rod, and where a loop stops being small.
Small loop antennas
A loop whose circumference is below about a tenth of a wavelength carries nearly uniform current, so it behaves like a magnetic dipole. Its pattern is a doughnut with nulls along the loop axis, its directivity is 1.5 (1.76 dBi) and its radiation resistance is only Rr = 20π²·(C/λ)⁴·N², or equivalently 31171·(N·A/λ²)². Because the radiation resistance grows with the fourth power of size, halving the loop diameter cuts it by 16 times, while the conductor loss falls only in proportion to the wire length. That is why small transmitting loops are efficient only with fat conductors, and why they have a very high Q and a very narrow bandwidth.
Ferrite loopsticks
Winding the coil on a ferrite rod concentrates the magnetic flux and raises the radiation resistance by the square of the effective permeability. The effective permeability of a rod is far below the material value, because of the demagnetizing field: it depends mostly on the length-to-diameter ratio of the rod. Ferrite loops are standard in AM receivers, where the received signal is limited by atmospheric noise, not by antenna efficiency. For transmitting they are very lossy.
Large loops
When the circumference approaches a wavelength the current is no longer uniform and the loop resonates like a full-wave element: a resonant loop has a circumference about 2% longer than λ, a feed resistance of roughly 100 to 130 Ω, and about 3 dBi of gain with maximum radiation perpendicular to the plane of the loop. The quad and delta loop antennas used by amateurs are examples.