4. Loop Antennas

A loop antenna is a closed conductor that carries current. Loops can be small (circumference much less than $\lambda$) or large (circumference close to $\lambda$). They behave very differently in those two regimes.

4.1 The small loop as a magnetic dipole

A small circular loop of $N$ turns and area $A$ carrying current $I$, with circumference much less than $\lambda$, radiates like a tiny magnetic dipole. The pattern is the same doughnut shape as an electric dipole, but oriented differently: the doughnut's hole now lies along the loop's axis, so the maximum radiation is in the plane of the loop, not along its axis.

Radiation resistance:

$R_r = 20\pi^2 \left(\frac{C}{\lambda}\right)^4 \cdot N^2$

where $C$ is the circumference. The fourth-power dependence is brutal. For $C = \lambda/10$, $R_r = 0.02$ Ω per turn. For $C = \lambda/100$, $R_r = 2 \times 10^{-6}$ Ω. To make it work, you need many turns and a high-Q matching network (low conductor loss, careful tuning).

Used in: AM-radio ferrite-rod antennas (the loop is wrapped around a high-permeability ferrite rod that concentrates the magnetic flux), RFID readers (13.56 MHz HF tags use near-field magnetic coupling, not radiation), wireless power transfer pads, and old direction-finding equipment.

For TEMPEST-style attacks, small loops are the antenna of choice for picking up the magnetic-field component of unintended emissions from a target chip. The chip's switching currents create local H-field that the loop converts to a measurable voltage. A few turns of wire on a ferrite rod, held centimeters from a CPU, can record spectrograms that leak processing activity.

4.2 The large loop and the quad antenna

A loop with circumference equal to $\lambda$ behaves nothing like a small loop. The current now varies around the loop, and the radiation has a pattern peaked along the loop's axis (perpendicular to the loop plane). With $C = \lambda$, the impedance is roughly 100 to 130 Ω, the gain is 1.5 dB more than a half-wave dipole, and the bandwidth is wider.

The quad antenna is a square loop of $\lambda/4$ on each side ($C = \lambda$). Often built as a Yagi-like array of quads (a "quad beam") for HF and VHF DX work because it gives slightly more gain than a Yagi of the same boom length and is less affected by nearby objects.

4.3 Loops vs dipoles: a comparison