Loop-gap resonator

A loop-gap resonator (LGR) is an electromagnetic resonator that operates in the radio and microwave frequency ranges. The simplest LGRs are made from a conducting tube with a narrow slit cut along its length. The LGR dimensions are typically much smaller than the free-space wavelength of the electromagnetic fields at the resonant frequency. Therefore, relatively compact LGRs can be designed to operate at frequencies that are too low to be accessed using, for example, cavity resonators. These structures can have very sharp resonances (high quality factors) making them useful for electron spin resonance (ESR) experiments, and precision measurements of electromagnetic material properties (permittivity and permeability).

Background

Loop-gap resonators (LGRs) can be modelled as lumped-element circuits. The slit along the length of the resonator has an effective capacitance

C

{\displaystyle C}

and the bore of the resonator has effective inductance

L

{\displaystyle L}

. At, or near, the resonance frequency, a circumferential current is established along the inner wall of the resonator. The effective resistance

R

{\displaystyle R}

that limits this current is, in part, determined by the resistivity

ρ

{\displaystyle \rho }

and electromagnetic skin depth

δ

{\displaystyle \delta }

of the conductor used to make the LGR. It is, therefore, possible to model the LGR as an

L

R

C

{\displaystyle LRC}

circuit. Since the LGR current is a maximum at the resonant frequency, the equivalent circuit model is a series

L

R

C

{\displaystyle LRC}

circuit.