Dielectric Resonator - Theory of Operation

Theory of Operation

Although dielectric resonators display many similarities to resonant metal cavities, there is one important difference between the two: while the electric and magnetic fields are zero outside the walls of the metal cavity (i.e. open circuit boundary conditions are fully satisfied), these fields are not zero outside the dielectric walls of the resonator (i.e. open circuit boundary conditions are approximately satisfied). Even so, electric and magnetic fields decay from their maximum values considerably when they are away from the resonator walls. Most of the energy is stored in the resonator at a given resonant frequency for a sufficiently high dielectric constant . Dielectric resonators can exhibit extremely high Q factor that is comparable to a metal walled cavity.

There are three types of resonant modes that can be excited in dielectric resonators: transverse electric (TE), transverse magnetic (TM) or hybrid electromagnetic (HEM) modes. Theoretically, there is an infinite number of modes in each of the three groups, and desired mode is usually selected based on the application requirements. Generally, mode is used in most non-radiating applications, but other modes can have certain advantages for specific applications.

Approximate resonant frequency of mode for an isolated cylindrical dielectric resonator can be calculated as :

Where is the radius of the cylindrical resonator and is its length. Both and are in millimeters. Resonant frequency is in gigahertz. This formula is accurate to about 2% in the range:

However, since a dielectric resonator is usually enclosed in a conducting cavity for most applications, the real resonant frequencies are different from the one calculated above. As conducting walls of the enclosing cavity approach the resonator, change in boundary conditions and field containment start to affect resonant frequencies. The size and type of the material encapsulating the cavity can drastically impact the performance of the resonant circuit. This phenomenon can be explained using cavity perturbation theory. If a resonator is enclosed in a metallic cavity, resonant frequencies change in following fashion :

- if the stored energy of the displaced field is mostly electric, its resonant frequency will decrease;

- if the stored energy of the displaced field is mostly magnetic, its resonant frequency will increase. This happens to be the case for mode.

Most common problem exhibited by dielectric resonator circuits is their sensitivity to temperature variation and mechanical vibrations. Even though recent improvements in materials science and manufacturing mitigated some of these issues, compensating techniques still may be required to stabilize the circuit performance over temperature and frequency.