Home / Solvers / Resonance

Resonance is the tendency of a system to oscillate with larger amplitude at some frequencies than at others. These are known as the system's resonant frequencies. At these frequencies, even small periodic driving forces can produce large amplitude oscillations, because the system stores energy. When loss is small, the resonant frequency is approximately equal to a natural frequency of the system, which is a frequency of unforced vibrations. Some systems have multiple, distinct, resonant frequencies. Resonance phenomena occur with all types of waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance, electron spin resonance and resonance of quantum wave functions.

**Applications**

In the Resonance analysis, we are concerned only with electromagnetic resonance. The vector wave equation, i.e. combination of the full Maxwell's equations, is solved using vector finite element to obtain the natural resonant frequencies and their corresponding electric/magnetic field distributions. It has many practical applications, including:

- Dielectric resonators
- Filters
- Resonators
- Microwave Circuits
- Microwave Ovens
- Food and industrial heating
- Wood drying and processing
- Resonator antennas
- High Q structures
- Linear accelerators

The Resonance module outputs the following results for each study:

- Resonant frequencies or the Eigen modes
- Dielectric quality factor
- Conductor quality factor
- Overall quality factor
- Electric field distribution
- Magnetic field distribution
- Specific absorption rate distribution

The Resonance module can help study a large number of RF & microwave devices and address numerous resonance and loss effects. Below is just a partial list:

- Design a resonator around a specific resonant frequency.
- Predict dielectric breakdown in a dielectric resonator and avoid it.
- Compute conductor and dielectric quality factors separately.
- Account for both conductivity and surface roughness of a conductor wall.
- Design high Q structures.
- Properly dimension the resonators in of multi-pole filters and optimize pole-zero placement.
- Adjust circuit housing to push resonances out the operational band and have a resonance-free structure.
- Compute the specific absorption rate (SAR) in microwave heating applications.
- Predict if a given design will resonate and locate resonance areas.
- Study the effect of material and dimension on the resonant frequency and the field distribution.