Enter Cavity Parameters
Example Data Table
| Mode | a (m) | b (m) | d (m) | εr | μr | Approx. Frequency |
|---|---|---|---|---|---|---|
| TE101 | 0.10 | 0.08 | 0.06 | 1.0 | 1.0 | 2.915 GHz |
| TE102 | 0.10 | 0.08 | 0.06 | 1.0 | 1.0 | 5.585 GHz |
| TM111 | 0.12 | 0.09 | 0.07 | 2.2 | 1.0 | 1.699 GHz |
Formula Used
For a rectangular cavity resonator, the resonant frequency is calculated from the selected mode indices and cavity dimensions.
Where:
- fmnp = resonant frequency
- c = speed of light in vacuum
- εr = relative permittivity of filling medium
- μr = relative permeability of filling medium
- a, b, d = cavity dimensions in meters
- m, n, p = integer mode indices
The wavelength inside the medium is found from λ = v / f, where v = c / √(εr μr). The displayed Q value is a simplified conductor-loss estimate based on wall conductivity and surface resistance.
How to Use This Calculator
- Select the cavity mode type, either TE or TM.
- Enter dimensions a, b, and d for the rectangular cavity.
- Choose the dimension unit that matches your measurements.
- Enter mode indices m, n, and p.
- Provide relative permittivity and permeability for the cavity filling.
- Enter wall conductivity if you want an approximate Q estimate.
- Click Calculate Resonance to see the result above the form.
- Review the table and graph, then export the values as CSV or PDF.
TM modes require all three indices to be nonzero in this calculator. TE modes allow zero values, but not all three at once.
Frequently Asked Questions
1. What does this cavity resonance calculator compute?
It calculates the resonant frequency of a rectangular cavity for a chosen TE or TM mode. It also reports wavelength, angular frequency, modal term, skin depth, and a simplified Q estimate.
2. What is the difference between TE and TM modes?
TE modes have no electric field component in the propagation direction, while TM modes have no magnetic field component in that direction. Their valid index combinations and field patterns differ.
3. Why do cavity dimensions strongly affect frequency?
Each dimension sets the standing-wave boundary condition inside the resonator. Smaller dimensions support shorter standing waves, which increases the resonant frequency for the same mode indices.
4. Why does higher permittivity reduce resonance frequency?
Higher relative permittivity lowers electromagnetic wave speed inside the cavity. Since resonance depends on both geometry and wave speed, the natural frequency decreases as permittivity increases.
5. Is the Q factor exact?
No. The displayed Q is a fast approximation for comparison and preliminary design. Real Q also depends on surface finish, seams, coupling, dielectric loss, radiation leakage, and manufacturing tolerances.
6. Can I use inches or millimeters?
Yes. The calculator converts meters, centimeters, millimeters, micrometers, inches, and feet into meters before applying the resonance formula. This keeps the final computation consistent.
7. Why does TM mode reject zero indices here?
For rectangular cavity TM modes, all three indices must be nonzero under the standard formulation used here. A zero index would violate the boundary conditions for that field family.
8. What does the graph show?
The graph shows how resonant frequency changes when dimension a varies around the selected value. It helps you visualize geometric sensitivity during resonator tuning and design optimization.