The Cavity Resonance Frequency Conversion Calculator determines the resonant or cut-off frequency (fmnp) of a rectangular microwave cavity. It is used to analyze cavity modes that can exist within a specific geometry, which helps in designing resonators, filters, and oscillators in microwave systems.
Formula
fmnp = ( c / ( 2 × √(εr × μr) ) ) × √((m/a)² + (n/b)² + (p/h)²)
Constants
- c = 3 × 10¹¹ mm/s (speed of light)
Formula Explanation
- m, n, p = Mode numbers that define the resonance pattern.
- a, b, h = Internal cavity dimensions in mm, cm, or inches.
- εr = Relative permittivity of the medium inside the cavity.
- μr = Relative permeability of the medium (usually 1 for air).
- fmnp = Resonant frequency in GHz for the given mode and geometry.
Uses of this calculator
- Designing and analyzing rectangular microwave cavity resonators.
- Determining mode frequencies for filters and oscillators.
- Optimizing cavity dimensions for specific frequency bands.
- Studying electromagnetic field distributions in cavity structures.
What is the resonant frequency for a 20×10×5 mm air-filled cavity in the TE101 mode?
Input: a = 20 mm, b = 10 mm, h = 5 mm, εr = 1, μr = 1, m = 1, n = 0, p = 1
Output:
- fmnp = (3 × 10¹¹ / (2 × √(1 × 1))) × √((1/20)² + (0/10)² + (1/5)²)
- fmnp = (1.5 × 10¹¹) × √(0.0025 + 0 + 0.04) = (1.5 × 10¹¹) × 0.206
- fmnp = 3.09 × 10¹⁰ Hz = 30.9 GHz
- Resonant Frequency = 30.9 GHz