Rectangular Waveguide Cut-Off Frequency Calculator (WR-90, TE10)
Cut-off frequency of the TE10, TE20, TE01 and TE11 modes of a rectangular waveguide, with the guide wavelength and group velocity at your operating frequency.
Results
The dashed line marks the value you entered.
What this tool does
A hollow waveguide is a high-pass filter: below the cut-off frequency of its first mode the wave cannot travel, and above it the wave travels with a wavelength longer than in free space. For a rectangular guide the cut-off of mode (m, n) is c ÷ 2 × √((m ÷ a)² + (n ÷ b)²), and the dominant TE10 mode has f_c = c ÷ 2a, 6.56 GHz for the standard WR-90 (22.86 × 10.16 mm). Guides are normally used between about 1.25 and 1.9 times the TE10 cut-off, where only that one mode propagates and the loss is low. Filling the guide with a dielectric lowers every cut-off by √ε_r.
Formula
f_c(m,n) = c ÷ (2√ε_r) × √((m ÷ a)² + (n ÷ b)²) · λ_g = λ ÷ √(1 − (f_c ÷ f)²) · v_g = c ÷ √ε_r × √(1 − (f_c ÷ f)²)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a | Wide inner dimension a | mm |
b | Narrow inner dimension b | mm |
f | Operating frequency | GHz |
er | Relative permittivity of the filling (1 for air) | — |
F10 | Cut-off of the dominant mode TE10 | GHz |
F20 | Cut-off of TE20 | GHz |
F01 | Cut-off of TE01 | GHz |
F11 | Cut-off of TE11 and TM11 | GHz |
LG | Guide wavelength at the operating frequency | mm |
VG | Group velocity (share of the speed of light) | % |
ST | What happens at this frequency | — |
Worked example
- Wide inner dimension a22.86 mm
- Narrow inner dimension b10.16 mm
- Operating frequency10 GHz
- Relative permittivity of the filling (1 for air)1
- Cut-off of the dominant mode TE106.5571 GHz
- Cut-off of TE2013.1143 GHz
- Cut-off of TE0114.7536 GHz
- Cut-off of TE11 and TM1116.1451 GHz
- Guide wavelength at the operating frequency39.71 mm
- Group velocity (share of the speed of light)75.5 %
- What happens at this frequencyOnly the dominant TE10 mode propagates
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.