Rectangular Waveguide Calculator
Calculates the cutoff frequency for every TEmn and TMmn mode, the dominant TE10 guide wavelength and wave impedance, phase and group velocities, and conductor loss at the operating frequency.
Equations & Parameters ▸
\(f_{c,mn} = \dfrac{c}{2\sqrt{\varepsilon_r}}\sqrt{\left(\dfrac{m}{a}\right)^2+\left(\dfrac{n}{b}\right)^2} \qquad \beta = \sqrt{k^2 - k_c^2} \qquad \lambda_g = \dfrac{2\pi}{\beta}\)
\(Z_{TE_{10}} = \dfrac{\omega\mu_0}{\beta} \qquad v_{ph} = \dfrac{\omega}{\beta} \qquad v_{gr} = \dfrac{\beta c^2}{\omega\varepsilon_r}\)
| a | Broad-wall dimension (determines TE₁₀ cutoff: f_c = c/(2a√εr)) |
| b | Narrow-wall dimension; typically b ≈ a/2 for standard waveguide |
| λg | Guide wavelength; longer than free-space λ (vph > c) |
| ZTE | Wave impedance; 377Ω at f → ∞, → ∞ as f → f_c |
| vph·vgr | Phase × group velocity = c²/εr (always) |
Standard waveguide bands: WR-90 (a=22.86mm, b=10.16mm, 8.2–12.4 GHz X-band), WR-42 (a=10.67mm, b=4.32mm, 18–26.5 GHz K-band), WR-28 (a=7.11mm, b=3.56mm, 26.5–40 GHz Ka-band).
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