Waveguide Calculator computes TE10 cutoff frequency and recommended single-mode operating band for a rectangular waveguide from its broad wall width, including the TE20 mode limit.
Waveguide Calculator for TE₁₀ Cutoff Frequency and Recommended Operating Band
This tool calculates the TE₁₀ dominant-mode cutoff frequency of a rectangular waveguide from its broad wall width, then derives the recommended single-mode operating band and the point where the next mode starts interfering. RF and microwave engineers use it to size a waveguide for a target frequency or to identify which standard WR waveguide size fits an existing system.
How to Use
Enter the broad wall width (the wider inner dimension of the waveguide cross-section). The calculator returns TE₁₀ cutoff frequency, recommended operating band, cutoff wavelength, a typical 2:1 height, and the TE₂₀ higher-order mode cutoff.
Formula
TE₁₀ cutoff frequency follows the standard rectangular waveguide relation used throughout microwave engineering (as derived in Pozar’s Microwave Engineering) and matches the naming convention set by the EIA (Electronic Industries Alliance) WR waveguide series:
$$f_c = \frac{c}{2W}, \quad \lambda_c = 2W$$
where $c = 299{,}792{,}458$ m/s. The recommended single-mode operating band is the standard industry rule of thumb, 1.25× to 1.89× cutoff:
$$f_1 = 1.25 f_c, \quad f_2 = 1.89 f_c$$
Band-edge wavelengths convert those frequencies back through $\lambda = c/f$. The next mode up, TE₂₀, cuts off at twice the dominant-mode frequency:
$$f_{c,TE_{20}} = \frac{c}{W} = 2f_c$$
Band clearance is the gap between the upper recommended limit and that TE₂₀ cutoff. The most common input mistake is entering the narrow wall (height) instead of the broad wall (width) — $f_c$ depends only on the broad wall, and swapping the two dimensions produces a cutoff frequency for a completely different waveguide size.
A width of 22.86 mm isn’t a generic example — it’s the EIA-standard broad wall dimension for WR-90, the common X-band waveguide. But EIA’s actual WR-90 narrow wall is 10.16 mm (0.400 in), giving a real aspect ratio near 2.25:1, not the 2:1 this calculator uses for “typical height.” The 2:1 figure is a widely used rule-of-thumb approximation, not the manufactured dimension — don’t use this calculator’s height output to spec a real WR-size part without checking the actual EIA table for that size.
Reference Table
| Dimension | This calculator (2:1 rule) | Actual EIA WR-90 standard |
|---|---|---|
| Broad wall (W) | 22.86 mm | 22.86 mm (0.900 in) |
| Narrow wall (H) | 11.43 mm | 10.16 mm (0.400 in) |
| Aspect ratio (W/H) | 2.00 | 2.25 |
FAQ
Why does the recommended band start above cutoff instead of at it?
Attenuation rises sharply near cutoff and propagation becomes unstable. Starting at 1.25× cutoff keeps the waveguide well clear of that region while still using it efficiently.
What happens above the upper recommended limit?
Above roughly 1.89× cutoff, the TE₂₀ mode can also propagate alongside TE₁₀. With two modes present, signal integrity, impedance, and field patterns become unpredictable.
Does waveguide height affect the cutoff frequency?
Not for the TE₁₀ dominant mode. $f_c$ depends only on the broad wall width $W$. Height affects power handling and some higher-order modes, but not TE₁₀ cutoff.
Can I use a waveguide below its cutoff frequency?
No. Below $f_c$ the wave decays exponentially instead of propagating — the waveguide behaves like a high-pass filter with a hard lower limit set by its geometry.
How do I match this to a standard WR waveguide size?
Match the broad wall width to a published EIA WR dimension (for example 22.86 mm is WR-90), then use that size’s actual EIA height rather than this calculator’s 2:1 estimate for a real part.