Analyze rectangular guide behavior with accurate cutoff calculations. Input dimensions, mode numbers, and material properties. Export results, inspect graphs, and validate designs using examples.
This example uses a rectangular air-filled guide with a = 22.86 mm, b = 10.16 mm, εr = 1, and μr = 1.
| Mode | a (mm) | b (mm) | εr | μr | Cutoff Frequency (GHz) |
|---|---|---|---|---|---|
| TE10 | 22.86 | 10.16 | 1.00 | 1.00 | 6.557140 |
| TE20 | 22.86 | 10.16 | 1.00 | 1.00 | 13.114281 |
| TE01 | 22.86 | 10.16 | 1.00 | 1.00 | 14.753566 |
| TE11 | 22.86 | 10.16 | 1.00 | 1.00 | 16.145086 |
| TM11 | 22.86 | 10.16 | 1.00 | 1.00 | 16.145086 |
For a rectangular waveguide, the cutoff frequency of mode m,n is:
fc = (c / (2√(μrεr))) × √[(m/a)² + (n/b)²]
Here, c is the speed of light in free space, a is the broad internal dimension, b is the narrow internal dimension, m and n are the mode indices, εr is relative permittivity, and μr is relative permeability.
The cutoff wavelength is:
λc = 2 / √[(m/a)² + (n/b)²]
If the operating frequency is above cutoff, the tool also estimates guide wavelength, phase velocity, and group velocity. These values help engineers judge whether the selected mode can propagate and how the guide behaves near the operating frequency.
Choose either TE or TM mode first. Then enter the mode indices m and n that match your design case. Add the broad dimension a and narrow dimension b in millimeters. Enter the material properties through relative permittivity and relative permeability. Finally, enter the operating frequency in gigahertz and press calculate.
The result section appears above the form after submission. It shows the cutoff frequency in hertz and gigahertz, the cutoff wavelength, the propagation status, and additional wave parameters when the operating frequency exceeds cutoff. Use the graph to study how width changes the cutoff point for the selected mode.
This calculator is intended for rectangular waveguide analysis. TE modes cannot use m = 0 and n = 0 together. TM modes require both indices to be greater than zero. Keep units consistent and verify internal dimensions rather than external housing dimensions for accurate engineering estimates.
Cutoff frequency defines the lower frequency limit for a specific waveguide mode. Below cutoff, the field decays and real power transmission does not occur. Above cutoff, propagation becomes possible and dispersion effects appear. In practice, designers usually choose operating bands that stay clear of unwanted higher-order modes.
The dominant mode in many rectangular guides is TE10 because it offers the lowest cutoff frequency. Increasing the broad dimension generally lowers the TE10 cutoff frequency, while increasing the narrow dimension mainly affects modes containing the n index. A dielectric filling raises effective capacitance and reduces wave velocity, which lowers cutoff frequency when other dimensions remain unchanged.
Near cutoff, phase and group behavior changes strongly. That is why this page also reports guide wavelength, phase velocity, and group velocity when the chosen operating frequency exceeds the calculated cutoff value. These extra outputs are useful in microwave component design, filter layout checks, antenna feed studies, laboratory teaching, and transmission path validation.
Cutoff frequency is the minimum frequency at which a chosen waveguide mode can propagate. Below that value, the electromagnetic field becomes evanescent instead of carrying power forward.
TE10 usually has the lowest cutoff frequency in a rectangular waveguide. Because it propagates first, engineers often design operating bands around this mode to avoid higher-mode interference.
In rectangular guides, TM modes require both indices to be positive to satisfy boundary conditions. If either index is zero, the field pattern does not represent a valid TM solution.
A larger relative permittivity lowers wave velocity inside the guide. That reduced velocity lowers the cutoff frequency for the same dimensions and selected mode numbers.
Enter the internal broad dimension a and internal narrow dimension b of the rectangular guide. Internal dimensions control the field solution and therefore determine the correct cutoff frequency.
Guide wavelength is only meaningful when operating frequency is above cutoff. If frequency is below cutoff, the selected mode does not propagate, so that value is not reported.
No. This page uses rectangular waveguide equations with dimensions a and b. Circular guides use different mode constants and different cutoff relationships.
The graph shows how cutoff frequency shifts when the broad dimension changes. It helps compare sensitivity, confirm trends, and support quick preliminary design decisions.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.