Calculator Inputs
Example Data Table
| Guide Example | a | b | Mode | Material | Approximate Cutoff |
|---|---|---|---|---|---|
| WR-90 | 22.86 mm | 10.16 mm | TE10 | Air | 6.557 GHz |
| WR-90 | 22.86 mm | 10.16 mm | TE20 | Air | 13.114 GHz |
| WR-90 | 22.86 mm | 10.16 mm | TE01 | Air | 14.754 GHz |
| WR-62 | 15.80 mm | 7.90 mm | TE10 | Air | 9.487 GHz |
| Dielectric WR-90 | 22.86 mm | 10.16 mm | TE10 | er 2.2 | 4.421 GHz |
Formula Used
The cutoff frequency for a rectangular waveguide mode is:
fc = v / 2 × √((m / a)² + (n / b)²)
Here, a is the broad wall. b is the narrow wall. m and n are mode numbers.
The material wave speed is:
v = c / √(er × ur)
The cutoff wavelength is:
λc = v / fc
For frequencies above cutoff, guide wavelength is:
λg = λ / √(1 - (fc / f)²)
TE modal impedance is:
ZTE = η / √(1 - (fc / f)²)
TM modal impedance is:
ZTM = η × √(1 - (fc / f)²)
How To Use This Calculator
- Select TE or TM mode.
- Enter mode numbers m and n.
- Add broad wall and narrow wall dimensions.
- Select dimension units.
- Enter material permittivity and permeability.
- Enter the operating frequency.
- Add the desired margin above cutoff.
- Press Calculate and review the result section.
- Use CSV or PDF export for saved analysis.
About Rectangular Waveguide Cutoff
A rectangular waveguide carries microwave energy inside a metal channel. It does not pass every signal. Each field pattern has a minimum frequency. That limit is the cutoff frequency. Below it, the mode fades quickly. Above it, energy can travel along the guide.
Why Cutoff Matters
Cutoff is important in radar, antennas, links, cavities, and lab fixtures. Designers usually want one dominant mode. For a common air filled guide, TE10 is normally the first mode. Higher modes start at higher cutoff values. If the operating frequency is too close to cutoff, guide wavelength becomes long. Group velocity drops. Dispersion rises. Measurements can become unstable.
What This Tool Checks
This calculator accepts broad wall size, narrow wall size, mode numbers, material values, and operating frequency. It supports TE and TM checks. It also estimates cutoff wavelength, guide wavelength, phase constant, phase velocity, group velocity, and modal impedance. The propagation status helps you see whether the chosen signal is above cutoff. The margin value shows how far the operating frequency sits above the mode limit.
Mode Selection Guidance
Use m and n carefully. TE modes allow either number to be zero, but not both at once. TM modes need both m and n above zero. The dominant rectangular waveguide mode is TE10. This mode depends mainly on the broad wall dimension. Wider guides have lower cutoff frequencies. Filling the guide with dielectric material also lowers cutoff because wave speed is reduced.
Design Use
Use the results as an engineering starting point. Leave enough margin between cutoff and operating frequency. Many practical guides operate well above TE10 cutoff and below the next unwanted mode. This supports cleaner propagation. It also reduces mode conversion risk. Loss, roughness, bends, flanges, and transitions still affect real systems.
Practical Notes
Always use consistent dimensions. The calculator converts millimeters, centimeters, inches, and meters to meters. Relative permittivity and permeability change the wave speed. For most air filled guides, use one for both values. Export the results when comparing sizes or preparing reports. Review the example table before entering custom values. It shows common inputs and expected behavior. Treat unusual material data with care. Verify critical microwave designs with measurement, simulation, or published guide standards.
FAQs
What is waveguide cutoff frequency?
It is the lowest frequency at which a selected waveguide mode can propagate. Below cutoff, the field decays instead of carrying useful power along the guide.
Which mode is dominant in a rectangular waveguide?
TE10 is usually the dominant mode. It has the lowest cutoff frequency in a standard rectangular guide when the broad wall is larger than the narrow wall.
Can TM10 exist in a rectangular waveguide?
No. TM modes need both m and n greater than zero. TM10 and TM01 are invalid because one field variation number is zero.
Why does dielectric filling reduce cutoff frequency?
Dielectric material reduces wave speed inside the guide. Since cutoff frequency depends on wave speed, higher permittivity lowers the cutoff value.
What happens below cutoff?
The wave becomes evanescent. It decays along the guide and does not propagate power efficiently over distance.
What is guide wavelength?
Guide wavelength is the wavelength measured along the waveguide path. It is longer than the material wavelength and becomes very large near cutoff.
Why is cutoff margin important?
A larger margin helps reduce dispersion and unstable operation. Designers often avoid running too close to cutoff unless a special effect is needed.
Can this replace full electromagnetic simulation?
No. It gives useful first estimates. Final high power, high frequency, or precision designs should use simulation, measurement, and verified guide data.