Calculator Inputs
Example Data Table
| Mode | a (mm) | b (mm) | Frequency (GHz) | εr | μr | Typical Use |
|---|---|---|---|---|---|---|
| TE10 | 22.86 | 10.16 | 10.00 | 1.00 | 1.00 | X-band lab and radar work |
| TE20 | 22.86 | 10.16 | 16.00 | 1.00 | 1.00 | Higher-order mode study |
| TM11 | 30.00 | 15.00 | 12.50 | 2.20 | 1.00 | Filled guide material comparison |
These values are sample inputs for validation, teaching, and comparison. They are not a substitute for manufacturer data.
Formula Used
Cutoff frequency: fc = (v / 2) × √[(m / a)2 + (n / b)2]
Medium velocity: v = c / √(εrμr)
Intrinsic impedance: η = η0 × √(μr / εr)
TE wave impedance: ZTE = η / √[1 - (fc / f)2]
TM wave impedance: ZTM = η × √[1 - (fc / f)2]
Guide wavelength: λg = λ / √[1 - (fc / f)2]
Propagation constant: β = (2π / λ) × √[1 - (fc / f)2]
This calculator uses standard rectangular waveguide relationships. Impedance rises sharply near cutoff for TE modes, while TM impedance drops as the cutoff boundary is approached.
How to Use This Calculator
- Choose TE or TM mode according to your design case.
- Enter mode indices m and n for the selected field pattern.
- Input broad and narrow guide dimensions in millimeters.
- Provide operating frequency in gigahertz and material constants.
- Click the calculate button to place results above the form.
- Review cutoff margin, wavelength, velocity, and impedance values.
- Use CSV or PDF export for reports, audits, and study notes.
Engineering Notes
Waveguide impedance is not constant like a lumped transmission line value. It changes with mode, dielectric filling, and distance from cutoff. Designers often target a stable band region above cutoff for smoother matching and more predictable performance.
If your operating frequency is too close to cutoff, guide wavelength becomes long and impedance shifts quickly. That can increase sensitivity to tolerance, connectors, and transitions in real systems.
Frequently Asked Questions
1. What is waveguide impedance?
Waveguide impedance is the ratio of transverse electric and magnetic fields inside a propagating mode. It depends on frequency, cutoff, material, and mode family.
2. Why does TE impedance increase near cutoff?
For TE modes, the denominator contains the propagation factor. As frequency approaches cutoff, that factor shrinks, causing the calculated impedance to rise strongly.
3. Why are TM modes restricted here?
Rectangular TM modes require both field indices above zero. A zero index would violate the boundary conditions for the selected transverse field pattern.
4. Can I use dielectric-filled waveguides?
Yes. Enter the relative permittivity and permeability values for the filling medium. The calculator adjusts intrinsic impedance, velocity, cutoff, and all dependent outputs.
5. What dimensions should I enter?
Use the internal broad wall dimension for a and the internal narrow wall dimension for b. External housing size should not replace internal guide size.
6. Does this calculator include conductor loss?
No. This tool focuses on ideal mode propagation and impedance behavior. Use a dedicated attenuation model when conductor roughness or finite conductivity matters.
7. When should I trust the results most?
Results are most stable when geometry, material data, and mode choice are correct, and the operating frequency stays comfortably above cutoff.