Enter transition dimensions
Use internal waveguide dimensions and actual coaxial conductor dimensions.
All dimensions are millimetres. Frequency is GHz.
Formula used
The calculator uses a lossless, uniformly filled rectangular-waveguide model and an ideal homogeneous coaxial model.
Here, c is the speed of light, εr is relative permittivity, a and b are internal guide dimensions, and D and d are coaxial diameters.
How to use this calculator
- Select the mode you plan to excite. Use TE10 for most basic rectangular transitions.
- Enter measured internal guide dimensions, not external flange dimensions.
- Enter the frequency where the transition should work best.
- Set the waveguide dielectric to 1.0 for dry air or vacuum.
- Enter the coaxial dielectric and both conductor diameters.
- Review cutoff status first. A mode below cutoff cannot carry the intended signal.
- Use probe length and backshort distance as initial build values.
- Simulate the complete geometry, then tune with measured S-parameters.
Example input data
| Input | Example value | Purpose |
|---|---|---|
| Waveguide | 22.86 mm × 10.16 mm | Typical WR-90 internal opening |
| Mode | TE10 | Common dominant mode |
| Frequency | 10.0 GHz | Example X-band center frequency |
| Guide dielectric | 1.0 | Air-filled guide |
| Coax geometry | d = 1.30 mm; D = 4.20 mm | Example internal conductor dimensions |
| Coax dielectric | 2.1 | Example solid dielectric value |
| Probe and backshort fractions | 0.25; 0.25 | Early tuning baseline |
Transition design basics
A rectangular waveguide-to-coaxial transition changes a TE field into a TEM field. The two transmission structures behave differently. Waveguide energy moves above a mode cutoff. Coaxial cable supports its TEM mode without a cutoff. A practical transition must couple energy efficiently while controlling reflections.
The broad wall dimension is the most important waveguide measurement. It sets the TE10 cutoff frequency. The narrow wall dimension affects higher-mode behavior and mechanical proportions. Your operating frequency must remain above the selected mode cutoff. It should also remain below the next unwanted mode cutoff. This is called single-mode operation.
Near cutoff, the guide wavelength becomes very long. The waveguide impedance also rises rapidly. A transition designed close to cutoff can become sensitive to tiny construction changes. Choose a center frequency with adequate separation from cutoff. Standard waveguide bands are designed around this principle.
A coaxial connector carries a different field pattern. Its impedance depends on conductor diameters and dielectric material. The calculator determines the ideal coaxial impedance from your dimensions. It also compares that value with your entered target. A large difference can require another coaxial geometry.
A probe transition uses the center conductor as an electric-field probe. It commonly enters through a broad wall. Probe position, length, and backshort distance control coupling. A centered probe position is a useful first arrangement for dominant-mode work. A backshort near one quarter guide wavelength is also a starting point. These values need electromagnetic simulation and vector-network-analyzer tuning.
Probe length is not fixed by one universal rule. A quarter of the dielectric wavelength provides an initial estimate. The effective shortening factor allows a cautious adjustment. The actual optimum depends on the connector body, probe diameter, wall thickness, and nearby discontinuities. Such details matter greatly.
This calculator is useful during early design reviews. Enter the internal waveguide dimensions, dielectric constant, and operating frequency. Then enter the coaxial dimensions and dielectric constant. Review the cutoff status before using any suggested lengths. Confirm that the selected mode propagates. Confirm that unwanted modes remain outside the intended operating region.
The displayed wave impedance is a modal quantity. It is not a simple conductor impedance. Therefore, a direct comparison with coaxial impedance is only an indicator. It does not predict the final return loss. Real transitions depend on three-dimensional fields. Use a full-wave solver when performance requirements are strict.
Manufacturing matters at microwave and millimeter-wave frequencies. Small drilling errors can alter coupling. Surface finish and joint alignment influence loss. Connector launches can introduce parasitic inductance. Calibration planes also affect measured results. Build test fixtures with repeatable flanges and screws. Measure several samples when production tolerance matters.
Use the calculated values as a documented starting design. Record dimensions, materials, and frequency assumptions. Simulate the assembly over the required band. Tune the probe and backshort in small steps. Finally, validate the manufactured transition with calibrated measurements. This approach reduces risk while keeping development practical.
Frequently asked questions
1. What does this calculator estimate?
It estimates cutoff frequencies, wavelength values, ideal coaxial impedance, probe length, backshort spacing, and basic transition positions. It is intended for early design work. Final hardware must be simulated and measured.
2. Why is TE10 commonly selected?
TE10 is the lowest-cutoff mode in a normal rectangular waveguide. It is usually the intended operating mode because it supports a simple field pattern and practical transition arrangements.
3. Can I use this below cutoff?
No. Below the selected mode cutoff, the mode does not propagate as intended. The calculator flags this condition and does not provide guide wavelength or backshort results.
4. Is the calculated coax impedance the connector rating?
No. It is the impedance predicted from the entered ideal diameters and dielectric. Real connector impedances also depend on their complete geometry, dielectric shape, and manufacturing tolerances.
5. Why is a probe shortening factor included?
A physical probe often becomes electrically longer because of end effects and surrounding metal. The factor supplies a controlled first adjustment. It does not replace optimization.
6. Should the backshort always equal one quarter guide wavelength?
No. One quarter guide wavelength is a common first value. The final distance changes with probe position, frequency, connector launch, matching structures, and required bandwidth.
7. Does modal impedance predict return loss?
No. Modal impedance is useful for understanding propagation. A waveguide-to-coaxial transition is a three-dimensional discontinuity. Its return loss needs full-wave analysis or calibrated measurement.
8. What dimensions should I measure?
Use the internal broad and narrow guide walls. For coax, use the inner conductor outside diameter and the outer conductor inside diameter at the relevant uniform section.
9. Can this design broadband transitions?
The calculator provides center-frequency starting values. Broadband transitions commonly need additional matching features, shaped probes, ridges, posts, tapers, or optimization across the full band.
10. Why does guide wavelength increase near cutoff?
As operating frequency approaches cutoff from above, the propagation constant decreases. That makes the guide wavelength grow. Small dimensional changes then become electrically significant.
11. What should I do after calculating?
Create a three-dimensional model using the calculated dimensions. Sweep frequency, tune probe and backshort values, build a prototype, and verify performance with a calibrated vector network analyzer.