How do I calculate the impedance of a rectangular waveguide for matching purposes?
Waveguide Impedance Definitions
Unlike coaxial cable where the characteristic impedance has a single, unambiguous definition (V/I for a traveling wave), waveguide impedance has multiple definitions because there is no unique way to define voltage and current for a waveguide mode. The electric and magnetic fields vary across the waveguide cross-section, so different integration paths give different V/I ratios.
| Parameter | Standard Rect. | Ridged | Circular |
|---|---|---|---|
| Single-Mode BW | 40% (1.25-1.9 fc) | 50-150% | 26% (1.31:1 ratio) |
| Attenuation | Low | Moderate (3-5x) | Low to very low |
| Power Handling | High (kW-class) | Moderate | High |
| Polarization | Single | Single | Dual (TE11) |
| Cost | Low (commodity) | Medium | High (specialty) |
Frequently Asked Questions
Which impedance definition should I use?
For waveguide circuit design (filters, couplers, matching): use wave impedance Zw. For calculating power from field measurements: use the power definitions. For equivalent circuit modeling of waveguide junctions: use the impedance definition that makes the junction model simplest (usually Zw).
Does waveguide impedance match like coax?
The same matching principles apply (reflection coefficient, Smith chart, quarter-wave transformers) using the wave impedance. However, the frequency dependence of Zw (due to the √(1-(fc/f)²) term) means that a perfect match at one frequency is not perfect across the band. Wideband matching requires multi-section designs.
What about normalized impedance?
In waveguide circuit design, impedances are typically normalized to the wave impedance at the center frequency. This normalization simplifies the design process and makes the design equations identical to those for TEM transmission lines. The denormalization to physical dimensions is done at the final design step.