How do I determine the cutoff frequency and usable bandwidth of a rectangular waveguide?
Waveguide Operating Range
Rectangular waveguide supports propagation only above the cutoff frequency of each mode. The dominant mode (TE10) has the lowest cutoff frequency, determined by the broad wall dimension: fc10 = c/(2a). Below this frequency, all modes are evanescent (decaying) and the waveguide acts as a high-pass filter with extreme rejection.
The next mode (TE20) has cutoff at fc20 = c/a = 2×fc10. Between fc10 and fc20, only the TE10 mode propagates, providing single-mode operation with predictable behavior. Operating in this single-mode region is essential for well-defined transmission characteristics. Above fc20, multiple modes propagate simultaneously, causing unpredictable interference.
The standard operating range avoids the extremes of the single-mode region: below 1.25×fc, the attenuation increases rapidly and the waveguide impedance changes dramatically; above 0.95×fc20, the proximity to the next mode's cutoff makes the waveguide susceptible to higher-mode excitation from imperfections. The standard bands (WR-XX designations) use approximately 1.25×fc to 1.9×fc for the operating range.
TE20 cutoff: fc20 = c / a = 2fc
TE01 cutoff: fc01 = c / (2b)
WR-90: a=22.86mm, fc=6.56 GHz
Band: 8.2-12.4 GHz
WR-42: a=10.67mm, fc=14.05 GHz
Band: 18-26.5 GHz
WR-10: a=2.54mm, fc=59.01 GHz
Band: 75-110 GHz
Frequently Asked Questions
Why not use the full range between fc and 2fc?
Near fc, the attenuation increases sharply (theoretically infinite at fc), the wavelength approaches infinity, and the dispersion becomes severe. Near 2fc, imperfections can excite the TE20 mode. The practical range (1.25fc to 1.9fc) avoids both problems while providing useful bandwidth.
Can I use waveguide below cutoff?
Yes, as an attenuator. Below cutoff, the attenuation is approximately 27.3/a dB per free-space wavelength (for TE10). This provides frequency-independent attenuation for cutoff attenuators, used as precision variable attenuators in measurement systems.
What if I need more bandwidth?
Use a larger waveguide that covers a wider absolute bandwidth (though the same percentage bandwidth). Or use ridged waveguide, which lowers the TE10 cutoff without lowering the TE20 cutoff, potentially doubling the single-mode bandwidth. Or switch to coaxial cable for multi-octave bandwidth.