Cutoff Frequency
Understanding Cutoff Frequency
Cutoff frequency is one of the most important concepts in waveguide engineering. It is the boundary between propagation and evanescence. Below cutoff, a waveguide acts as a high-pass filter, attenuating signals exponentially. Above cutoff, the waveguide supports propagation with relatively low loss.
Cutoff Frequency by Mode
Each waveguide mode (TE_mn and TM_mn) has its own cutoff frequency. The mode with the lowest cutoff frequency is called the dominant mode. For rectangular waveguide, this is the TE10 mode. The waveguide is designed to operate in the frequency range where only the dominant mode propagates (single-mode region).
Single-Mode Bandwidth
The single-mode region extends from the TE10 cutoff to the TE20 cutoff (which is exactly 2x the TE10 cutoff for standard rectangular waveguide). In practice, waveguide is used from about 1.25x to 1.9x the TE10 cutoff to avoid performance degradation near the band edges.
Why Cutoff Matters
- Waveguide selection: The cutoff frequency determines which waveguide size to use for a given frequency band.
- Filter design: Evanescent-mode sections (below cutoff) are used as coupling elements in waveguide filters.
- Mode suppression: Understanding higher-order mode cutoffs ensures clean single-mode operation.
fc = (c/2) × √((m/a)² + (n/b)²)
Dominant mode TE10:
fc = c / (2a)
where a = broad wall dimension
Circular waveguide cutoff (TE_mn mode):
fc = (c × p'mn) / (2πr)
where p'mn = m-th zero of J'n Bessel function
Example: WR-90 (a = 22.86 mm):
fc(TE10) = 3e8 / (2 × 0.02286) = 6.557 GHz
fc(TE20) = 13.114 GHz
Common Waveguide Cutoff Frequencies
| WR Size | a (mm) | TE10 Cutoff | TE20 Cutoff | Usable Band |
|---|---|---|---|---|
| WR-284 | 72.14 | 2.08 GHz | 4.16 GHz | 2.60-3.95 GHz |
| WR-90 | 22.86 | 6.56 GHz | 13.11 GHz | 8.20-12.40 GHz |
| WR-42 | 10.67 | 14.05 GHz | 28.10 GHz | 18.0-26.5 GHz |
| WR-28 | 7.11 | 21.08 GHz | 42.16 GHz | 26.5-40.0 GHz |
| WR-10 | 2.54 | 59.01 GHz | 118.03 GHz | 75-110 GHz |
Frequently Asked Questions
What is cutoff frequency in a waveguide?
Cutoff frequency is the minimum frequency at which a given mode can propagate in a waveguide. Below this frequency, the electromagnetic fields decay exponentially and no power is transmitted. For the dominant TE10 mode in rectangular waveguide, fc = c/(2a), where a is the broad wall dimension.
What happens below cutoff frequency?
Below cutoff, the waveguide acts as a high-pass filter. Fields decay exponentially with distance, and the attenuation increases rapidly as frequency decreases further below cutoff. This evanescent behavior is deliberately used in some filter designs as a coupling mechanism.
How do you choose the right waveguide size?
Select a waveguide whose TE10 cutoff is below your operating frequency and whose TE20 cutoff is above it. The standard operating band is approximately 1.25x to 1.9x the TE10 cutoff frequency. WR designation numbers correspond to the broad wall dimension in hundredths of an inch.