Waveguide Cutoff
Frequency Calculator
Determine the cutoff frequency for standard rectangular and circular waveguide sizes across dominant and higher-order modes. Includes a complete WR size reference from WR-284 to WR-03.
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Standard Rectangular Waveguide Sizes (WR Series)
The complete EIA WR series from S-band through WR-03 (220-330 GHz). The recommended frequency range ensures single-mode TE₁₀ operation with margin from cutoff.
| EIA | Band | a (mm) | b (mm) | a (inches) | Freq Range (GHz) | fc TE₁₀ (GHz) |
|---|---|---|---|---|---|---|
| WR-284 | S | 72.136 | 34.036 | 2.840 | 2.60 – 3.95 | 2.078 |
| WR-187 | C | 47.549 | 22.149 | 1.872 | 3.95 – 5.85 | 3.153 |
| WR-137 | C | 34.849 | 15.799 | 1.372 | 5.85 – 8.20 | 4.301 |
| WR-90 | X | 22.860 | 10.160 | 0.900 | 8.20 – 12.40 | 6.557 |
| WR-62 | Ku | 15.799 | 7.899 | 0.622 | 12.40 – 18.00 | 9.488 |
| WR-42 | K | 10.668 | 4.318 | 0.420 | 18.00 – 26.50 | 14.051 |
| WR-28 | Ka | 7.112 | 3.556 | 0.280 | 26.50 – 40.00 | 21.077 |
| WR-22 | Q | 5.690 | 2.845 | 0.224 | 33.00 – 50.00 | 26.346 |
| WR-19 | U | 4.775 | 2.388 | 0.188 | 40.00 – 60.00 | 31.391 |
| WR-15 | V | 3.759 | 1.880 | 0.148 | 50.00 – 75.00 | 39.875 |
| WR-12 | E | 3.099 | 1.549 | 0.122 | 60.00 – 90.00 | 48.373 |
| WR-10 | W | 2.540 | 1.270 | 0.100 | 75.00 – 110.00 | 59.015 |
| WR-08 | F | 2.032 | 1.016 | 0.080 | 90.00 – 140.00 | 73.768 |
| WR-06 | D | 1.651 | 0.826 | 0.065 | 110.00 – 170.00 | 90.791 |
| WR-05 | G | 1.295 | 0.648 | 0.051 | 140.00 – 220.00 | 115.714 |
| WR-03 | Y | 0.864 | 0.432 | 0.034 | 220.00 – 330.00 | 173.571 |
How Waveguide Propagation Works
A waveguide is a hollow metallic tube that confines and guides electromagnetic waves. Unlike coaxial cable, which supports TEM (transverse electromagnetic) mode propagation at all frequencies, waveguide supports only specific modes, each with its own cutoff frequency.
The Cutoff Frequency Formula
fc = (c / 2) × √((m/a)² + (n/b)²)
Dominant mode TE₁₀ (m=1, n=0):
fc = c / (2a)
Where c = 3×10⁸ m/s, a = broad wall, b = narrow wall
Why Single-Mode Operation Matters
Waveguide components are designed to operate with only the dominant mode (TE₁₀) propagating. If the operating frequency exceeds the cutoff of a higher-order mode, that mode can also propagate, causing interference, unpredictable impedance, and measurement errors. The recommended operating band for each WR size is carefully set between the TE₁₀ cutoff and the next higher mode to avoid this.
Waveguide vs. Coaxial Cable
- Loss: Waveguide has 5-20× lower loss than flexible coaxial cable at the same frequency. At 40 GHz, typical waveguide loss is 0.1-0.3 dB/ft vs. 1-3 dB/ft for coax.
- Power handling: Waveguide handles 10-100× more power than coaxial cable due to the larger cross-section and absence of a center conductor.
- Bandwidth: Each waveguide size covers roughly a 50% bandwidth (e.g., 26.5-40 GHz for WR-28). Coaxial cable covers DC to its upper frequency limit.
- Cost: Waveguide components are more expensive than coaxial counterparts due to precision machining requirements.
Frequently Asked Questions
What is waveguide cutoff frequency?
The cutoff frequency is the lowest frequency at which a particular mode can propagate through a waveguide. Below cutoff, signals are exponentially attenuated. Waveguides are operated between the dominant mode cutoff and the next higher mode cutoff for single-mode propagation.
What does the WR number mean?
WR stands for Waveguide Rectangular. The number is the broad wall dimension in hundredths of an inch. WR-28 has a 0.280-inch (7.112 mm) broad wall. The narrow wall is typically half the broad wall.
What is the frequency range of WR-28?
WR-28 operates from 26.50 to 40.00 GHz (Ka-band). Its TE₁₀ cutoff is 21.077 GHz and the TE₂₀ cutoff is 42.154 GHz. The recommended band sits between these with margin at both ends.
When should I use waveguide instead of coaxial cable?
Generally above 18 GHz, and always when loss, power handling, or PIM performance is critical. Above 40 GHz, waveguide is the standard low-loss option. At 77 GHz and above, it is essentially the only practical choice for low-loss signal routing.