A rectangular waveguide is a type of electromagnetic waveguide with a rectangular cross-section. It is used to guide electromagnetic waves, typically in the microwave frequency range. The dimensions of the waveguide are critical for determining its operating characteristics.
The standard rectangular waveguide has two parallel broad walls and two narrow walls. The width (a) and height (b) of the waveguide are essential parameters that influence the cutoff frequency, mode propagation, and other properties. The dominant mode of propagation in a rectangular waveguide is the TE10 mode, where the electric field is transverse (T) to the direction of propagation, and the subscript 10 indicates that there is one half-wavelength along the width of the guide.
Rectangular waveguides are commonly used in microwave communication systems, radar systems, and other applications where the controlled propagation of electromagnetic waves is required. They are often preferred in situations where coaxial cables or other transmission lines may not be suitable.
The standard
there are various standard waveguide sizes designated by different WR (Waveguide Rectangular) numbers. The specific dimensions depend on the frequency range and application for which the waveguide is designed. Keep in mind that these dimensions are standardized by organizations like the International Electrotechnical Commission (IEC) and the Institute of Electrical and Electronics Engineers (IEEE).
| Waveguide name | Recommended frequency | Cutoff frequency lowest order mode | Cutoff frequency next mode | Inner dimensions of waveguide opening | |||
|---|---|---|---|---|---|---|---|
| EIA | RCSC * | IEC | A inch[mm] | B inch[mm] | |||
| WR2300 | WG0.0 | R3 | 0.32 to 0.45 GHz | 0.257 GHz | 0.513 GHz | 23 [584.2] | 11.5 [292.1] |
| WR2100 | WG0 | R4 | 0.35 to 0.50 GHz | 0.281 GHz | 0.562 GHz | 21 [533.4] | 10.5 [266.7] |
| WR1800 | WG1 | R5 | 0.45 to 0.63 GHz | 0.328 GHz | 0.656 GHz | 18 [457.2] | 9 [228.6] |
| WR1500 | WG2 | R6 | 0.50 to 0.75 GHz | 0.393 GHz | 0.787 GHz | 15 [381] | 7.5 [190.5] |
| WR1150 | WG3 | R8 | 0.63 to 0.97 GHz | 0.513 GHz | 1.026 GHz | 11.5 [292.1] | 5.75 [146.05] |
| WR975 | WG4 | R9 | 0.75 to 1.15 GHz | 0.605 GHz | 1.211 GHz | 9.75 [247.65] | 4.875 [123.825] |
| WR770 | WG5 | R12 | 0.97 to 1.45 GHz | 0.766 GHz | 1.533 GHz | 7.7 [195.58] | 3.85 [97.79] |
| WR650 | WG6 | R14 | 1.15 to 1.72 GHz | 0.908 GHz | 1.816 GHz | 6.5 [165.1] | 3.25 [82.55] |
| WR510 | WG7 | R18 | 1.45 to 2.20 GHz | 1.157 GHz | 2.314 GHz | 5.1 [129.54] | 2.55 [64.77] |
| WR430 | WG8 | R22 | 1.72 to 2.60 GHz | 1.372 GHz | 2.745 GHz | 4.3 [109.22] | 2.15 [54.61] |
| WG9 | 2.20 to 3.30 GHz | 1.686 GHz | 3.372 GHz | 3.5 [88.9] | 1.75 [44.45] | ||
| WR340 | WG9A | R26 | 2.20 to 3.30 GHz | 1.736 GHz | 3.471 GHz | 3.4 [86.36] | 1.7 [43.18] |
| WR284 | WG10 | R32 | 2.60 to 3.95 GHz | 2.078 GHz | 4.156 GHz | 2.84 [72.136] | 1.34 [34.036] |
| WG11 | 3.30 to 4.90 GHz | 2.488 GHz | 4.976 GHz | 2.372 [60.2488] | 1.122 [28.4988] | ||
| WR229 | WG11A | R40 | 3.30 to 4.90 GHz | 2.577 GHz | 5.154 GHz | 2.29 [58.166] | 1.145 [29.083] |
| WR187 | WG12 | R48 | 3.95 to 5.85 GHz | 3.153 GHz | 6.305 GHz | 1.872 [47.5488] | 0.872 [22.1488] |
| WR159 | WG13 | R58 | 4.90 to 7.05 GHz | 3.712 GHz | 7.423 GHz | 1.59 [40.386] | 0.795 [20.193] |
| WR137 | WG14 | R70 | 5.85 to 8.20 GHz | 4.301 GHz | 8.603 GHz | 1.372 [34.8488] | 0.622 [15.7988 |
| WR112 | WG15 | R84 | 7.05 to 10 GHz | 5.26 GHz | 10.52 GHz | 1.122 [28.4988] | 0.497 [12.6238] |
| WR102 | 7.00 to 11 GHz | 5.786 GHz | 11.571 GHz | 1.02 [25.908] | 0.51 [12.954] | ||
| WR90 | WG16 | R100 | 8.20 to 12.40 GHz | 6.557 GHz | 13.114 GHz | 0.9 [22.86] | 0.4 [10.16] |
| WR75 | WG17 | R120 | 10.00 to 15 GHz | 7.869 GHz | 15.737 GHz | 0.75 [19.05] | 0.375 [9.525] |
| WR62 | WG18 | R140 | 12.40 to 18 GHz | 9.488 GHz | 18.976 GHz | 0.622 [15.7988] | 0.311 [7.8994] |
| WR51 | WG19 | R180 | 15.00 to 22 GHz | 11.572 GHz | 23.143 GHz | 0.51 [12.954] | 0.255 [6.477] |
| WR42 | WG20 | R220 | 18.00 to 26.50 GHz | 14.051 GHz | 28.102 GHz | 0.42 [10.668] | 0.17 [4.318] |
| WR34 | WG21 | R260 | 22.00 to 33 GHz | 17.357 GHz | 34.715 GHz | 0.34 [8.636] | 0.17 [4.318] |
| WR28 | WG22 | R320 | 26.50 to 40 GHz | 21.077 GHz | 42.154 GHz | 0.28 [7.112] | 0.14 [3.556] |
| WR22 | WG23 | R400 | 33.00 to 50 GHz | 26.346 GHz | 52.692 GHz | 0.224 [5.6896] | 0.112 [2.8448] |
| WR19 | WG24 | R500 | 40.00 to 60 GHz | 31.391 GHz | 62.782 GHz | 0.188 [4.7752] | 0.094 [2.3876] |
| WR15 | WG25 | R620 | 50.00 to 75 GHz | 39.875 GHz | 79.75 GHz | 0.148 [3.7592] | 0.074 [1.8796] |
| WR12 | WG26 | R740 | 60 to 90 GHz | 48.373 GHz | 96.746 GHz | 0.122 [3.0988] | 0.061 [1.5494] |
| WR10 | WG27 | R900 | 75 to 110 GHz | 59.015 GHz | 118.03 GHz | 0.1 [2.54] | 0.05 [1.27] |
| WR8 | WG28 | R1200 | 90 to 140 GHz | 73.768 GHz | 147.536 GHz | 0.08 [2.032] | 0.04 [1.016] |
| WR6 | WG29 | R1400 | 110 to 170 GHz | 90.791 GHz | 181.583 GHz | 0.065 [1.651] | 0.0325 [0.8255] |
| WR7 | WG29 | R1400 | 110 to 170 GHz | 90.791 GHz | 181.583 GHz | 0.065 [1.651] | 0.0325 [0.8255] |
| WR5 | WG30 | R1800 | 140 to 220 GHz | 115.714 GHz | 231.429 GHz | 0.051 [1.2954] | 0.0255 [0.6477] |
| WR4 | WG31 | R2200 | 172 to 260 GHz | 137.243 GHz | 274.485 GHz | 0.043 [1.0922] | 0.0215 [0.5461] |
| WR3 | WG32 | R2600 | 220 to 330 GHz | 173.571 GHz | 347.143 GHz | 0.034 [0.8636] | 0.017 [0.4318] |
| WR2 | – | – | 325-500 GHz | – | – | 0.020 [0.508] | 0.010 [0.254] |
| WR1 | – | – | 750-1100 GHz | – | – | 0.010 [0.254] | 0.0050 [0.127] |
The cutoff frequencies
The cutoff frequency of a rectangular waveguide is the frequency below which no electromagnetic wave propagation can occur in a particular mode. The most common mode in rectangular waveguides is the TE10 mode. The cutoff frequency for the TE10 mode in a rectangular waveguide can be calculated using the following formula: \[ f_c = \frac{c}{2\sqrt{\epsilon_r}} \cdot \sqrt{\left(\frac{m}{a}\right)^2 + \left(\frac{n}{b}\right)^2} \]
where: \( f_c \) is the cutoff frequency,
\( c \) is the speed of light in a vacuum (\(3 \times 10^8 \) meters per second),
\( \epsilon_r \) is the relative permittivity of the material inside the waveguide (dimensionless),
\( m \) and \( n \) are integers representing the mode indices (for the TE10 mode, \( m = 1 \) and \( n = 0 \)),
\( a \) is the width of the waveguide,
\( b \) is the height of the waveguide.
We define the fc10 and fc01 as the basic variable, then
`fc=sqrt((m fc_(10))^2+(n fc_(01))^2)`
As a result,
`fc_(m0)=sqrt(m) fc_(10) and fc_(0n)=sqrt(n) fc_(01)`
The single mode frequency range
The single-mode frequency range for a rectangular waveguide is the frequency range where only one mode (typically the dominant TE10 mode) can propagate. To determine the single-mode frequency range, you need to consider the cutoff frequencies for different modes and identify the range where only the desired mode is supported.
Single-Mode Range is alwayls from fc10 to fc20.