Size rectangular and circular waveguides, compare cutoff modes, estimate propagation behavior, and match standard WR bands using practical engineering inputs and clear results instantly.
For a rectangular waveguide, the mode cutoff frequency is:
For dominant TE10 operation, the expression becomes:
For a circular waveguide, common-mode cutoff uses a Bessel-root factor:
Guide wavelength and velocities use:
Waveguides carry electromagnetic energy through hollow conducting structures. Their dimensions determine which field patterns can propagate. Each pattern has a cutoff frequency. Signals below cutoff decay instead of traveling normally. Rectangular waveguides commonly use the TE10 dominant mode. Its broad wall mainly controls the lowest cutoff frequency.
A practical design normally operates safely above dominant cutoff. It should also stay below unwanted higher-mode cutoffs. This creates a useful single-mode frequency window. Standard WR waveguides simplify this selection process. Their internal dimensions and recommended bands are widely used in microwave systems.
The calculator can estimate dimensions from a desired cutoff. For TE10 rectangular operation, width equals wave velocity divided by twice cutoff frequency. Height can follow a chosen aspect ratio. A ratio near two is common, but special designs may differ.
Waveguide wavelength differs from free-space wavelength. It becomes longer near cutoff. Phase velocity rises above medium wave velocity. Group velocity becomes lower. Their product follows the waveguide dispersion relationship. The calculator also estimates propagation constant and TE or TM impedance.
Relative permittivity and permeability change wave velocity. These values also shift cutoff frequencies. Conductor conductivity affects surface current behavior. Skin depth becomes smaller as frequency increases. Copper therefore shows very shallow current penetration at microwave frequencies.
Choosing an operating point farther above cutoff reduces extreme dispersion near the boundary. However, moving too high can approach the next permitted mode. Designers therefore balance bandwidth, loss, size, and modal purity. Standard WR bands provide a useful practical compromise for many laboratory, communications, radar, and measurement systems.
Always treat computed dimensions as engineering starting values. Real hardware needs tolerances, transitions, flanges, loss analysis, and manufacturing checks. High-power systems also require electric-field and thermal review. Reliable sizing begins with correct frequency and mode choices.
| Standard | Width a (mm) | Height b (mm) | Typical band (GHz) | TE10 cutoff (GHz) |
|---|
TE10 is normally the lowest-cutoff rectangular mode. It is the usual design reference.
Below cutoff, the field becomes evanescent. Power does not propagate normally along the guide.
Higher modes can change field distribution and impedance. They may cause unexpected coupling or measurement errors.
WR indicates rectangular waveguide. The number historically reflects broad-wall size in hundredths of an inch.
Yes. Enter relative permittivity and permeability. The calculator adjusts wave velocity and cutoff values.
It estimates skin depth only. Detailed attenuation needs surface resistance and field-dependent loss calculations.
Yes. Dimension inputs and result units support inches, mils, centimetres, metres, and millimetres.
No. Verify bandwidth, power, attenuation, flange compatibility, tolerances, and higher-mode requirements before manufacturing.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.