Visual calculator 04 · Waveguides
Rectangular waveguide
Each mode is a standing pattern across the guide and a wave along it. Below its cutoff it does not travel. It fades.
Attenuation of the selected mode
Below cutoff: evanescent decay. Above: wall and dielectric loss. Note the log scale.
Phase and group velocity
vp · vg = v². Near cutoff the phase races ahead and the energy crawls.
Check
Method
kc = √((mπ/a)² + (nπ/b)²), fc = c·kc / (2π√εr)
β = √(k² − kc²) propagating (f > fc)
α = √(kc² − k²) evanescent (f < fc)
λg = 2π/β, vp = ω/β, vg = v√(1 − (fc/f)²)
Z_TE = ηk/β, Z_TM = ηβ/k
TE10: αc = Rs/(bη√(1−(fc/f)²)) · (1 + (2b/a)(fc/f)²)
αd = k² tan δ / (2β)
TE: Hz = cos(mπx/a) cos(nπy/b), E lines = Hz contours
TM: Ez = sin(mπx/a) sin(nπy/b), H lines = Ez contours
Conductor loss: perturbation method, smooth walls, formulas for TEm0, TE0n, TEmn and TMmn. Field forms as in Pozar Table 3.2.
Reference values
- D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012, Sec. 3.3 and Example 3.1 (Teflon-filled K-band guide).
- R. E. Collin, Foundations for Microwave Engineering, 2nd ed., IEEE Press, 2001, Sec. 3.13 (attenuation of TEmn and TMmn modes).
- N. Marcuvitz, Waveguide Handbook, 1951, Sec. 2.2.
- Guide dimensions: EIA RS-261-B / MIL-DTL-85 (WR designations, inside dimensions in inches).