- 2077 Chaitra · 6 marks
Rectangular waveguide cut-off and phase velocity
Short answer
For WR-90 air-filled waveguide at 10 GHz in TE10 mode: cut-off frequency 6.562 GHz, phase velocity 3.976e8 m/s, guide wavelength 3.976 cm, characteristic impedance about 500 ohms.
For a rectangular waveguide, with suitably assumed breadth, width and frequency (for dominant mode), determine cut-off frequency, phase velocity, propagation wavelength in the waveguide and the characteristic impedance.
Assumption: a standard WR-90 (X-band) air-filled waveguide, a = 2.286 cm (breadth), b = 1.016 cm (height), operating at f = 10 GHz in the dominant TE10 mode. Constants: c = 3 × 10⁸ m/s, η0 = 120π ≈ 377 Ω.
Cut-off frequency (TE10):
fc = c/(2a) = (3 × 10⁸)/(2 × 0.02286) = 6.562 GHz
Next mode TE20 (13.12 GHz) and TE01 (c/2b = 14.76 GHz) are above 10 GHz, so only TE10 propagates.
Common factor:
√(1 - (fc/f)²) = √(1 - (6.562/10)²)
= √(1 - 0.4306) = 0.7546
λ0 = c/f = 3 cm
Phase velocity:
vp = c/0.7546 = 3.976 × 10⁸ m/s
Guide (propagation) wavelength:
λg = λ0/0.7546 = 3/0.7546 = 3.976 cm
Characteristic (wave) impedance:
Z_TE = η0/0.7546 = 377/0.7546 = 499.6 Ω
| Quantity | Value |
|---|---|
| Cut-off frequency fc | 6.562 GHz |
| Phase velocity vp | 3.976 × 10⁸ m/s |
| Guide wavelength λg | 3.976 cm |
| Wave impedance Z_TE | ≈ 500 Ω |
Answer: fc = 6.562 GHz, vp = 3.976 × 10⁸ m/s, λg = 3.976 cm, Z_TE ≈ 500 Ω (for a = 2.286 cm, b = 1.016 cm, f = 10 GHz). Group velocity for reference: vg = c × 0.7546 = 2.264 × 10⁸ m/s.
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- Dominant mode and 2.254 cm waveguide at 6 GHz · RF and Microwave Engineering, chapter 4
- Air-filled 3 cm waveguide at 6 GHz; coupler parameters · RF and Microwave Engineering, chapter 4
- Circular waveguide TM field strength and dominant mode · RF and Microwave Engineering, chapter 4
- Short note: Dominant mode in waveguide · RF and Microwave Engineering, chapter 4
- Rectangular waveguide TM mode field equations · RF and Microwave Engineering, chapter 4 · asked 11×
- Rectangular waveguide TE mode field equations · RF and Microwave Engineering, chapter 4 · asked 11×
- Cut-off of TM11 and dominant mode · Electromagnetism, chapter 6
- Dominant cut-off, dielectric-filled guide · Electromagnetism, chapter 6
- Cut-off of dominant and TE11, 2.5×1.2 cm · Electromagnetism, chapter 6
- Cut-off and single-mode range, 4×2 cm · Electromagnetism, chapter 6