Antennas and Microwave Engineering
Antennas and Microwave Engineering tests radiation parameters, arrays, Friis transmission, waveguide cutoff and microwave tube or s-parameter basics.
Core rules
- Directivity D = 4πUmax/Prad; gain G = ηradD. Effective aperture Ae = λ²D/(4π).
- Friis: Pr/Pt = GtGr(λ/(4πR))², valid in far field R > 2D²/λ.
- Short dipole: Rr ≈ 80π²(l/λ)²; half-wave dipole Rr ≈ 73 Ω, D ≈ 1.64 or 2.15 dBi.
- Uniform linear array factor: AF = sin(Nψ/2)/(N sin(ψ/2)), ψ = kd cosθ + β. Grating lobes appear when d ≥ λ.
- Rectangular waveguide TE10 cutoff: fc = c/(2a). Below cutoff the wave is evanescent.
- Microwave tubes: klystron uses velocity modulation, magnetron uses crossed fields, TWT uses a helix for broad bandwidth.
- S-parameters: S11 is input reflection, S21 forward transmission; |S11|² is reflected power fraction.
Worked example
A WR-90 rectangular waveguide has a = 2.286 cm. For TE10, fc = c/(2a) = 3×10^8/(2×0.02286) ≈ 6.56 GHz. At 10 GHz the guide wavelength is λg = λ0/sqrt(1−(fc/f)²). λ0 = 3 cm, fc/f = 0.656, sqrt(1−0.430) = 0.755, so λg ≈ 3.97 cm. The guide wavelength is longer than the free-space wavelength, which is a common exam check.
Traps
- Confusing directivity with gain.
- Using the Friis formula in the near field.
- Forgetting the array phase term β.
- Using a instead of 2a in waveguide cutoff.
- Reporting S11 in dB without converting to reflection coefficient.