- 2077 Chaitra · 2+4 marks
Aperture antennas and rectangular horn radiation
Short answer
Aperture antennas radiate from fields across an opening (Huygens sources) unlike wire antennas using currents, giving high gain at microwaves. A rectangular horn flares a TE10 waveguide; the aperture field is cosine across H-plane and uniform across E-plane. Optimum horn: phase error <0.25λ E-plane, <0.4λ H-plane; HPBWE≈56λ/a_E, HPBWH≈67λ/a_H, directivity≈7.5 a_E a_H/λ².
How are aperture type of antennas different from the conventional antennas? Explain the theory of radiation from a rectangular horn.
Aperture antennas vs conventional (wire) antennas
| Point | Wire (conventional) antenna | Aperture antenna |
|---|---|---|
| Radiating source | Currents on thin conductors | Fields across an opening |
| Analysis | Current distribution integrated along wire | Aperture field (Huygens sources), Fourier transform |
| Size | Comparable to λ (λ/2, λ/4) | Many wavelengths across |
| Frequency | LF to UHF | Microwave (above ~1 GHz) |
| Gain | Low to moderate | High (gain ∝ aperture area) |
| Examples | Dipole, monopole, loop | Horn, slot, dish, lens |
Theory of radiation from a rectangular horn
A rectangular horn is a rectangular waveguide (dominant TE₁₀ mode) flared into a larger aperture of size a_H × a_E. The flare matches the guide impedance to free space (377 Ω) and enlarges the aperture to give a directive beam.
side view (E or H plane)
.-‾‾‾‾‾|
____ .-' δ | L = axial length
|____|<-----L--->| a = aperture width
'-._______| δ = path difference
- Aperture field: the TE₁₀ field is carried to the aperture. Across the H-plane width the amplitude is cosine shaped, cos(πx/a_H); across the E-plane it is uniform.
- Phase error: waves from the throat reach the aperture edge by a longer path than along the axis. The extra path is
δ = √(L² + (a/2)²) − L ≈ a²/(8L)
A large δ gives a non-uniform phase, broadening the beam and lowering gain. 3. Radiation: each element of the aperture acts as a Huygens source; integrating them (a Fourier transform of the aperture field) gives the far field. Uniform E-plane distribution gives a sin(u)/u pattern (narrow beam, higher side lobes ≈ −13 dB); cosine H-plane distribution gives a wider beam with lower side lobes (≈ −23 dB). 4. Optimum horn: δ ≈ 0.25λ in the E-plane and ≈ 0.4λ in the H-plane gives maximum gain for a given length, L = a²/(8δ). 5. Optimum-horn results:
HPBW (E-plane) ≈ 56 λ / a_E degrees
HPBW (H-plane) ≈ 67 λ / a_H degrees
Directivity D ≈ 7.5 a_E a_H / λ² (η ≈ 0.6)
So a longer horn with a bigger mouth gives more gain, as long as the phase error is kept within the optimum limit.
✓ Answer checked by Claude Opus 5.5 (high effort)
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