---
title: "Aperture antennas and rectangular horn radiation"
subject: "Propagation and Antenna"
chapter: 3
key: "semester_6/propagation_and_antenna:aperture-antenna-rectangular-horn"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/aperture-antenna-rectangular-horn
site: BCT Engineering
---

# Aperture antennas and rectangular horn radiation

Propagation and Antenna · Chapter 3: Antenna Classification

- Asked in: 2077 Chaitra, 2+4 marks
- Video: [Horn Antenna (Basics, Structure, Flaring, Types, Designing Parameters, Applications) Explained](https://www.youtube.com/watch?v=MOvVkotklfE) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/aperture-antenna-rectangular-horn
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-3

## Question

How are aperture type of antennas different from the conventional antennas? Explain the theory of radiation from a rectangular horn.

## 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.

## Answer

#### 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.

```text
          side view (E or H plane)
            .-‾‾‾‾‾|
   ____  .-'   δ   |   L = axial length
  |____|<-----L--->|   a = aperture width
         '-._______|   δ = path difference
```

1. **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**.
2. **Phase error**: waves from the throat reach the aperture edge by a longer path than along the axis. The extra path is

```text
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**:

```text
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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How do aperture antennas differ from conventional wire antennas?
   A. They have low gain proportional to length
   B. They radiate from currents on thin wires and are small
   C. They work only at LF
   D. They radiate from fields across an opening and are many wavelengths across, with high gain
   Answer: D. Aperture antennas use aperture fields (Huygens sources), are large, and have gain proportional to area. (Key point: Aperture vs wire)

2. What is the aperture field distribution of a rectangular horn fed in TE10?
   A. Cosine in H-plane, uniform in E-plane
   B. Uniform in H-plane, cosine in E-plane
   C. Uniform in both planes
   D. Cosine in both planes
   Answer: A. The TE10 amplitude varies as cos(pi x/a_H) across the H-plane width and is uniform in the E-plane. (Key point: Horn aperture field)

3. What causes phase error in a horn, and what is its effect?
   A. The throat is too wide; it narrows the beam
   B. Edge path is longer than axial path (delta = a^2/8L); large delta broadens beam and lowers gain
   C. Standing waves in the guide; it raises gain
   D. Ground reflection; it tilts the beam up
   Answer: B. delta = sqrt(L^2 + (a/2)^2) - L, about a^2/(8L); large values give non-uniform phase. (Key point: Phase error)

4. Which statement about the optimum horn is correct?
   A. delta should be 2 lambda
   B. delta should be zero
   C. delta about 0.25 lambda (E-plane) and 0.4 lambda (H-plane) gives max gain for a length
   D. Optimum horn has zero flare
   Answer: C. Optimum delta values give maximum gain for a given length with L = a^2/(8 delta). (Key point: Optimum horn)

## Related in Propagation and Antenna

- [Aperture antenna advantages and horn types](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aaperture-advantages-horn-types) — Propagation and Antenna, chapter 3

## Related in other subjects

- [Sub-sampling theory and aperture effect](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asubsampling-aperture-effect) — Communication Systems, chapter 4
- [BTS radiation fields at 900 and 1800 MHz](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Abts-900-1800-radiation-fields) — RF and Microwave Engineering, chapter 7