---
title: "Features of end-fire array"
subject: "Propagation and Antenna"
chapter: 2
key: "semester_6/propagation_and_antenna:endfire-array-features"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/endfire-array-features
site: BCT Engineering
---

# Features of end-fire array

Propagation and Antenna · Chapter 2: Antenna Parameters and Arrays

- Asked in: 2078 Chaitra, 4 marks
- Video: [Broadside and End Fire Array Antenna](https://www.youtube.com/watch?v=l7_uRINfIog) — WIT Solapur - Professional Learning Community
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/endfire-array-features
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-2

## Question

Write the features of end-fire array.

## Short answer

End-fire array radiates maximum along array axis with progressive phase lag α=-βd. Features: unidirectional pencil beam, null-to-null beamwidth ≈2√(2λ/L), directivity ≈4L/λ, Hansen-Woodyard condition (α=-(βd+π/n)) raises directivity to ≈7.2L/λ, small spacing (≈λ/4) avoids grating lobes, used in Yagi-Uda and helical antennas.

## Answer

An **end fire array** is a linear array whose maximum radiation is **along the array axis**. It is obtained by feeding equal-amplitude elements with a progressive phase lag equal to their spacing in radians (α = −βd), so the fields add only in the direction of the array line.

```text
  ● → ● → ● → ● → ●  ====> main beam
  phase: 0  -βd -2βd -3βd -4βd
```

#### Features

1. **Direction of maximum**: θ = 0° (or 180°) along the axis; ψ = βd(cosθ − 1) = 0 at θ = 0°.
2. **Phase condition**: α = −βd; for d = λ/4, α = −90° between neighbours.
3. **Pattern**: usually unidirectional (e.g. two elements at λ/4 give a cardioid); a pencil-shaped beam for many elements.
4. **Beamwidth**: null-to-null beamwidth ≈ 2√(2λ/(nd)) = 2√(2λ/L), wider in angle than broadside for the same length.
5. **Directivity**: D ≈ 4L/λ (= 4nd/λ), about twice that of a broadside array of the same length.
6. **Hansen–Woodyard condition**: extra phase δ = π/n (α = −(βd + π/n)) narrows the beam and raises directivity to about 7.2L/λ (1.8 times ordinary end fire).
7. **Spacing**: kept small (≈ λ/4, < λ/2) to avoid a back lobe and grating lobes.
8. **Applications**: Yagi-Uda TV antennas, axial-mode helix, VHF/UHF point-to-point links.

## Check yourself

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

1. For a lambda/4 spaced end fire array, the phase between neighbours is
   A. -90°
   B. 0°
   C. -180°
   D. +45°
   Answer: A. alpha = -beta d = -(2pi/lambda)(lambda/4) = -90°. (Key point: Phase condition)

2. Two end fire elements at lambda/4 spacing give what pattern?
   A. A figure-eight bidirectional
   B. A cardioid, unidirectional
   C. A circle in all directions
   D. Two equal side lobes only
   Answer: B. Spacing lambda/4 with -90° phase cancels backward radiation, giving a unidirectional cardioid. (Key point: Pattern of two elements)

3. Compared with broadside of the same length, the end fire beamwidth is
   A. narrower (about 2 lambda/L)
   B. exactly equal
   C. wider (about 2 sqrt(2 lambda/L))
   D. zero
   Answer: C. The null-to-null beamwidth is 2 sqrt(2 lambda/L), wider than broadside's 2 lambda/L. (Key point: Beamwidth)

4. What extra phase delta does the Hansen-Woodyard condition add?
   A. pi/2
   B. 2 pi
   C. beta d
   D. pi/n
   Answer: D. alpha = -(beta d + pi/n) narrows the beam and increases directivity about 1.8 times. (Key point: Hansen-Woodyard)

## Related in Propagation and Antenna

- [Two-element array: broadside and end fire](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Atwo-element-array-broadside-endfire) — Propagation and Antenna, chapter 2
- [Two-element array and end fire pattern](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Atwo-isotropic-endfire-pattern) — Propagation and Antenna, chapter 2
- [Linear array; broadside vs end fire](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Alinear-array-broadside-endfire) — Propagation and Antenna, chapter 2
- [Importance of arrays; end fire vs broadside](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aarray-importance-endfire-broadside) — Propagation and Antenna, chapter 2, asked 2×

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