---
title: "Current distribution of λ/2 and 3λ/2 dipoles"
subject: "Propagation and Antenna"
chapter: 1
key: "semester_6/propagation_and_antenna:dipole-current-distribution-half-wave"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/dipole-current-distribution-half-wave
site: BCT Engineering
---

# Current distribution of λ/2 and 3λ/2 dipoles

Propagation and Antenna · Chapter 1: Radiation and Antenna Fundamentals

- Asked in: 2076 Baisakh, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/dipole-current-distribution-half-wave
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-1

## Question

Sketch the current distribution and radiation pattern of center-fed vertical dipole for following lengths: i) λ/2 ii) 3λ/2

## Answer

For a centre-fed thin dipole of length L, the current is a standing wave that is **zero at the ends**:

```text
I(z) = I0 sin[k(L/2 − |z|)],  k = 2π/λ
E(θ) ∝ [cos((kL/2)cosθ) − cos(kL/2)] / sinθ
```

#### i) L = λ/2

```text
 Current            E-plane pattern
   .                     z
   |\                    |
   | \  max at       .-. | .-.
 ~ |  > centre      (   )|(   )
   | /               '-' | '-'
   |/                    |
   '              max at θ = 90°
```

- Current: half sine loop, maximum at the feed, zero at both ends; all in phase.
- Pattern: E(θ) = cos[(π/2)cosθ]/sinθ – figure-of-eight, slightly narrower than sinθ.
- HPBW ≈ 78°, D = 1.64 (2.15 dBi), R_in ≈ 73 Ω.

#### ii) L = 3λ/2

```text
 Current (3 half loops)     E-plane pattern
   |  +  |                       z
   | -   |   centre loop      \  |  /
   |  +  |   opposite phase    ( )|( )
   ends: zero                (  )-+-(  )
                               ( )|( )
                              /   |   \
```

- Current: three half-wave loops; the centre loop is in **opposite phase** to the two outer loops; maximum (in magnitude) at the feed.
- Pattern: 6 lobes in the vertical plane. Major lobes at θ ≈ 42.6° and 137.4° from the axis, a smaller lobe broadside at 90° (≈ 2.9 dB below), nulls at θ ≈ 70.5° and 109.5°.
- D ≈ 2.23 (3.48 dBi), R_in ≈ 105 Ω.

## Check yourself

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

1. In a centre-fed thin dipole, what is the current at the open ends?
   A. Maximum
   B. Equal to the feed current
   C. Infinite
   D. Zero, as a standing wave I0 sin[k(L/2 - |z|)]
   Answer: D. The current is a standing wave that vanishes at the ends. (Key point: Current boundary condition)

2. For the λ/2 dipole, which is correct?
   A. Half-sine current, maximum at the feed, pattern cos[(π/2)cosθ]/sinθ with maximum at 90°
   B. Current zero at the feed
   C. Pattern with null at 90°
   D. Two opposite-phase loops
   Answer: A. A single in-phase half-loop peaks at the feed and gives a figure-of-eight with broadside maximum, D = 1.64. (Key point: λ/2 current and pattern)

3. In the 3λ/2 dipole, how is the centre current loop phased relative to the outer loops?
   A. In phase
   B. Opposite phase
   C. 90° ahead
   D. Zero amplitude
   Answer: B. There are three half-wave loops, with the centre loop in opposite phase to the two outer loops. (Key point: 3λ/2 current phase)

4. What is the lobe structure of the 3λ/2 dipole?
   A. Two lobes at 90°
   B. Four lobes at 57.4°
   C. Six lobes: major near 42.6° and 137.4°, a smaller lobe at 90°
   D. A single circular lobe
   Answer: C. Major lobes are at 42.6° and 137.4°, with a smaller broadside lobe about 2.9 dB down and nulls at 70.5° and 109.5°. (Key point: 3λ/2 pattern)

## Close variants set in other exams

- [Current distribution of λ, 3λ/2 and 2λ dipoles](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Adipole-current-distribution-full-wave) — Propagation and Antenna, chapter 1, asked 2×

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- [Comparing λ/2, λ and 3λ/2 dipoles](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Adipole-lengths-comparison) — Propagation and Antenna, chapter 1

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