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

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

Propagation and Antenna · Chapter 1: Radiation and Antenna Fundamentals

- Asked in: 2072 Magh, 6 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-full-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 ii) 3λ/2 iii) 2λ

## Answer

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

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

(θ measured from the dipole axis; patterns are omnidirectional in the horizontal plane.)

#### i) L = λ

```text
 Current               E-plane pattern
  /\                        z
 /  \  upper half-loop      |
 \  /  feed: I ≈ 0     .--. | .--.
  \/   lower half-loop(    )|(    )
  (both in phase)      '--' | '--'
```

- Two half-wave loops, **in phase**, with current minimum (zero) at the feed point, so input impedance is very high.
- E(θ) = [cos(π cosθ) + 1]/sinθ; single broadside lobe each side, narrower than λ/2.
- HPBW ≈ 47.8°, D ≈ 2.41 (3.82 dBi).

#### ii) L = 3λ/2

```text
 Current: + | − | +   (3 half-loops,
          centre loop opposite phase)
 Pattern:      \  |  /
             ( )  |  ( )     major lobes
            ( )---+---( )    at 42.6°, 137.4°
             ( )  |  ( )     minor lobe at 90°
              /   |   \
```

- Three half-loops; centre loop opposite to the outer ones; current maximum at the feed (R_in ≈ 105 Ω).
- 6 lobes: major lobes at θ ≈ 42.6° and 137.4°, smaller broadside lobe at 90° (≈ −2.9 dB), nulls at ≈ 70.5° and 109.5°.
- D ≈ 2.23 (3.48 dBi).

#### iii) L = 2λ

```text
 Current: + − | − +  →  2 loops each arm;
          adjacent loops opposite phase,
          zero current at feed
 Pattern:     \   |   /
           (  )   |   (  )   4 lobes at
          ---------+---------  57.4°, 122.6°
           (  )   |   (  )   null at 90°
              /   |   \
```

- Four half-loops; the two loops on each arm are in opposite phase; current zero at the feed.
- E(θ) = [cos(2π cosθ) − 1]/sinθ → **null broadside** (θ = 90°) and along the axis.
- 4 lobes (cloverleaf), maxima at θ ≈ 57.4° and 122.6°; D ≈ 2.53 (4.03 dBi).

As L increases beyond λ, phase reversals in the current split the pattern into more lobes.

## Check yourself

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

1. For the L = λ dipole, what is the current at the feed point?
   A. Maximum
   B. Approximately zero, so input impedance is very high
   C. Exactly I0 with opposite phase
   D. Equal to the end current
   Answer: B. Two in-phase half-loops meet at the feed with a current minimum, giving very high input impedance. (Key point: Full-wave current at feed)

2. What is the λ dipole's pattern compared with the λ/2 dipole?
   A. Wider with a null at 90°
   B. Identical
   C. Single broadside lobe each side, narrower (HPBW about 47.8°)
   D. Omnidirectional in the E-plane
   Answer: C. E(θ) = [cos(π cosθ) + 1]/sinθ is narrower; D about 2.41 (3.82 dBi). (Key point: Full-wave pattern)

3. For the 3λ/2 dipole, which is correct?
   A. Current minimum at the feed
   B. Four lobes only
   C. Null at 42.6°
   D. Centre loop opposite to outer ones, 6 lobes, major lobes at 42.6° and 137.4°
   Answer: D. Current is maximum at the feed with a reversed centre loop; the pattern has six lobes with nulls at 70.5° and 109.5°. (Key point: Phase of loops for 3λ/2)

4. What happens to the 2λ dipole's pattern at θ = 90°?
   A. It has a null broadside, since the formula [cos(2π cosθ) - 1]/sinθ vanishes there
   B. It has its maximum
   C. It equals the λ/2 value
   D. It is a minor lobe
   Answer: A. At θ = 90°, cos(2π·0) - 1 = 0, so a null; four lobes have maxima near 57.4° and 122.6°. (Key point: 2λ dipole broadside)

5. How are the current loops of the 2λ dipole arranged?
   A. Four loops all in phase
   B. Two loops only
   C. Four half-loops, adjacent loops opposite in phase, zero current at the feed
   D. One loop with maximum at the feed
   Answer: C. Each arm has two half-loops in opposite phase, and the current is zero at the feed. (Key point: 2λ current)

6. What happens to the pattern as L increases beyond λ?
   A. Phase reversals in the current split the pattern into more lobes
   B. The pattern stays a single lobe
   C. Directivity falls to 1
   D. The pattern becomes isotropic
   Answer: A. Current phase reversals create additional lobes. (Key point: Trend with length)

## Close variants set in other exams

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

## Related in Propagation and Antenna

- [Pattern multiplication for two short dipoles](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Apattern-multiplication-short-dipoles) — Propagation and Antenna, chapter 2
- [Antenna radiation pattern and lobes](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aradiation-pattern) — Propagation and Antenna, chapter 2, asked 4×
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- [Folded dipole and Yagi design 785–895 MHz](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afolded-dipole-yagi-design) — Propagation and Antenna, chapter 3
- [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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