---
title: "Characteristics of λ/2, λ and 1.28λ dipoles"
subject: "Propagation and Antenna"
chapter: 1
key: "semester_6/propagation_and_antenna:dipole-characteristics-1-28-lambda"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/dipole-characteristics-1-28-lambda
site: BCT Engineering
---

# Characteristics of λ/2, λ and 1.28λ dipoles

Propagation and Antenna · Chapter 1: Radiation and Antenna Fundamentals

- Asked in: 2069 Bhadra, 6 marks
- Video: [Antenna #23. Dipole Antenna Explained (Animated): How It Works, Radiation Pattern, Impedance & Uses](https://www.youtube.com/watch?v=mhEMra9IUyQ) — Technologies Discussion
- 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-characteristics-1-28-lambda
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-1

## Question

Explain the characteristics of λ/2, λ and 1.28λ length dipoles where λ is the wavelength of operating frequency.

## Short answer

λ/2 dipole: single half-sine current, figure-8 pattern, HPBW 78°, D=2.15 dBi, R_r=73 Ω. λ dipole: two in-phase half-loops, current zero at feed, HPBW 47.8°, D=3.82 dBi, R_r=199 Ω, high Z_in. 1.28λ dipole (extended double Zepp): opposite-phase ends, HPBW 31°, D=5.17 dBi (max broadside directivity), minor lobes -8.5 dB.

## Answer

For a centre-fed dipole of length L (current I(z) = I0 sin[k(L/2 − |z|)]), the pattern is

```text
E(θ) ∝ [cos((kL/2)cosθ) − cos(kL/2)] / sinθ
```

#### λ/2 dipole
- Current: single half-sine loop, maximum at the feed, zero at the ends.
- Pattern: cos[(π/2)cosθ]/sinθ, figure-of-eight, maximum broadside; HPBW ≈ 78°.
- Directivity 1.64 (2.15 dBi); R_r ≈ 73 Ω, Z_in ≈ 73 + j42.5 Ω (resonant when about 5 % shorter).
- Easy to match; used as the reference antenna and as driven element in Yagi arrays.

#### λ (full-wave) dipole
- Current: two half-loops **in phase**; current zero at the feed.
- Pattern: [cos(π cosθ) + 1]/sinθ, single broadside lobe, narrower: HPBW ≈ 47.8°.
- Directivity ≈ 2.41 (3.82 dBi); R_r ≈ 199 Ω (at current maximum).
- Very high input impedance at the centre, so it is difficult to feed there.

#### 1.28λ dipole (near 1.25λ, "extended double Zepp")
- Current: each arm is longer than λ/2, so a small part near each end carries current of **opposite phase**.
- The opposite-phase parts are short, so they only slightly reduce the broadside field; the long in-phase parts make the main beam very narrow.
- Calculated with the formula: main lobe at θ = 90°, HPBW ≈ 31°, minor lobes at about 33° from the axis, ≈ 8.5 dB down.
- **Directivity ≈ 3.29 (5.17 dBi)** – about the **maximum** broadside directivity a single centre-fed dipole can have (1.25λ gives 3.28).
- Beyond about 1.28λ the opposite-phase current grows, the minor lobes become major lobes and broadside gain drops (3λ/2 gives only 2.23).

```text
     λ/2            λ            1.28λ
  .-. | .-.     .--.|.--.    \ .---|---. /
 (   )|(   )   (    |    )   ( (   |   ) )
  '-' | '-'     '--'|'--'    / '---|---' \
 HPBW 78°       47.8°        31° + small side lobes
```

| Length | D (dBi) | HPBW | Side lobes |
|---|---|---|---|
| λ/2 | 2.15 | 78° | None |
| λ | 3.82 | 47.8° | None |
| 1.28λ | 5.17 | ≈ 31° | Small, ≈ −8.5 dB |

## Check yourself

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

1. Which is correct for the λ/2 dipole?
   A. HPBW 47.8° and D 2.41
   B. Current zero at the feed
   C. R_r about 199 Ω
   D. HPBW about 78°, D 1.64 (2.15 dBi), R_r about 73 Ω
   Answer: D. It has a single in-phase half-loop, figure-of-eight pattern and is easy to match. (Key point: λ/2 dipole features)

2. Why is the λ dipole difficult to feed at the centre?
   A. Current is zero at the feed so input impedance is very high
   B. Its beam is too wide
   C. Its current is in opposite phase
   D. It has D below 1
   Answer: A. Two in-phase half-loops give a current minimum at the centre, hence very high impedance. (Key point: Full-wave dipole)

3. In the 1.28λ dipole, what is the current in the small end portions?
   A. Same phase as the centre
   B. Zero
   C. Of opposite phase, but short so they only slightly reduce the broadside field
   D. Maximum amplitude
   Answer: C. The short opposite-phase parts barely reduce broadside radiation while the long in-phase parts narrow the beam. (Key point: 1.28λ current)

4. What is notable about the 1.28λ dipole's directivity?
   A. It is the minimum of all dipoles
   B. It equals the λ/2 value
   C. It is about 3.29 (5.17 dBi), roughly the maximum broadside directivity of a centre-fed dipole
   D. It is 1
   Answer: C. HPBW is about 31° with small minor lobes; 1.25λ gives 3.28. (Key point: Maximum broadside directivity)

5. What happens to broadside gain beyond about 1.28λ?
   A. It keeps increasing
   B. It drops as opposite-phase current grows and minor lobes become major
   C. It stays constant
   D. It becomes isotropic
   Answer: B. Growing opposite-phase currents raise the minor lobes; 3λ/2 gives only D = 2.23. (Key point: Beyond 1.28λ)

## Related in Propagation and Antenna

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