--- title: "Comparing λ/2, λ and 3λ/2 dipoles" subject: "Propagation and Antenna" chapter: 1 key: "semester_6/propagation_and_antenna:dipole-lengths-comparison" source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/dipole-lengths-comparison site: BCT Engineering --- # Comparing λ/2, λ and 3λ/2 dipoles Propagation and Antenna · Chapter 1: Radiation and Antenna Fundamentals - Asked in: 2070 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-lengths-comparison - Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-1 ## Question Differentiate between λ/2, λ and 3λ/2 length dipoles in terms of their individual radiation pattern, self impedance and directivity; where λ is the wavelength of operation frequency. ## Short answer λ/2 dipole: two broadside lobes, HPBW 78°, R_rad 73 Ω, Z_in 73+j42.5 Ω, D=2.15 dBi. λ dipole: two narrower broadside lobes, HPBW 47.8°, R_rad 199 Ω, very high Z_in, D=3.82 dBi. 3λ/2 dipole: six lobes (four major at 42.6°), HPBW 33°, R_rad 105 Ω, Z_in 105 Ω, D=3.48 dBi. ## Answer For a centre-fed dipole of length L with sinusoidal current I(z) = I0 sin[k(L/2 − |z|)], the far-field pattern is ```text E(θ) ∝ [cos((kL/2)cosθ) − cos(kL/2)] / sinθ ``` The values below are computed from this formula (R_r referred to the current maximum). | Property | λ/2 dipole | λ dipole | 3λ/2 dipole | |---|---|---|---| | Current | One half-loop, max at feed | Two in-phase loops, zero at feed | Three loops, centre loop reversed | | Pattern formula | cos(π/2·cosθ)/sinθ | [cos(π cosθ)+1]/sinθ | cos(3π/2·cosθ)/sinθ | | Lobes (E-plane) | 2 (broadside) | 2 (broadside, narrower) | 6 (4 major at 42.6°, 2 minor at 90°) | | Max direction | θ = 90° | θ = 90° | θ ≈ 42.6°, 137.4° | | HPBW | ≈ 78° | ≈ 47.8° | ≈ 33° (major lobe, half-power points at ≈ 24.4° and 57.2°) | | Radiation resistance | ≈ 73 Ω | ≈ 199 Ω | ≈ 105 Ω | | Input impedance at centre | ≈ 73 + j42.5 Ω (resonant when slightly shortened) | Very high (kΩ), current minimum | ≈ 105 Ω | | Directivity | 1.64 (2.15 dBi) | 2.41 (3.82 dBi) | 2.23 (3.48 dBi) | ```text λ/2 λ 3λ/2 .-. | .-. .--.|.--. \ | / ( )|( ) ( | ) ( ) | ( ) '-' | '-' '--'|'--' ( )--+--( ) ( ) | ( ) / | \ ``` Key points: - The **λ/2 dipole** is resonant, easy to match to 75 Ω coax, and is the reference antenna. - The **λ dipole** has higher directivity and a narrower beam, but its very high input impedance makes it hard to feed at the centre (it is often end-fed instead). - The **3λ/2 dipole** has a phase reversal in its current; the main beam splits into tilted cones, so broadside gain falls and directivity is lower than for the λ dipole. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which lists directivities of λ/2, λ and 3λ/2 dipoles in order? A. 1.64, 2.23, 2.41 B. 2.41, 1.64, 2.23 C. 1.64, 2.41, 2.23 D. 2.15, 3.82, 3.48 Answer: C. D = 1.64 (2.15 dBi), 2.41 (3.82 dBi) and 2.23 (3.48 dBi) respectively; the λ dipole is highest of the three. (Key point: Directivity values) 2. Why is the 3λ/2 dipole's directivity lower than the λ dipole's? A. Its current is zero at the ends B. Phase reversal in the current splits the beam into tilted lobes, reducing broadside gain C. It has a higher radiation resistance D. It is shorter Answer: B. The reversed centre loop tilts the main beams to about 42.6° from the axis and lowers broadside directivity. (Key point: Why 3λ/2 has lower directivity) 3. Why is a centre-fed λ dipole hard to feed? A. Its radiation resistance is 73 Ω B. Its pattern is omnidirectional C. It has no main lobe D. Current is a minimum at the centre, so input impedance is very high Answer: D. The current minimum at the feed gives very high (kΩ) input impedance, so it is often end-fed. (Key point: Feeding the λ dipole) 4. Which radiation resistances match λ/2, λ and 3λ/2 dipoles? A. 73 Ω, 199 Ω, 105 Ω B. 199 Ω, 73 Ω, 105 Ω C. 73 Ω, 105 Ω, 199 Ω D. 105 Ω, 73 Ω, 199 Ω Answer: A. The values are about 73, 199 and 105 Ω. 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