Characteristics of λ/2, λ and 1.28λ dipoles

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

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).

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