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

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

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

 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

 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.