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

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

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

 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

 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

 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.