In dealing with thin linear antennas, it is sometimes convenient to define an effective le...

In dealing with thin linear antennas, it is sometimes convenient to define an effective length, ℓe, of the antenna, which is the current moment normalized with respect to the current at the feed point. For a center-fed dipole of half-length h, the maximum effective length (at θ = π/2) is

 (10-85)

Determine the effective length of

a) a Hertzian dipole of length dℓ,

---

b) a half-wave dipole with sinusoidal current distribution I0 cos βz, and

---

c) a half-wave dipole with triangular current distribution I0(1 − 4|z|/λ).