Short note: Effective antenna height

Effective height (effective length) of an antenna is the height of an imaginary antenna carrying a uniform current equal to the actual feed-point current that would radiate the same field in the direction of maximum radiation. It converts the real, non-uniform current distribution into an equivalent uniform one.

Definition

h_e · I0 = ∫₀^h I(z) dz      (transmitting)

h_e = V_oc / E               (receiving)

where I0 is the base current, I(z) the current along the antenna, V_oc the open-circuit voltage induced and E the incident field. The effective height is always less than the physical height because current tapers to zero at the tip.

Typical values

Use in propagation

• Ground wave field strength from a vertical antenna: E = 120π·h_e·I/(λd) V/m. A larger h_e gives a stronger field, which is why MF broadcast towers use top loading to make the current nearly uniform.
• In space-wave (LOS) links, "effective antenna height" also means the height of the antenna above the average (effective) ground level of the reflecting area, not above the local foot of the tower. This height is used in d = 4.12(√ht + √hr) km and in the plane-earth path loss formula.