How it works
Directivity D = (Maximum radiation intensity U_max)/(Average radiation intensity U_avg) = 4π·U_max/P_rad. It is a purely geometric measure of how focused the radiation pattern is. Gain G = η·D, where η is radiation efficiency accounting for ohmic losses in the antenna conductors and matching network. Both D and G are typically expressed in dBi (relative to isotropic). The half-power beamwidth (HPBW) is the angular width where the radiation pattern falls to half (−3 dB) of its maximum; a narrow HPBW means high directivity. Friis transmission equation: Pr = Pt·Gt·Gr·(λ/4πR)² links received power Pr to transmitted power Pt, transmit gain Gt, receive gain Gr, and the path loss term (λ/4πR)².
Key points to remember
A half-wave dipole has directivity of 1.64 (2.15 dBi) — this number appears in nearly every antenna exam problem as a reference. An isotropic antenna has directivity of exactly 1 (0 dBi) by definition. The effective aperture Ae = Gλ²/4π relates gain to the equivalent collecting area, and is particularly useful for aperture antennas like horn and parabolic reflectors. Radiation efficiency η is typically 0.9–0.99 for well-designed metal antennas but can fall below 0.5 for electrically small antennas on lossy substrates. Antenna bandwidth is defined as the frequency range over which VSWR remains below 2:1, or equivalently |Γ| < 1/3.
Exam tip
The examiner always asks you to distinguish between gain and directivity and state the relationship G = ηD — then immediately applies it in a numerical problem where η = 0.9 and D = 10 dBi, expecting you to compute G in both linear and dBi.