How it works
Radiation resistance R_rad is the equivalent resistance that would dissipate the same average power as the antenna radiates, defined by P_rad = ½|I₀|²R_rad. For a short dipole (length l << λ), R_rad = 80π²(l/λ)² Ω — a 0.1λ dipole gives R_rad ≈ 8Ω, far too small to match efficiently. Directivity D = 4πU_max/P_total where U is radiation intensity. Gain G = η_ant × D, where η_ant is antenna radiation efficiency. For a lossless half-wave dipole, G = D = 1.64. Effective aperture A_eff = Gλ²/(4π), linking receive area to gain.
Key points to remember
Reciprocity theorem: an antenna's radiation pattern, gain, and impedance are identical whether it transmits or receives. The Friis transmission equation P_r = P_t·G_t·G_r·(λ/4πR)² gives received power between two antennas at distance R, demonstrating that path loss increases as frequency squared. Polarisation match between transmit and receive antennas is mandatory — a vertically polarised transmit antenna paired with a horizontal receive antenna gives ideally zero received signal (polarisation loss factor cos²θ = 0). EIRP = P_t × G_t in watts (or dBW) represents the equivalent isotropic radiated power. Bandwidth of a half-wave dipole is approximately 10–15% of centre frequency.
Exam tip
The examiner always asks you to derive or state the Friis transmission equation and use it to calculate received power — convert all gains to linear scale before multiplying, then convert back to dBm if required.