Multipole Expansion — Radiation Patterns

Far-field radiation from oscillating multipoles: dipole, quadrupole, and antenna arrays. Power P ∝ (d/dt)ⁿ of multipole moments. Pattern shaping via phased arrays and element spacing.

Multipole Config

Source type: Phase shift δ: 0.00 π Spacing d/λ: 0.50 Frequency ratio: 1.00

Directivity D: —
Max gain dir: —°
Nulls: —

P(θ) = |Σ aₙ e^{iknd·cos θ+iδₙ}|²
× element pattern