A frequency-reconfigurable dipole antenna, whose dual resonant frequencies are independently controlled, is introduced. The antenna's conductor consists of radiating conductors, lumped and distributed elements, and varactors. To design the antenna, current distribution, input impedance, and radiation power including higher-order modes, are analyzed for a narrow-angle sectorial antenna embedded with passive elements. To derive the formulae used, radiation power is analyzed in two ways: using Chu's equivalent circuit and the multipole expansion method. Numerical estimations of electrically small antennas show that dual-band antennas are feasible. The dual resonant frequencies are controlled with the embedded series and shunt inductors. A dual-band antenna is fabricated, and measured input impedances agree well with the calculated data. With the configuration, an electrically small 2.5-/5-GHz dual-band reconfig-urable antenna is designed and fabricated, where the reactance values for the series and shunt inductors are controlled with varactors, each connected in series to the inductors. Varying the voltages applied to the varactors varies the measured upper and lower resonant frequencies between 2.6 and 2.9GHz and between 5.1 and 5.3GHz, where the other resonant frequency is kept almost identical. Measured radiation patterns on the H-plane are almost omni-directional for both bands.

Evaluation of addition coefficients introduced by the addition theorems for vector spherical harmonics is one of the most intractable problems in electromagnetic scattering by multi-sphere systems. The derivation of the analytical expressions for the addition coefficients is lengthy and complex while the computation of the addition coefficients is annoyingly time-consuming even with the reasonably fast computers available nowadays. This paper presents an efficient algorithm for calculating addition coefficients which is based on the recursive relations of scalar addition coefficients. Numerical results from the formulation derived in this paper agree with those of previous published results but the algorithm proposed here reduces the computational time considerably. This paper also discusses the strengths and limitations of other formulations and numerical techniques found in the literature.