Radiation of an Antenna Enclosed by a Spherical Radome Made of an Orthorhombic Dielectric-Magnetic Medium

The radiation of a structure comprising a spherical radome enclosing an antenna and made of an orthorhombic dielectric-magnetic medium is treated semi analytically in this paper. Inside the radome, the radiation field phasors due to the antenna and reflected field phasors due to the radome are expanded into vector spherical wave functions of the radome's medium. This yields two sets of unknown expansion coefficients: the radiation-field expansion coefficients, and the reflected-field expansion coefficients. The radiation-field expansion coefficients are obtained in terms of the current distribution in the antenna upon using the bilinear-form dyadic Green functions of the radome's medium. Outside the radome, the exterior field phasors due to the radome and the antenna are expanded into the conventional vector spherical wave functions of free space, yielding unknown exterior-field coefficients. Application of standard boundary conditions across the radome's surface yields the reflected and exterior-field coefficients in terms of the radiation-field coefficients, from which the radiation-field resistance and gain of the radome-antenna structure are calculated. For numerical illustration, as a nontrivial example, we considered a toroidal antenna carrying a uniform current distribution. The role of the anisotropy of the radome on the radiation resistance of the toroidal antenna is dictated by (i) the electrical size of the radome, (ii) the radome's relative impedance, and (iii) the distinguished axis of the radome's medium. Moreover, those factors can be used in shaping the gain pattern, as well as in raising or lowering the maximum gain.