The recent advent of ULF/ELF signal generation by high-latitude HF ionospheric interaction facilities increases the need for quick estimates of radiated field strength distributions worldwide. This paper is a first step in that direction, cataloguing the exact spherical harmonic basis function solutions for all field component combinations excited by the four source dipole possibilities. Ideally conducting spherical boundaries are assumed here as the lowest-order representation of the problem. Emphasis is directed toward simple algorithmic computation of field strengths within and below the Schumann resonance region. A method to speed the problematic numerical convergence of the summations is presented and demonstrated. Field calculations are accurate both near and far from the source. They reveal that only the vertical electric and horizontal magnetic dipoles produce appreciable field strength at great distances, as the other two dipole pairs cannot excite the far-traveling cavity-waveguide mode when the boundaries are perfectly conducting. Plots show complex distributions of excited fields around the Earth. The methods form the basis for later extensions that incorporate a representative ionospheric refractive index profile and the terrestrial magnetic field.