This paper provides a theoretical basis for idealized concurrent dual-band class-D power amplifiers. It applies an alternate representation of the sum of two sinusoids which helps the formulation of a technique to analytically extract the complex Fourier series coefficients of the current and voltage waveforms of the power amplifier. Expressions for output power and efficiency are derived, showing a theoretical drain efficiency of 100 percent. While the analysis is conducted for an ideal concurrent dual-band class-D power amplifier, the technique developed in this paper can be adapted to perform Fourier analysis of other concurrent dual-band systems.