Recently, a concurrent dual-band class-D power amplifier has been demonstrated to overcome the limitations of reduced efficiency in concurrent dual-band linear power amplifiers. However, the configuration could not be symbolically analyzed like its single-band counterpart due to the complicated nature of dual-band signals. This paper aims to provide a theoretical basis for idealized concurrent dual-band class-D operation. 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%. The theoretically obtained results are validated using observations from literature as well as independent Harmonic Balance simulation.