The ideal diode equation is regularly used to describe the JV-characteristic of single junction solar cells. The connection between the diode equation and fundamental physics is the application of the Boltzmann approximation to describe the fluxes of photons emitted by the cell. In this paper, this approximation is used to derive analytic JV-characteristics for three photovoltaic high-efficiency concepts, intermediate band solar cells, and solar cells optically coupled to up and downconverters. These three concepts share the common feature that they allow excitation of electrons between at least three energy levels, which assures a better utilization of the solar spectrum and leads to limiting efficiencies surpassing the Shockley-Queisser limit. Although being considerablysimpler to implementand use, the resulting JV-characteristics reproduce the limiting efficiencies obtained from full detailed balance models. The simplicity facilitates the intuitive understanding of such devices. The presented models also have the potential to serve as a useful framework for further modeling, through savings in computation time and complexity.