Light-emitting diodes (LEDs) are becoming increasingly important for general lighting applications. The remote phosphor technology, with the phosphor located at a distance from the LEDs, offers an increased extraction efficiency for phosphor converted LEDs compared to intimate phosphor LEDs where the phosphor is placed directly on the die. Additionally, the former offers new design possibilities that are not possible with the latter. In order to further improve the system efficiency of remote phosphor LEDs, realistic simulation models are required to optimize the actual performance. In this work, a complete characterization of a remote phosphor converter (RPC) consisting of a polycarbonate diffuser plate with a phosphor coating on one side via the bi-directional scattering distribution function (BSDF) is performed. Additionally, the bi-spectral BSDF which embraces the wavelength conversion resulting from the interaction of blue light with the RPC is determined. An iterative model to predict the remote phosphor module power and photon budget, including the recuperation of backward scattered light by a mixing chamber, is introduced. The input parameters for the model are the bi-spectral BSDF data for the RPC, the emission of the blue LEDs and the mixing chamber efficiency of the LED module. A good agreement between experimental and simulated results was found, demonstrating the potential of this model to analyze the system efficiency with errors smaller than 4%.