In this paper, a theoretical model for an Interleave-Chirped Arrayed Waveguide Grating (IC-AWG) is presented. The model describes the operation of the device by means of a field (amplitude and phase) transfer response. The validation of the model is accomplished by means of simulations, using parameters from previously fabricated devices. A novel design procedure is derived from the model, and it is later on employed to demonstrate the design of colorless universal IC-AWGs. The model can be readily applied to the analysis and design of future multi-wavelength optical coherent communications receivers and optical waveform analyzers.