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A method for the analysis of solar cells incorporating high-low junctions, and operating between the well-studied cases of low-and high-level injection, has been developed. It is a numerical extension of the transport velocity transformation method, oriented to the determination of I-V characteristics. The model is derived from a one-dimensional analytical treatment of minority-and majority-carrier transport, approximating the electrostatic field and spatially varying material parameters by piecewise constant functions. The analytical method is extended beyond the charge neutrality case by use of a numerical iteration process to achieve consistency of the fields with the charge imbalances between the minority- and majority-carrier distributions. Between iteration steps, the minority-carrier lifetime values are readjusted to fit the changing carrier concentrations, applying commonly used models. The method has the advantage of providing final I-V data by subdivision of the device regions into a rather small number of layers. Results obtained by applying this model to several structures are presented in Part II of this paper.