Recently a simple explicit model was introduced to represent the J–V characteristics of an illuminated solar cell with parasitic resistances and bias dependent photocurrent as vm + jn = 1. Here the normalized voltage, v and normalized current density j can be represented as v = V/Voc and j = J/Jsc respectively, where Voc is the open circuit voltage and Jsc is the short circuit current density. This model is useful for design, characterization and simple fill factor calculation and its applicability was demonstrated with the measured data of a wide variety of solar cells. This explicit form is intuitive and hence the model lacks the analytical support. In this paper an analytical derivation of this closed form explicit model is presented, which is derived from the physics based implicit J–V equation.The derivation expands the scope of model applicability and provides a new insight of analytical modeling of the solar cell.