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 j = (1 - upsilon(m))/(1 + alpha upsilon), here the normalized voltage, upsilon and normalized current density j can be represented as upsilon = V/V-oc, and j = J/J(sc) respectively, where V-oc is the open circuit voltage and J(sc) is the short circuit current density. The model is an equivalent rational function form and useful for design, characterization and calculation of maximum power point voltage. The model is intuitive and lacks the analytical support. In this paper an analytical derivation of the model is presented using the physics based implicit J-V equation. (C) 2014 Elsevier Ltd. All rights reserved.