The Ebers-Moll, charge control, and Linvill lumped models are systematically derived from a common mathematical origin. Approximations are discussed in detail, and the models are compared on the basis of their ability to represent physical processes, the ease with which they lend themselves to analysis, and the degree of approximation involved. It is shown that all three models are equivalent with regard to over-all degree of approximation, and therefore yield the same results in the solution of large-signal transient problems. However, the lumped model best portrays physical processes and lends itself most easily to intuitive understanding.