We revisit the analytic derivation of the dc and low frequency ac behavior of the p-n step junction and suggest all preexisting treatments are flawed for three important reasons. First, not all contributions to the diode current are included. We derive a rigorous expression for each component of current that can be used to judge the completeness of existing analytic theories. Additionally, wrong boundary conditions for minority carrier concentrations and incorrect equivalent circuit topologies undermine present analytic theories of the diode. We propose a new analytic equivalent circuit model which institutes correct boundary conditions. The resulting circuit model demonstrates excellent dc and ac accuracy for symmetric and asymmetric junctions, for long, short, or intermediate base regimes. Inductive behavior associated with short base diodes at large forward bias is reproduced, as is the decrease in capacitance observed in long base diodes. The assumptions and limitations of our new circuit model are thoroughly investigated.