Exact Analytical Expressions of Graëtz Bridge Currents and Voltages Using Lambert W Function

In the present study, we determine exact analytical expressions for the currents and the voltages of the circuit known as diodes-bridge or Graëtz bridge. This circuit is used in electronics as full wave rectifier, it is formed by four non-ideal identical diodes and one diagonal resistance. At the beginning, we determine analytical solution for the transcendental equation giving the output current. Then, we derive analytical expressions for the voltages at the leads of all elements in the circuit. Next, we determine exact expressions for the currents through all the branches of the bridge. Finally, we calculate dynamical resistances of different diodes in the network. The proposed analytical solutions are all expressed as functions of the Lambert W function.