New approximate analytical solution of the diode-resistance equation

Abstract The problem of finding an analytical solution for the circuit formed by a diode with series resistance (D-R circuit) has been investigated for a long time and several authors have proposed approximate solutions. Most solutions use the Lambert function and numerical methods. However, an analytical solution independent of experimental parameters is still missing to replace the D-R circuit with an analytical expression, in which only the diode and circuit parameters appear. In this paper, using a Taylor series expansion of the equation VD = f (VS, R, ID), we propose a new analytical solution that fits the exact solution with more accuracy than all known approximations. The average of the absolute error vector is the best, with an order of magnitude of difference compared to the other 3 approximations studied. This new function can be expressed by voltage analysis, which allows analytical solutions. Our solution may have many applications, such as a simple and accurate way, in circuit simulation programs or numerical calculation programs. In particular, it can be used as well in circuits with D-R branches, exponential amplifiers, logarithmic amplifiers and waveform shapers. On another level, a comparison with other state of the art approximations is presented.