Invertible Approximate Analytical Solutions for Time–Current Relationships in Nonlinear R–L–D Circuits Using Padé Approximation

This paper proposes a new analytical approach for nonlinear series resistor–inductor–diode (R–L–D) circuits based on the Padé rational [1/1] approximation of the diode's exponential characteristic. Starting from the nonlinear differential equation governing the circuit, explicit approximate closed‐form expressions for time as a function of current, as well as invertible approximate closed‐form expressions for current as a function of time, are derived. The proposed method is validated through systematic comparison with numerical simulations conducted in MATLAB/Simscape and with existing analytical methods from the literature. The results demonstrate that the Padé‐based approximate solutions achieve high accuracy, stable transient response, and significantly reduced computational complexity, making the approach suitable for efficient and rapid analysis and design of nonlinear electronic circuits.