Analytical solution for the inductor current of BOOST converter

This study proposes an analytical solution for the inductor current of the BOOST converter using the relative inductance as an independent variable based on the relative variable method. First, the expressions of the actual and relative values of current and energy for BOOST circuits are derived, based on the principle of KCL and conservation of energy. Second, three different cases for calculating the minimum and maximum values of the critical inductance are discussed under a variable input voltage. Then, the analytical solutions for inductor current and duty cycle in CCM and DCM are derived by taking the relative inductance as an independent variable. Furthermore, based on the inductor current equations, the authors deduce the analytical solutions for RMS, derivatives of RMS, delta, the maximum and minimum of the inductor current, and the maximum energy of the inductor. Finally, simulation and experimental results are presented to verify those formulas.