This research paper considers the mathematical model and simulation of InGaP/GaAs/InGaAs/InGaSb quadruple junction solar cell with a Double diode model for higher conversion efficiency (46.88%) in MATLAB/Simulink environment. The effect of different parameters like lattice constant, bandgap energy, and current matching on the 4-junction solar cell is considered. Also, the effect of environmental factors like temperature and irradiance on conversion efficiency is demonstrated on the Quadruple junction solar cell. Maximum PowerPoint Tracking (MPPT) methods are widely used for fast and accurate outcomes in PV systems. This paper considered two methods Perturb Observe and Artificial Neural Network MPPT methods. These two methods were compared and analyzed for better conversion efficiency from multi-junction solar cells. Simulation results are obtained for different solar irradiation and temperatures, detailed interpretation and discussion are carried out. Also, the simulation results are obtained for MPPT methods, and their analysis is carried out in conjunction with quadruple junction solar cell.