A General Mathematical Model for Complex Circuit Analysis

Circuit analysis is a fundamental aspect of electrical engineering and plays a vital role in the design and optimisation of complex electrical systems. Several methods provide circuit analysis, but the complexity of modern circuits, especially with nonlinear components and feedback loops, demands more comprehensive and flexible mathematical models. This research attempts to solve a variable coefficient differential Equation arising from an oscillator circuit. The circuit is a part of the wireless synchronisation design. The Equation representing the circuit poses difficulties in analysis due to the multiplication by the ramp function. The known theoretical methods, such as Laplace and Fourier transformation methods, may need to produce a direct solution to the differential Equation. The presented mathematical transform provides a valuable tool for engineers and researchers involved in circuit analysis and design. The mathematical transform overcomes the problem arising from multiplying the ramp function by the second-order derivative Equation. The applicability and effectiveness of the proposed transform were analysed through case studies involving circuits of varying complexity. The circuit design is performed in the Simulink workspace, and the results are plotted and compared with those obtained using the proposed mathematical solution. The simulation outcomes verify the solutions obtained from the proposed mathematical transform.