Differential Equation Solution to Circuit Problems
In this chapter we use analytic differential equations to solve for currents and voltages in various circuits. For simpler circuits we end up with differential equations of first order, where only initial conditions are needed; and for more complicated circuits we end up with differential equations of second order where both initial conditions and derivatives thereof are needed. We decompose the solution in terms of a homogeneous one and a particular one. Equivalently we decompose the solution into a transient one and a steady state one. The applied stimuli included sine, unit step, and a pulse. We study the 2nd order RLC problem and examine the three damping conditions: critically damped, over damped, and under damped cases. We compare to SPICE and observe excellent match.