10.5.2 Computer Analysis using the State Equation

• One advantage of state equation formulation is that even in the nonlinear case, the equations can be readily solved on a computer
• The value of state variable at time t + dt can be estimated by standard numerical method ie. Euler's method:

• The value of vC at time t = t + 2dt can be determined in like manner from the value of vC(t0+dt) and i(t0+dt) . Subsequent value of vC can be determined in same process
• By choosing small value of dt, a computer can determine the waveform of vC(t) to a certain degree of accuracy
• This process illustrates the fact that the initial state contains all the information that is necessary to determine the entire future behavior of the system from the initial state and subsequent input
• This procedure works even for circuits with many capacitors and inductors, linear or nonlinear, because these higher-order circuits can be formulated in term of a set of first order state equations, one for each energy storage element ( with an independent state variable) in the network