| While most traditional circuit simulation programs such as SPICE rely upon numerical integration techniques to perform transient analysis, this dissertation presents an alternative approach that relies on closed-form integration. Traditional numerical approaches offer no hope of finding an analytical solution, even if it is known that the solutions will be in a simple functional form. By using closed-form methods, the computer can find the exact analytical solution to the network and completely avoid problems associated with numerical approximations, determining appropriate integration step sizes, stiff systems of differential equations, or accumulated global error. Computer run time is independent of the amount of time simulated. The closed-form analysis program described in this paper constructs state equations from a SPICE-like input deck and solves the network by computing its eigenvalues. The program automatically separates out the complementary solution and the particular solution due to each input, combining them to produce the complete solution. The program can recursively handle hierarchically defined networks. With closed-form solutions, the design engineer can determine exponential decay rates, phase shifts, time delays and oscillation periods directly from the formulas rather than having to estimate them from an output plot. Resonance conditions and network instability are automatically detected by examining the eigenvalues. The design engineer may numerically evaluate the closed-form formulas at any point in time by compiling the output with another program. |
