Monograph Topic 1: Traditional SPICE Simulation Architecture and Modified Nodal Analysis (MNA) Differential-Algebraic Equation (DAE) Foundations

Abstract: Circuit simulation in Electronic Design Automation (EDA) requires balancing physical device model fidelity, numerical solver stability, and computational resource allocation. Since the publication of the Berkeley SPICE report (UCB/ERL M382) in 1973 by Nagel and Pederson, traditional SPICE-class tools have relied on Modified Nodal Analysis (MNA) to assemble nonlinear Differential-Algebraic Equations (DAEs), solved subsequently via damped Newton-Raphson iteration and direct sparse LU factorization. This monograph provides an exhaustive mathematical and microarchitectural derivation of Topic 1: examining how MNA systematically maps circuits containing floating voltage sources and inductors into Index-1/Index-2 DAE systems, analyzing Jacobian asymmetry introduced by active semiconductor transconductances (gm), and detailing double-precision convergence criteria (KCL current residuals and nodal voltage updates). This establishes the rigorous numerical baseline required for modern Web EDA architectures.