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

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.