Theory of Operation for DC Simulation

This section discusses the theory of operation for DC simulation. It can help you understand the underlying technology. Typical users should not need to examine this material.

Simulation Basics

The simulators compute the response of a given circuit to a particular stimulus by converting, based on certain assumptions, a system of nonlinear ordinary differential circuit equations into a system of nonlinear algebraic equations and then solving them numerically. The various simulators convert ordinary differential equations to algebraic equations differently and use different numerical techniques for solving the resulting algebraic equations, leading to the many different simulator flavors (DC, AC, S-parameter, transient, harmonic balance, circuit envelope). For example, the DC and the harmonic balance simulators treat the d/dt operator differently, leading to different algebraic equations. The numerical simulation techniques rely on various iterative processes to achieve mathematical convergence toward an equilibrium point in the nonlinear algebraic equations that describe the circuit. Once this equilibrium point is reached to within certain tolerances, a solution is said to have been found.

The specific assumptions for the DC simulator are described in Simulation Assumptions.

Simulation Assumptions

DC voltages and currents are signals of zero frequency. The simulator uses this concept when performing a DC simulation, and the following conditions apply:

• Independent sources are constant valued.
• Linear elements are replaced by their (real) conductances at zero frequency.
• Capacitors, microstrip gaps, AC coupled lines, and similar items are treated as open circuits.
• Inductors, conductive discontinuities, and similar items are treated as short circuits.
• Time-derivatives are constant (zero).
• Transmission lines are replaced by DC conductance values calculated from their length, cross-sectional area, and conductivity.
• Scattering parameter (S-parameter) files must include zero frequency data to operate properly at DC (this is also required for harmonic balance analysis). Otherwise, the simulator extrapolates each S-parameter for the zero-frequency case, and uses the real part as the DC response.
• The simulator has built-in safeguards against nodes that are DC-isolated (that have no DC path to ground), as well as against DC source-inductor loops. Nevertheless, try to avoid these conditions.

For More Details

The descriptions of the various convergence modes in the table DC Simulation Advanced Settings Parameters mention techniques such as the Newton-Raphson algorithm, source-level sweeping, arc-length continuation, Gmin relaxation, and pseudo-transient analysis. For more details about these and related techniques, see the publications listed in References for DC Simulation.