Solving the Circuit Equations in Nexxim DC Analysis — Ansoft Designer 7.0 在线帮助文档，Ansys Designer 教程

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Solving the Circuit Equations in Nexxim DC Analysis

In general, the equations for a system with a large number of nonlinear elements cannot be solved directly. The DC solver uses the Newton-Raphson (NR) method, a well-known iterative method.

The Newton-Raphson loop begins with vectors of initial values for the node voltages and branch currents. In each NR iteration, the simulator linearizes the circuit around the solution calculated in the previous iteration, and calculates the Jacobian matrix associated with the linearization point. The linear circuit models are represented in matrix/vector form. The simulator then uses a matrix solver to calculate a new vector of unknowns. At the end of each iteration, the Newton-Raphson method updates the solution and checks to see if the new solution satisfies the specified tolerances. If the result is within tolerance, the loop terminates. Otherwise, the loop uses the new result to start the next iteration.

Convergence is a critical issue with the Newton-Raphson method. Convergence to a correct solution is guaranteed by NR only when the initial starting point is sufficiently close to the final solution. Initial voltages set with .NODESET can help, but in many cases the DC solver starts with zero values, which may be too far from the correct values. Thus, convergence is often a serious problem that causes the DC solver to fail, which in turn prevents any further analysis such as transient analysis to be performed. In the Nexxim circuit simulator, the basic Newton-Raphson method is combined with sophisticated continuation schemes to ensure robust convergence without loss of simulation speed and accuracy.


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