Alpha Continuation — Ansoft Designer 7.0 在线帮助文档，Ansys Designer 教程

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Alpha Continuation

Alpha continuation (also called G_min stepping) improves the robustness of the DC simulator. Some circuits may have floating nodes due to open devices. A floating node does not have a unique voltage solution, and so the circuit is a singular system that does not have a unique solution. Alpha continuation is one way to reach a solution that is unique and meaningful.

For the alpha continuation method, the simulator inserts a small conductance G_min(equivalent to a large resistor) in parallel with every branch. The value of the conductances is equal to the value of the alpha option, which defaults to 1e-13 mho. This conductance is small enough that the effect of the conductances on the circuit is typically negligible.

If the Newton-Raphson method fails to converge with the initial small conductance value, alpha stepping attempts to reach convergence by setting the conductances to a relatively large value, so that the circuit is affected by the conductances and becomes more “linear.” The solver then attempts to solve this more “linear” circuit. The solution of the modified circuit is not the same as that of the original. However, if the modified circuit converges, the solution should be close to the solution of the original circuit. The solver uses the solution for the modified circuit as the input to the next NR loop, and decreases the value of the alpha conductances to decrease their effect on the circuit.

Alpha stepping progresses through smaller and smaller conductance values until convergence is achieved with the minimum value, unless an intermediate value of conductance fails to achieve convergence. The solution is accepted when the conductance equals the alpha option, which defaults to 1e-13 mho. If the behavior of the circuit is strongly affected by the G_min conductances, you can reduce alpha or even set it to zero.


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