DC analysis of nonlinear circuits using solution-tracing circuits

The dc driving-point and transfer characteristics of nonlinear circuits are the multivalued curves that arise from the nature of the circuit. These curves cannot be analyzed by general-purpose circuit simulators. One known method for analyzing these kinds of characteristic curves is the backward differentiation formula (BDF) curve-tracing algorithm proposed by Ushida and Chua. In this method, the circuit equations f(x) = 0, f (·): R^N+1 → Rⁿ, where the input voltage is assumed to be a variable, are analyzed by the predicator-corrector algorithm where the arc-length of the solution curve in n + 1-dimensional space is the parameter. However, it is not clear that this method is practical for large-scale circuits. In this paper, we extend the Ushida-Chua method from a practical method standpoint and demonstrate that the multivalued characteristic curves of large-scale circuits can easily be analyzed using general-purpose circuit simulators. In the proposed method, first, the solution curve in n + 1-dimensional space is projected into m + 1-dimensional space, where m ≤ n and the arc-length of this new curve is used as the parameter. Second, the relationship between the arc-length and the components of the curve is expressed by a function generator circuit, the solution-tracing circuit. Finally, transient analysis is performed using a general-purpose circuit simulator and the solution curve is traced. The effectiveness of this method is verified through several examples, including a bipolar analog IC with 296 nodes.