Dc analysis of nonlinear circuits using solution‐tracing circuits

Abstract 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 → R n , where the input voltage is assumed to be a variable, are analyzed by the predictor‐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.