## 1 Introduction
The paper [32] brought a numerical method for determining multiple DC solutions based on the concept of separable Newton homotopy and partitioning the solution space into currently changing rectangles. In the literature, also papers applying a different approach to determining multiple DC solutions can be found. For example, the paper [3] discussed an approach based on evolutionary computation for determining multiple solutions using parallel search. The paper [33] presented a procedure for approximating DC operating points of nonlinear circuits based on the Carleman linearization. The idea of deflation combined with the discrete circuit equivalent of the Newton method was used to search for multiple solutions in bipolar [34] and short-channel CMOS circuits [15]. The methods usually allow multiple DC solutions to be determined, but cannot guarantee that all operational points will be found. Their implementation is generally tedious, and their use often involves specific classes of circuits. Identifying circuits with multiple DC solutions can be solved in two ways: finding more than one operating point by applying the methods described above or by searching for some topological structure. A good design tool should indicate the possible presence of more than one operating point [28]. A circuit can be claimed to have multiple solutions when more than one operating point is found [10; 28]. The approach presented in [28] is based on dividing the original circuit into sub-circuits and building an oriented dependency graph. If the graph has oriented loops, they can be sources of multiple operating points. The loops are opened by removing a minimum number of circuit nodes. Next, multiple solutions are searched, sweeping specific voltage sources over appropriate intervals. A systematic method for automatically identifying positive feedback loops in analog/mixed-signal CMOS circuits was proposed in [10; 35; 36]. The method first transforms a circuit netlist into a directed dependence graph that captures the critical relationships between branch currents and node voltages. Next, all feedback loops are found, and finally, some criteria are applied to determine the positive feedback loop. Moreover, paper [36] proposed a divide and contraction verification method against undesired operating points in CMOS circuits. Unlike traditional methods for finding all operating points, this method only targets the search for voltage ranges containing operating points. The main objective of this work was to develop a method that allows the finding of multiple solutions in a broad class of nonlinear circuits. In addition, the method should be fast, and its use should not require preliminary steps by the designer, e.g., identifying positive feedback loops, selecting an initial guess, or creating a hybrid description. The successful operation of the method should be independent of the engineer's knowledge, and the semiconductor devices should be described with adequate nonlinear equations corresponding to the technologies used. Therefore, applying the method using the SPICE software as the computational core was decided. In order to circumvent the limitations of the software resulting from the Newton algorithm used in the DC analysis (with built-in improvements), the circuit was modified by introducing nonlinear dependent current sources implementing the deflation idea discussed in Section 2. The method can be applied using a graphical user interface (ICAP/4 environment [12] in the proposed approach). However, a more efficient approach was to develop a host application that generates the appropriate netlists for IsSpice4 [13] and processes the simulation results. Both approaches are described in Section 3. In contrast to existing SPICE-oriented methods, the proposed method does not use time domain analysis, but typical DC analysis. It can be used to analyze circuits at the level of bipolar and MOS transistors (with models of long- and short-channel MOSFETs) and circuits with macromodels, e.g., of operational amplifiers.