## 4 Results and Discussion  
In order to verify the effectiveness of the proposed method, a database of 35 electronic circuits with multiple operating points was created based on the available literature and the author's own experience. These circuits differ in fabrication technology (bipolar, MOS circuits), transistor models (Ebers-Moll and Gummel-Poon models for bipolar transistors, Level 1, Level 2, and BSIM for MOS transistors), IC macromodels, complexity, and the number of DC solutions. Four of these circuits are shown in Figures 1 and 6-8. The most-important parameters of the circuits and the results are summarized in Table 1. Cases corresponding to the circuits discussed in this work are marked in the _Circuit type_ column with the number of the figure where the original schematic of the analyzed circuit is shown. Figure 6: A circuit based on the MC75140 possessing three DC solutions. Figure 8: CMOS circuit with transistors represented by the BSIM4.6 model and DC solutions found by the proposed method. Figure 7: A circuit containing an operational amplifier LMV321 modeled using the default ISpice-macromodel and DC solutions found by the proposed method. The calculations were performed on a computer with an Intel(R) Core(TM) i7-6700 processor and 64 GB RAM. The total computation time consists of the time consumed by the algorithm in the Delphi environment, the circuit analysis time performed by IsSpice4, and the time spent on communication between the two environments, including the process of creating new and deleting old files for IsSpice4, searching for output files, and opening and closing windows. In addition to simulation studies, laboratory tests were conducted, and selected nodal voltages were measured in the two circuits shown in Figures 1 and 6. These tests were carried out by making the circuit using a typical solderless breadboard, the corresponding integrated circuit (MC75140), transistors (BC 107A), and discrete resistors with a 1% tolerance. A 34401A digital multimeter was used to measure the voltages, and the circuits were \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{\begin{tabular}{c} **Number of** \\ **All DC** **Solutions** \\ \end{tabular} } & \multirow{2}{*}{**Circuit Type**} & \multirow{2}{*}{\begin{tabular}{c} **Number of** \\ **Macromodels** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Number of** \\ **Transistors *** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Number of** \\ **Diodes *** \\ \end{tabular} } & \multirow{2}{*}{**Time in s**} \\ \hline  
\hline \hline \end{tabular}  
* Without elements used in macromodels; (1)—bipolar technology; (2)—MOS technology (Model Level 2); (3)—circuit with LM318L macromodel (In addition to resistors and linear capacitors, the macromodel contains two bipolar transistors, nine diodes, and six linear controlled sources); (4)—circuit with LMV321 macromodel (In addition to resistors and linear capacitors, the macromodel contains 2 bipolar transistors, 20 diodes and 30 linear controlled sources).; (5)—MOS technology (Model BSIM4.6); (6)—MOS technology (Model Level 1); (7)—a circuit with two tunnel diodes; (8)—11 solutions are found after connecting the BC source to another node, in 5.5 s.  
\end{table} 
Table 1: Key parameters and results of calculations for exemplary circuits with multiple DC solutions. powered by a VLP-2403 PRO power supply. As a result of the measurements, voltages corresponding to the two solutions found numerically were obtained for both circuits. At the prototyping stage, the circuit shown in Figure 1 was made of selected BC 107A transistors with the parameter BF being about 100. The BC 107A model was downloaded from the IsSpice4 libraries, and the parameter BF was set to 100. The measured voltage values were \(V_{A}^{(1)}=9.988\,\mathrm{V}\), \(V_{B}^{(1)}=6.823\,\mathrm{V}\) and \(V_{A}^{(2)}=6.781\,\mathrm{V}\), \(V_{B}^{(2)}=9.480\,\mathrm{V}\), respectively.