Thevenin- and Norton-equivalent circuits, among the most fundamental circuit-analysis theorems, can be useful for determining a load resistance for maximum power transfer, simplifying circuit models, and a variety of other analysis techniques. Unfortunately, calculating the Thevenin voltage and resistance can become difficult as circuit complexity increases. Figure 1, Figure 2, and Figure 3 illustrate a simple method for obtaining the Thevenin voltage and resistance—and, subsequently, the Norton equivalence—with the aid of simulation. First, you choose an arbitrary load resistance, R_LOAD—2 kΩ in this example—and run the simulation to get the current through the load resistance. Next, you remove the load resistance and simulate the open-circuit voltage across nodes A and B to obtain the Thevenin voltage. You obtain the Thevenin resistance from those two values.

The Thevenin-equivalent circuit must produce the same current through the load. The total resistance in the Thevenin circuit is R_TOTAL=(V_TH/I_LOAD)=(374.095 mV/60.301 µA)≈6.203 kΩ, where R_TOTAL is the total resistance. Therefore, the Thevenin resistance is simply [(V_TH/I_LOAD)–R_LOAD]=(R_TOTAL–R_LOAD)=6.203 kΩ –2 kΩ≈4.203 kΩ, where V_TH is the Thevenin voltage and I_LOAD is the load current.

Figure 4 shows the Thevenin-equivalent circuit, and Figure 5 shows the Norton-equivalent circuit. Note that, because the net current through the load flows to the left, the positive Thevenin terminal is grounded. Without the aid of simulation, you can calculate V_THEVENIN and R_THEVENIN as follows. The array for the loop currents in Figure 2, assuming a clockwise current flow in each loop, gives the current through the load resistance (Equation 1).

From Equation 1, you can calculate I₂ and I₅: I₂≈217.77 µA, and I₅≈157.47 µA. Thus, I₂–I₅≈60.3 µA, assuming a leftward flow through the load resistor.

You calculate the array for the loop currents in Figure 3 without the load resistance, as Equation 2 shows. From Equation 2, you can calculate the following currents: I₁≈807.92 µA, I₂≈1.744 mA, I₃≈179.87 µA, I₄≈53.64 µA, and I₅≈148.27 µA. Thus, V_A= –V₄+[(I₂–I₃)×R₇]≈–1.8719V, where the net current flows downward. Further, V_B= [(–V₄+(I₃×R₉))+((I₃–I₅)×R₁₀)+V₂]≈–1.498V, where the net current in R₁₀ flows downward. Thus, V_THEVENIN=V_A–V_B≈–374 mV, and you can calculate R_THEVENIN according to the previous description.