Method employs PSpice for Theveninequivalent circuits
18 Dec 2015  David KarpatyShare this page with your friends
Figure 1: To calculate Theveninequivalent circuits, you first choose a load resistance—2 kV in this circuit. 
Figure 2: The simulation for current through the load resistance yields 260.3 mA. 
Figure 3: The simulation for the opencircuit voltage yields approximately 2374 mV. 
The Theveninequivalent 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/60.301µA)≈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: In the Theveninequivalent circuit, current flows to the left, so the VTHEVENIN terminal is grounded. 
Figure 5: In the Nortonequivalent circuit, RNORTON is 4.203 kV. 
Figure 4 shows the Theveninequivalent circuit, and figure 5 shows the Nortonequivalent 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 I_{2} and I_{5}: I_{2}≈217.77µA, and I_{5}≈157.47µA. Thus, I_{2}–I_{5}≈60.3µA, 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: I_{1}≈807.92µA, I_{2}≈1.744 mA, I_{3}≈179.87µA, I_{4}≈53.64µA, and I_{5}≈148.27µA. Thus, V_{A}= –V_{4}+[(I_{2}–I_{3})×R_{7}]≈–1.8719V, where the net current flows downward. Further, V_{B}= [(–V_{4}+(I_{3}×R_{9}))+((I_{3}–I_{5})×R_{10})+V_{2}]≈–1.498V, where the net current in R_{10} flows downward. Thus, V_{THEVENIN}=V_{A}–V_{B}≈–374 mV, and you can calculate R_{THEVENIN} according to the previous description.
About the author
David Karpaty contributed this article.
This article is a Design Idea selected for republication by the editors. It was first published on April 23, 2009 in EDN.com.
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