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In this Design Idea, we explore several ways to use SPICE [1-3] circuit analysis software to determine the Thevenin and Norton equivalent circuit parameters of linear active networks. The Thevenin open circuit voltage and impedance are determined by the algebraic sum and difference of two complex ac voltages respectively. The Norton short circuit current and admittance are determined by the algebraic sum and difference of two complex ac currents.

**Figure 1** shows a general linear active network (LAN) whose Thevenin equivalent is to be determined between nodes R and S.

**Figure 1** A general linear active network.

**Figure 2** shows the equivalent Thevenin representation of the linear active network (LAN) of Figure 1 connected to a 1 amp AC current source with current flowing from nodes R to S (**Figure 2a**) and the Thevenin equivalent of the LAN shown in Figure 1 connected to a 1 Amp AC current source with current flowing from S to R (**Figure 2b**).

**Figure 2 **The equivalent Thevenin representation of the linear active network of Figure 1 connected to a 1 A AC current source with current flowing from nodes R to S (left) and from S to R (right).

The polarities of voltages developed across Thevenin impedance are shown in Figure 2a and 2b. The voltage differences between R and S are given by (E_{T }– Z_{T}) for Figure 2a and (E_{T }+ Z_{T}) for Figure 2b respectively. By adding these voltages (and using a scaling factor of ½),we get the Thevenin open circuit voltage E_{T} and by subtracting these voltages (with a proper scaling factor of ½), we get the Thevenin Impedance Z_{T}.

The addition and subtraction can be carried out by SPICE polynomial voltage sources or by the VALUE option of PSPICE’s analog behavioral modeling voltage source feature. **Figure 3a** shows the equivalent Norton representation of a linear active network (LAN) of Figure 1 connected to a 1 V ac voltage source (with polarity as shown). **Figure 3b** shows the equivalent Norton network of the linear active network (LAN) of Figure 1 connected to a 1 V AC voltage source of the opposite polarity.

**Figure 3** The equivalent Norton representation of a linear active network of Figure 1 connected to a 1 V ac voltage source with opposite polarities (left and right).

Now, the currents (I_{SC }– Y_{T}) and (I_{SC }+ Y_{T}) flowing through the independent voltage sources can be added and subtracted by polynomial current controlled current sources to derive the Norton short circuit current and Norton admittance values. The current source feature in the Analog behavioral modeling of PSPICE can also be used to carry out the algebraic complex addition/subtraction of currents with a proper scaling factor of 1/2. **Figure 4** shows the linear active network where the values for E_{T} and Z_{T} are to be determined across R and S.

**Figure 4** A linear active network for which Thevenin equivalent is to be obtained.

**Figure 5** shows another linear active network for which the Norton circuit parameters are to be determined.

**Figure 5** A linear active network for which the Norton equivalent is to be obtained.

**Figures 6**, **7**, **8**, and **9** show the magnitude and phase of E_{T} and the magnitude and phase of Z_{T }for the network of Figure 4.

**Figure 6** Thevenin’s open circuit voltage magnitude vs frequency.

**Figure 7** Thevenin’s open circuit voltage phase vs frequency.

**Figure 8** Thevenin’s impedance magnitude vs frequency.

**Figure 9** Thevenin’s impedance phase vs frequency.

**Table I** shows the magnitude and phase of Norton I_{SC }and Y_{T} for Figure 5 between the terminals R and S.

**Table I** Norton equivalent circuit parameters vs frequency.

The SPICE file to obtain the Thevenin equivalent circuit parameters (Figure 4) in the 1GHz to 5GHz range is given in **Table II.**

**Table II** SPICE circuit file to determine Thevenin circuit parameters for Figure 4.

Finally, the SPICE file (Figure 5) to obtain Norton equivalent parameters is given in **Table III**.

**Table III** SPICE circuit file to determine Norton circuit parameters for Figure 5.

**References**

- PSpice Manual. Irvine, California: MicroSim Corporation, 1992.
- Paul Tuinenga, SPICE: A Guide to Circuit Simulation and Analysis Using PSpice, 3d. Englewood Cliffs, New Jersey: Prentice Hall, 1995.
- Andrei Vladimirescu, The Spice Book. New York: John Wiley & Sons, 1994.

*This article was originally published on **EDN**.*

**K. Bharath Kumar** obtained B. Tech degree in E & CE with highest honours from JNT University, Anantapur,India in 1981 and M. Tech degree from Indian Institute of Technology, Kharagpur, India in the area of Microwave and Optical Communication in the year 1983. Later joined Indian Telephone Industries, Bangalore, India and worked in the area of Fiber optics, and in the year 1990 obtained M. S. degree in electrical engineering from the Illinois Institute of Technology, Chicago, USA and joined the Oki Electric, Japan as a researcher in the semiconductor laboratory. He has over twenty publications in the area of simulation and modeling of electronics circuits in various national and international journals. He is now retired from Oki Electric, and can be reached at bbkrishnapuram3@yahoo.com.