Thevenin and Norton equivalent circuits [1-3] are valuable analysis tools for circuit designers and researchers. How to use the available network theorem to obtain the davining resistance and Norton conductance of the network?

In this design concept, the substitution theorem of network analysis has been used to obtain equivalent resistance / conductance using SPICE circuit simulation software [4-5]. The Thevenin equivalent representation of a network with any load resistance value (K · R T) and k > 0 is shown in Fig. 1a. Thevenin resistance R T will be determined between terminals a and B. The load resistance K · r t can be determined by the equivalent voltage source according to the substitution theoremE c ·k/(k+1) Instead, where E C is the Thevenin open circuit voltage, which can be obtained by separately defining the network of interested Thevenin resistance as a sub circuit described in the spice netlist file. The product of E C and K / (K + 1) is realized by a voltage related voltage source (in spice), as shown in Fig. 1b. Figure 1A Thevenin equivalent representation (1a) of a network with any load resistance value (K · R T) and k > 0 is shown; The product of E C and K / (K + 1) is realized by a voltage related voltage source (in spice), as shown in 1b.

R t value of network（Figure 3）[6-7] can be obtained by dividing this voltage by the product of currents I K and K through the voltage dependent voltage source, and its value is defined as:E C / (I k)(k+1))。 Figure 3For a network, the davining resistance across terminals a and B will be determined.

Figure 3In table IThe calculated Thevenin resistance for different K values is given: The Norton equivalent circuit of a linear network with arbitrary load conductance value (g nor / k) and k > 0 is shown in Fig. 2A. The Norton conductance (g nor) of the network will be determined between terminals C. the load conductance g nor / K in D. Norton equivalent representation can be used as an equivalent current source according to the substitution theoremI SC /(k+1) Instead (Fig. 2b), where I SC is the Norton short-circuit current, which can be obtained from the single subcircuit spice description of the network under consideration. Figure 2The Norton equivalent circuit of a linear network with arbitrary load conductance (g nor / k) and k > 0 is shown in Fig. 2A; The load conductance g nor / K in the Norton equivalent representation can be replaced by an equivalent current source through the substitution theorem (2b).

The final Norton conductance value can be obtained by the following expression:k·I SC /((k+1)·V k )

The voltage V K (voltage across the current control current source) can be derived using the spice program.Figure 4Shows a network whose Norton conductance across terminals C and D will be determined. Figure 4The network whose Norton conductance across terminals C and D is to be determined.

Table 2The Norton conductance g nor (in milliohm) of various k values in Fig. 4 is given: Obtain spice file description of Thevenin resistance (R T)

Subcircuit thev is used to describeTable 3Network in (Figure 3): Thevenin open circuit voltage is available at node 1 of sub circuit x1. The voltage source esubs required by the substitution theorem is connected to node 3 of sub circuit x2. The current through the zero voltage source V23 is given   Current I K through voltage dependent voltage source esubs. The current I k is converted to a DC voltage of the same value at node 4 using a current controlled current source fsubs and a 1 ohm resistor rr40 (I k = V (4)). Expression equivalent to the DC voltage (V (5)) of node 5E c /((k+1)·I k）Is the gram * voltage V (5) * (K + 1) obtained by equalizing the triple product current of the polynomial source gsubs, that is, the current I, and the current carried by the voltage controlled current source gsubs1 (= e c). Now, after running the spice / PSpice file, the Thevenin resistance (in ohms) can be obtained by reading the DC voltage V (5) of node 5.

Get spice file description of Norton conductance (g nor)

To determine the Norton conductance (g nor) of the network (Fig. 4) inIn Table 4The sub circuit name is described under nort: The short-circuit Norton current I SC is obtained from the current through the zero voltage source V10 connected between node 1 and ground 0. The short-circuit current is converted to DC voltage (V (4) = I SC) by current control current, and the source fnort uses 1 ohm resistance. According to the substitution theorem, the equivalent current sourceI SC /(k+1)Connect to node 2. This is connected through Norton equivalent circuitG NOR /kThe conductance is the same. Norton conductance gnor（k·I SC)/((k+one)·V k）Given the dc node voltage at (where v k = V (2)), cross node 5 and grounding node 0 are obtained by equating the current of polynomial voltage dependent current source (triple product) v k * (K + 1) * V (5) with the current of connected voltage dependent current source gnor1. Running spice / PSpice file will generate the value of dc node voltage V (5), which gives the value of G nor in Figure 4.