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updated 2001.04.17
Author Ananda Murthy R. S.
THEVENIN THEOREM IN A DC CIRCUIT

This example is meant for novice users of SPICE OPUS to help them become familiar with verification of Thevenin Theorem in a resistive circuit excited by DC source/s.

This is unsolved Problem No. 51, taken from Problems in Electrical Engineering, VIII Edition, page no. 47,  by 
S. Parker Smith and N. N. Parker Smith.
 

PROBLEM: 

Using Thevenin Theorem, find the current in a 2 Ohm resistor connected between terminals A and B in the circuit shown in Figure-1.   Answer: 0.8175A
 

EXPLANATION:

Figure-2 shows the circuit simulated using SPICE OPUS. The right portion of this figure shows the Thevenin equivalent of the circuit of Figure-1 as seen from the terminals A and B with a 2 Ohm resistor connected.
 

In this method of simulation, we use tf command to find Voc and Rth. This method can be applied when the circuit has one or more independent DC sources only. 

The general format of tf command is as shown below:

tf output_node input_source

This command performs transfer function analysis returning the transfer_function (output/input), output_impedance and input_impedance between the given output node and the given input source. Observe how we can print these results.

In the simulation given below, we have also used the op command to find the current through the Thevenin equivalent circuit.

Observe how we can change the value of a source using the alter command during simulation.

Observe how we can print the value of a source by prefixing the source name with @.

Create the circuit file given below using a text editor without any formatting and save it as a *.cir file. Then start SPICE OPUS. At SPICE OPUS prompt type `source filename.cir' to run simulation and get results. Your results should tally with what is given below. 
 

CIRCUIT FILE:

THEVENIN THEOREM IN DC CIRCUIT: METHOD-1

* These are given voltage sources.

v1  1 0 dc 2v
v2  3 0 dc 4v

* This is Thevenin equivalent voltage source.
* This is later set equal to open circuit voltage.

voc 4 0 dc 0v

r1  1 2 2
r2  2 0 12
r3  2 a 1
r4  3 a 3
r5  5 0 2

* This is Thevenin equivalent resistance. It is
* initially set to an arbitrary value, say 10 Ohm.
* Later it is altered to the correct value of rth.

rth 4 5 10

.control

* This deletes any data in the SPICE OPUS memory
* calculated during earlier runs of simulation.

destroy all

* You must conduct tf analysis with respect to each
* independent source in the given circuit.

tf v(a) v1
tf v(a) v2

* Observe how the values of sources are
* included in expressions as @v1 and @v2.
* Also how we can use let command to define new variables.
* The equation given below calculates Voc by applying
* principle of superposition.

let ocvolt=(tf1.transfer_function*@v1+tf2.transfer_function*@v2)
let zth=output_impedance
echo
echo Voc is
print ocvolt
echo
echo Rth is
print zth

* Now find current in Thevenin equivalent circuit.
alter voc=ocvolt
alter rth=zth
op
let i2ohm=-i(voc)
echo
echo Current through 2 Ohm resistor is
print i2ohm
echo
destroy all
.endc

.end

 

RESULTS:

Circuit: THEVENIN THEOREM IN DC CIRCUIT: METHOD-1


Voc is
ocvolt = 2.800000e+00

Rth is
zth = 1.425000e+00

Current through 2 Ohm resistor is
i2ohm = 8.175182e-01

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