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updated 2001.03.06
Author Ananda Murthy R. S. |
RECIPROCITY THEOREM IN A DC CIRCUIT
This example is meant for novice users of SPICE OPUS to help them become
familiar with verification of Reciprocity Theorem in a resistive circuit
excited by a DC source.
PROBLEM: Verify Reciprocity Theorem in the circuit shown in Figure-1. Take the
current flowing through 47 Ohm resistance as response.
EXPLANATION: You know the following statement of Reciprocity Theorem: In any linear bilateral passive network, the ratio of excitation to response, with a single source applied at one point and the response observed at another, is invariant to an interchange of the points of excitation and observation. This statement is verified using SPICE OPUS in the circuit shown in Figure-1. Figure-2 shows the same circuit with a dummy voltage source Vx inserted in series with 47 Ohm resistance to measure current. We can make SPICE OPUS display messages when it runs simulation using the statement echo message We can print a blank line by just typing echo without any message. 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 dummy source. 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: RECIPROCITY THEOREM IN DC CIRCUIT * Observe that nodes may be identified with
* DC Source
* This source measures current through 47 Ohm resistor
* Resistors
.control
alter vin=0
.end
RESULTS: Circuit: RECIPROCITY THEOREM IN DC CIRCUIT First vin=6V and vx=0V
i(vx) = 2.577041e-02
Now positions of excitation and response are interchanged.
@vin = 0.000000e+00
The values displayed in both cases are same.
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