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updated 2001.03.07
Author Ananda Murthy R. S.
RECIPROCITY THEOREM IN AC CIRCUIT

This example is meant for novice users of SPICE OPUS to help them become familiar with verification of Reciprocity Theorem in a circuit excited by a sinusoidal source.
 

PROBLEM: 

Verify Reciprocity Theorem in the circuit shown in Figure-1. Take the current flowing through 10 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 10 Ohm resistance to measure current.

Observe how we can change the magnitude and phase angle of an AC source using the alter command during simulation.

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 AC CIRCUIT

* This is AC input source.
* It has 0 dc value, 200V rms value and
* a phase angle of 45 degrees.

vin 1 0 dc 0v ac 200 45

* This dummy source measures current
* through 10 Ohm resistor
vx 4 0 dc 0v

* Passive components
r1 1 2 20
r2 2 3 20
r3 3 4 10
l1 2 0 31.831mH
c1 3 0 318.31uF

.control
* This command makes SPICE OPUS output
* angles in degrees
set units=degree

* This conducts single frequency ac analysis.
ac dec 10 50 50
echo Current through 10 Ohm resistor:

* This prints a blank line
echo

* This prints magnitude and phase angle of current
* through 10 Ohm resistor:
print mag(i(vx)) ph(i(vx))

* Here we are setting ac magnitude (acmag) and
* phase angle (acphase) to zero to make vin
* a dummy source.
alter vin acmag=0
alter vin acphase=0

* Here we are setting ac magnitude of vx to 200V
* and its phase angle to 45 degrees.
alter vx acmag=200
alter vx acphase=45

* Now we are conducting ac analysis after
* interchanging the positions of excitation
* and response. Draw circuit diagram after this
* interchange.

ac dec 10 50 50
echo
echo After interchanging positions
echo of excitation and response
echo current through 20 Ohm resistor:
echo
print mag(i(vin)) ph(i(vin))
echo
echo Hence Reciprocity Theorem is verified.
echo
echo
.endc

.end
RESULTS:

Circuit: RECIPROCITY THEOREM IN AC CIRCUIT

Current through 10 Ohm resistor:

mag(i(vx)) = 2.169305e+00
ph(i(vx)) = 5.752879e+01

After interchanging positions
of excitation and response
current through 20 Ohm resistor:

mag(i(vin)) = 2.169305e+00
ph(i(vin)) = 5.752879e+01

Hence Reciprocity Theorem is verified.
 

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