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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 .endRESULTS: Circuit: RECIPROCITY THEOREM IN AC CIRCUIT Current through 10 Ohm resistor: mag(i(vx)) = 2.169305e+00
After interchanging positions
mag(i(vin)) = 2.169305e+00
Hence Reciprocity Theorem is verified.
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