Introduction to the Principle of Superposition

EE 442 Laboratory Experiment 4

EE 442

Lab Experiment No. 4

02/13/2008

Introduction to the Principle of Superposition

I.INTRODUCTION

The purpose of this experiment is to study the principle of superposition. This principle will first be studied by numerically analyzing a circuit in the preliminary part of this lab. Then the same circuit will be measured in the laboratory. Corresponding calculated and measured circuit response values will be compared.

II.PRELAB EXERCISES

We will demonstrate the validity of the superposition principle in the laboratory by applying it to the circuits shown in Figure 1 and Figure 4.

Figure 1 Circuit to which superposition will be applied

i1 = ______

i2 = ______

i3 = ______

A.Solve the circuit shown in Figure 1 for i1, i2, and i3 and record your results above. Use either the node voltage method or the mesh current method. Do not use superposition in this step.

B.Suppress the lower voltage source in the circuit of Figure 1 by replacing it with a short circuit. Solve the circuit, shown in Figure 2, for i1’, i2’, and i3’, and record your results in the spaces provided (below Figure 2).

Figure 2 Circuit in Figure 1 with the lower source suppressed

i1’ = ______

i2’ = ______

i3’ = ______

C.Suppress the upper voltage source in the circuit of Figure 1 by replacing it with a short circuit. Solve the resulting circuit, shown in Figure 3, for i1’’, i2’’, i3’’, and record your results in the spaces provided.

Figure 3 Circuit of Figure 1 with the upper source suppressed

i1’’ = ______

i2’’ = ______

i3’’ = ______

D.Combine the solutions of parts B and C and compare with the solution of part A.

Figure 4 Circuit with current sources to which superposition will be applied.

V1 = ______

V2 = ______

V3 = ______

VS1 = ______

VS2 = ______

E.Solve the circuit shown in Figure 4 for V1, V2, V3, VS1, and VS2. Record your results above. Use either the node voltage method or the mesh current method. Do not use superposition in this step.

F.Suppress the lower current source in the circuit of Figure 4 by replacing it with an open circuit. Solve the circuit, shown in Figure 5, for V1’, V2’, and VS2’, and record your results in the spaces provided (below Figure 5).

Figure 5 Circuit in Figure 4 with lower source suppressed

V1’ = ______

V2’ = ______

VS2’ = ______

G.Suppress the upper current source in the circuit of Figure 4 by replacing it with a open circuit. Solve the resulting circuit, shown in Figure 3, for V2’’, V3’’, VS1’’, and record your results in the spaces provided.

Figure 6 Circuit in Figure 5 with upper source suppressed

V2’’ = ______

V3’’ = ______

VS1’’ = ______

H.Combine the solutions of parts F and G and compare with the solution of part E.

III.LABORATORY EXPERIMENTS (VOLTAGE SOURCE)

1.Connect the circuit shown in Figure 7using the Agilent E3630A. (Make sure the tracking ratio knob is locked in the Fixed position, this position will guarantee that both the +20 and -20 V taps deliver the same voltage magnitude with respect to the common tap.)

Figure 7 Laboratory version of the circuit in Figure 1

2.Energize the circuit of Figure 7 and then measure and record the following data:

Ammeter readings A1 and A2 (compare with preliminary calculations)

A1 = ______

A2 = ______

Voltage across the 4.7kΩ and 10kΩ resistors

V4.7kΩ = ______

V10kΩ = ______

Voltage across the upper 12 Volt source terminals

V12 V = ______

3.Using the data obtained in Step 2, apply KVL by calculating the sum of all the voltage drops around the upper closed loop (remember to take the algebraic signs into account). Is KVL satisfied?

4.Turn off the DC supply and reconnect the circuit as shown in Figure8.

Figure 8 Laboratory version of the circuit in Figure 2

Note that the circuit in Figure 8 is equivalent to replacing the lower voltage source in Figure 7 with zero Ohms (short circuit). Do not connect the -20 V tap directly to the common tap when suppressing the lower supply.

Energize the circuit in Figure 8 and the measure and record the following data:

Ammeter readings A1 and A2 (compare with prelim calculations)

A1 = ______

A2 = ______

Voltage across the 10 kΩ resistor

V10 kΩ = ______

Turn off the DC supply and rearrange the circuit according to Figure 9.

Figure 9 Laboratory version of the circuit in Figure 3

What does the circuit arrangement of Figure 9 accomplish in terms of the original circuit?

Energize the circuit given in Figure 9 and then measure and record the following data:

Ammeter readings A1 and A2 (compare with prelim calculations)

A1 = ______

A2 = ______

Voltage across the 10 kΩ resistor

V10 kΩ = ______

Turn the DC supply off, but before dismantling the circuit, apply KCL and the principle of superposition by making the following calculations:

Add the component values of i1 measured in step 6 to the value of i1 measured in step 9. (Be careful to account for the signs!) Compare the resultant i1 to that of step 2.

Add the component values of i2, measured in steps 6 and 9 and compare with that measured in step 2.

Add the component values of the voltage across the 10 kΩ resistor measured in steps 6 and 9 and compare with that measured in step 2.

IV.LABORATORY EXPERIMENTS (CURRENT SOURCE)

Connect the circuit shown in Figure 10 using the Agilent E3631A. This power supply can be set up as a current source in the following manner.
Connect the circuit to the power supply as shown.
Turn the power supply on.
Once the power supply has booted, push the +25V button, then turn the output on.
Push the display limit button. (This action will bring up a screen that will read zero volts, 1 amp with the cursor flashing over the voltage display. This display will last 5 seconds after the last button is pushed.)
Push the current voltage button to toggle the cursor over to the current display.
Use the knob to set the display to current level specified in the diagram. (In this case, 5 mA.)
Push the Voltage/Current button again to toggle back to the voltage display.
Set the voltage to about 15 V or so. (This is the maximum voltage limit the supply will produce when it is acting as a current source. Hence, the exact value isn’t important as long as it is higher than the voltage needed to supply the specified current for a given load.) The supply will now act as a constant current source. (You should the letters CC illuminated in the lower right hand corner of the screen.
Repeat the above steps for the -25 V output. This time set the current to 10 mA and the limiting voltage to 15 V.

Figure 10 Laboratory version of the circuit in Figure 4

2.Measure and record the following datafrom the circuit of Figure 10:

Ammeter readings A1, A2, and A3

A1 = ______

A2 = ______

A3 = ______

Voltages V1, V2, V3, VS1, and VS2 (compare with preliminary calculations)

V1= ______

V2= ______

V3 = ______

VS1 = ______

VS2 = ______

3.Using the data obtained in Step 2, apply KVL by calculating the sum of all the currentsaround the closed loops (remember to take the algebraic signs into account). Is KVL satisfied?

4.Turn off the DC supply and reconnect the circuit as shown in Figure 11.

Figure 11 Laboratory version of the circuit in Figure 5

5.Note that the circuit in Figure 11 is equivalent to replacing the lower current source in Figure 10 with an open circuit.

Energize the circuit in Figure 11 and the measure and record the following data (There is no need to reset the bottom source for the above circuit.):

Ammeter readings A1 and A2

A1= ______

A2= ______

VoltagesV1, V2, and VS2 (compare with prelim calculations)

V1= ______

V2= ______

VS2 = ______

Turn off the DC supply and rearrange the circuit according to Figure 12.

Figure 12 Laboratory version of the circuit in Figure 6

What does the circuit arrangement of Figure 12 accomplish in terms of the original circuit?

Energize the circuit given in Figure 12 and then measure and record the following data:

Ammeter readings A1 and A2

A2= ______

A3= ______

Voltages V2, V3, and VS1 (compare with prelim calculations)

V2= ______

V3 = ______

VS1 = ______

Turn the DC supply off, but before dismantling the circuit, apply KVL and the principle of superposition by making the following calculations:

Add the component values of V1 measured in step 6 to the value of V1 measured in step 9. (Be careful to account for the signs!) Compare the resultant V1 to that of step 2.

Add the component values of V2, measured in steps 6 and 9 and compare with that measured in step 2.

Add the component values of V3 measured in steps 6 and 9 and compare with that measured in step 2.

IV.CONCLUSION

Do your results from both circuits support the superposition theorem? If all the measured values compare favorably to you calculated values, you are finished.