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ELC 131 Lab 5: Circuit Theorems

Introduction: There are several theorems used in electronics to simplify the analysis of complex circuits. Thevenin's and Norton's theorems allow complex circuits to be reduced to a single source and a single resistance. The superposition theorem allows a multisource series-parallel circuit to be analyzed using Ohm's law and basic circuit analysis techniques. The source conversion theorem is used to convert a voltage source to a current source and visa-versa.

Objectives: Upon completion of this lab exercise the student will be able to:

1. Derive the Thevenin and Norton equivalent circuits for a simple series-parallel circuit.

2. Use Thevenin's and Norton’s theorems to find the voltage across and the current through a changing load in a simple seriesparallel circuit.

3. Use the superposition theorem to calculate the voltage across and the current through the load of a multi-source series-parallel circuit.

4. Use the source conversion theorem to determine the current through the load of a multisource series-parallel circuit.

5. Use MultiSIM to determine the voltage across and the current flow through selected components.

Parts and Equipment: personal computer with MultiSIM installed

Prelab: Instructor Initials

Complete Section 1, Step 4.

Complete Section 2, Step 4.

Complete Section 3, Step 4.

Complete Section 4, Step 3.

Section 1: Thevenin’s Theorem

Thevenin’s theorem states that any two-terminal linear bilateral network can be replaced with an equivalent circuit consisting of a voltage source and a series resistance as shown in Figure 1.

Figure 1: Thevenin’s Equivalent Circuit

Deriving the Thevenin equivalent circuit is accomplished by performing the following steps:

1. Open the circuit at the two terminals. Find the open circuit voltage across the two terminals. This is the Thevenin voltage, VTH.

2. Find the resistance between the two terminals with all sources replaced by their internal resistances. This is the Thevenin resistance, RTH.

3. Place VTH and RTH in series with the two terminals. This is the Thevenin’s equivalent circuit.

4. Replace the device or circuit that was originally connected to the two terminals.

Figure 2: Circuit for Section 1 and Section 2

Step 1: Create a circuit file in MultiSIM with the circuit of Figure 2 with RL=2.4 kΩ.

Step 2: Measure VRL and record this value in Table 1.

Step 3: Repeat Step 2 for the remaining values of RL from Table 1.

Do not delete the circuit file of Figure 2. It will be used again in Section 2.

Step 4: Derive the Thevenin equivalent circuit as seen by RL in the circuit of Figure 2.

Step 5: Create a circuit file in MultiSIM with your Thevenin equivalent circuit.

Step 6: Connect the 2.4 kΩ resistor to the Thevenin equivalent circuit. Measure the voltage across the 2.4 kΩ load resistor. Record this value in Table 1.

Step 7: Repeat Step 6 for the remaining values of RL listed in Table 1.

RL	VRL—Figure 2	VRL—Thevenin Ckt
2.4 kΩ	2.66V	1.063V
5.1 kΩ	3.43V	1.79V
10 kΩ	3.93V	2.54V

Table 1: Data for the Circuit of Figure 2 and the Thevenin Equivalent Circuit

Section 2: Norton’s Theorem

Norton's theorem states that any two-terminal linear bilateral network can be replaced by an equivalent circuit consisting of current source and a parallel resistance as shown in Figure 3.

Figure 3: Norton’s Equivalent Circuit

Deriving the Norton equivalent circuit is accomplished by performing the following steps:

1. Short the circuit between the two terminals. Find the short-circuit current through the two terminals. This is the Norton current, IN.

2. Find the resistance between the two terminals with all sources replaced by their internal resistances. This is the Norton resistance, RN.

3. Place IN and RN in parallel with the two terminals. This is the Norton's equivalent circuit.

4. Replace the device or circuit that was originally connected to the two terminals.

Step 1: Replace RL in the circuit of Figure 2 with the 2.4 kΩ resistor.

Step 2: Measure IRL and record this value in Table 2.

Step 3: Repeat Step 2 for the remaining values of RL from Table 2.

Step 4: Derive the Norton equivalent circuit as seen by RL in the circuit of Figure 2.

Step 5: Create a circuit file in MultiSIM with your Norton equivalent circuit.

Step 6: Connect the 2.4 kΩ resistor to the Norton equivalent circuit. Measure the current through the 2.4 kΩ load resistor. Record this value in Table 2.

Step 7: Repeat Step 6 for the remaining values of RL listed in Table 2.

RL	IRL—Figure 2	IRL—Norton Ckt
2.4 kΩ	4.44mA
5.1 kΩ	4.44mA
10 kΩ	4.44mA

Table 2: Data for the Circuit of Figure 2 and the Norton’s Equivalent Circuit

Section 3: Superposition Theorem

The superposition theorem states that the current through, or voltage across, any element in a linear bilateral network is equal to the algebraic sum of the currents or voltages produced by each source acting independently.

The following procedure is used to implement the superposition theorem.

1. Replace all sources but one with their internal resistances.

2. Determine the current through, or the voltage across, the element(s) of concern. Denote the direction of the current flow or the polarity of the voltage drop.

3. Repeat steps 1 and 2 for all remaining sources.

4. Find the algebraic sum of the currents or voltages.

Figure 4: Circuit for Section 3

Step 1: Create a circuit file in MultiSIM with the circuit of Figure 4.

Step 2: Measure the current through RL. Record the magnitude and the direction of current in Table 3.

Step 3: Measure the voltage across RL. Record the magnitude and the polarity of the voltage drop in Table 3.

Step 4: Use the superposition theorem to calculate the current through and the voltage across RL in the circuit of Figure 4. Record these values in Table 3.

	MultiSIM	Calculated
IRL	11.36mA
VRL	10.48V	17.48A

Table 3: Data for the Circuit of Figure 4

Section 4: Source Conversion Theorem

The source conversion theorem allows a constant voltage source and series resistance to be interchanged with a constant current source and parallel resistance, as illustrated in Figure 3.

Figure 5: Illustration of the Source Conversion Theorem

A constant voltage source and its series resistance are converted to a constant current source and a parallel resistance by performing the following steps:

1. Place a short between the two terminals. Find the short-circuit current through the two terminals. This is the current source, IS.

2. Remove the short and find the resistance between the two terminals with the voltage source replaced by its internal resistance. This is the parallel resistance, RP.

3. Place IS and RP in parallel with the two terminals. This is the equivalent constant current source.

4. Replace the device or circuit that was originally connected to the two terminals.

A constant current source and its parallel resistance are converted to a constant voltage source and a series resistance by performing the following steps:

1. Find the open circuit voltage across the two terminals. This is the constant voltage source, VS.

2. Find the resistance between the two terminals with the current source replaced by its internal resistance. This is the series resistance, RS.

3. Place VS and RS in series with the two terminals. This is the equivalent constant voltage source.

4. Replace the device or circuit that was originally connected to the two terminals.

Figure 6: Circuit for Section 4

Step 1: Create a circuit file in MultiSIM with the circuit of Figure 6.

Step 2: Measure IR3 and record this value in Table 4.

Step 3: For the circuit of Figure 6, change the constant voltage source, VS, and its series resistance, R1, to a constant current source and a parallel resistance.

Step 4: Create a circuit file in MultiSIM with the equivalent constant current source circuit.

Step 5: Measure the current through R3. Record this value in Table 4.

IR3— Circuit of Figure 6	IR3—Constant Current Circuit
36.364mA

Table 4: Data for Constant Current Source Circuit

Questions:

1. Derive the Thevenin equivalent circuit as seen by RL for the circuit shown in Figure 6.

Figure 6

2. Derive the Thevenin equivalent circuit as seen by RL for the circuit shown in Figure 7.

Figure 7

3. Use the superposition theorem to calculate the voltage across R3 in the circuit of Figure 8.

Figure 8

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