ENGI 241 LABORATORY EXERCISE 3 NETWORK THEOREMS
PURPOSE
There are some powerful network theorems that allow us to easily analyze complex circuits. In
Thevenin's Theorem, we reduce the circuit to a simple series circuit consisting of a Thevenin
equivalent Voltage Source, a Thevenin Equivalent Resistance, and the load. Norton's Theorem allows
us to reduce a circuit to a simple parallel circuit consisting of a Norton equivalent Current Source, a
Norton Equivalent Resistance, and the load. The purpose of this experiment is to verify these network
theorems.
EQUIPMENT AND PARTS REQUIRED
1
Powered Protoboard
2
Fluke Model 37 DVM
1
Resistor 1/2 W, 5%, 470Ω, 560Ω, 1kΩ (4 each), 1.2kΩ, 1.5kΩ, 2.2kΩ
1
10kΩ potentiometer
THEVENIN'S THEOREM
To use Thevenin's Theorem:
1.
Identify the load and remove it. (RL in Figure 3−1)
2.
Calculate VTH, the voltage present at the load terminals with the load removed. (VAB in Figure
3−1)
3.
Remove all sources. Replace voltage sources with a short, and all current sources with an open
but retain all internal source resistances. Calculate RTH, the resistance seen at the load
terminals. (RAB in Figure 3−1)
4.
Construct a series circuit consisting of VTH, RTH, and RL. Calculate VL and IL.
NORTON'S THEOREM
To obtain the Norton Equivalent Circuit:
1.
Identify the load and remove it. (RL in Figure 3−1)
2.
Short the load terminals and calculate IN, the current that flows into the load terminals with the
load removed. If you know VTH, IN may be calculated using the equation:
VTH
ISC = IN =
RTH
3.
Remove all sources. Replace voltage sources with a short, and all current sources with an open
but retain all internal source resistances. Calculate RN, the resistance seen at the load terminals.
(RAB in Figure 3−1) RN = RTH.
4.
Construct a parallel circuit consisting of IN, RN, and RL. Calculate VL and IL.
MAXIMUM POWER TRANSFER THEOREM
A resistive load receives maximum power from a linear, bilateral dc circuit if the load resistance is
equal to the Thevenin Equivalent resistance seen by the load. This process is sometimes referred to as
impedance matching.
Page 1
ENGI 241 LABORATORY EXERCISE 3 NETWORK THEOREMS
PROCEDURE - THEVENIN'S AND NORTON'S THEOREMS
1. Measure the resistors in Table 3−1A and record their values.
2. Build the circuit of Figure 3−1 using RL1. Adjust VS
to +15V. Measure the current through RL1 and the
VAB with a DVM and record in Table 3−1B.
3. Remove RL. Measure VAB and record in Table
3−1C. Turn off power and remove the VS
connections. Replace VS with a short. Use an
ohmmeter and measure RAB. Record the value as
RTH1 in Table 3−1C.
FIGURE 3−1
4. Draw the schematic diagram of the Thevenin
equivalent circuit. Using the measured values for VTH1 and RTH1, calculate IL1 and VL1 and record
in Table 3−1C. In your discussion, compared these calculated values to the measured values.
5. Repeat steps 2 through 4 for RL2.
6. Build the circuit of Figure 3−1 using RL1. Remove RL. Place an ammeter across nodes A and B,
apply power. Measure IN and record in Table 3−1C. Turn off power and remove the VS
connections. Replace VS with a short. Use an ohmmeter and measure RN, and record in Table
3−1C.
7. Draw the schematic diagram of the Norton Equivalent Circuit. Using the measured values for IN
and RN, calculate IL and VL and record in Table 3−1D. In your discussion, compared these
calculated values to the measured values in Table 3−1C and 3−1D.
8. Repeat steps 6 and 7 for RL2.
9. For the Bridge Circuit in Figure 3−2, use Data Tables 3−2A, 3−2B, 3−2C, and 3−2D Measure
and record the values for all the resistors in Table 3−2A.
10. For Figure 3−2, calculate the value for VAB and IAB for both load resistors and record in Table
3−2B.
11. Build the circuit of Figure 3−2 using RL1 as the load resistor.
Adjust VS to +15V. Measure VAB and IAB and record in Table
3−2C. In your discussion, compared these calculated values with
the measured values in Table 3−2C and 3−2D.
12. Repeat step 2 through 8 as appropriate to perform Thevenin's
Theorem for the Bridge Circuit.
13. Usinig PSpice, draw the circuit for Figure 3-1 and 3-2. Perform a
FIGURE 3−2
PSpice Bias Point analysis for each circuit with RL1 and RL2. Run a
separate simulation with each load resistor. Display the voltages and currents on the schematic
and print each schematic. In your conclusion, compare the calculated values, measured values an
simulated values for VL and IL.
EQUIPMENT LIST
Device
Power Supply
BCC ID #
Page 2
DVM 1
DVM 2
ENGI 241 LABORATORY EXERCISE 3 NETWORK THEOREMS
Resistor
Rated Value
R1
R2
R3
RL1
RL2
1kΩ
1kΩ
1kΩ
1kΩ
2.2kΩ
Measured Value
TABLE 3-1A
RL1
Figure 3-1
VL
RL2
IL
VL
IL
VOM
DVM
TABLE 3-1B
DVM
RL
Parameter
Calculated
Thevenin
Measured
Equivalent
VTH1
RTH1
1kΩ
VL1
IL1
VTH2
RTH2
2.2kΩ
VL2
IL2
TABLE 3-1C
DVM
RL
Parameter
Calculated
IN1
1kΩ
RN1
VL1
IL1
IN2
2.2kΩ
RN2
VL2
IL2
TABLE 3-1D
Page 3
Measured
ENGI 241 LABORATORY EXERCISE 3 NETWORK THEOREMS
Resistor
Rated Value
R1
R2
R3
R4
RL1
RL2
.47kΩ
2.2kΩ
1kΩ
1kΩ
1kΩ
2.2kΩ
Measured Value
TABLE 3-2A
RL1
Figure 3-2
VL1
RL2
IL1
VL2
IL2
VOM
DVM
TABLE 3-2B
DVM
RL
Parameter
Calculated
Thevenin
Measured
Equivalent
VTH1
RTH1
1kΩ
VL1
IL1
VTH2
RTH2
2.2kΩ
VL2
IL2
TABLE 3-2C
DVM
RL
Parameter
Calculated
IN1
1kΩ
RN1
VL1
IL1
IN2
2.2kΩ
RN2
VL2
IL2
TABLE 3-2D
Page 4
Measured
ENGI 241 LABORATORY EXERCISE 3 NETWORK THEOREMS
MAXIMUM POWER TRANSFER THEOREM
14. For the circuit in Figure 3−3, use Data Table 3−3. Measure and
record the values for all the resistors in Table 3−3.
15. Calculate VTH and RTH for the circuit of Figure 3−3 when VS is
+15V and R1 is 1kΩ. Record these values in Table 3−3.
16. For each value of RL in Table 3−3, calculate and record VL and PL.
17. Build the circuit of Figure 3−3. VS is +15V and RL is 470Ω.
Measure VL and record in Table 4−2. Based in the measured value
FIGURE 3−3
for VL, calculate PL and record as the measured value in Table 3−3.
In your discussion, compare the measured and calculated values.
18. Repeat steps 16 and 17 for all remaining resistors in Table 3−3.
19. On rectangular coordinate graph paper, plot the measured values of PL vs the measured values of
RL. In your report, discuss if the Maximum Power Transfer Theorem is verified.
Calculated
VTH
RTH
Rated
Measured
RL
RL
470 Ω
560 Ω
1kΩ
1.2kΩ
1.5kΩ
2.2kΩ
TABLE 3-3
Page 5
Calculated
VL
VL2
RL
Measured
VL
VL2
RL