Maximum Power Transfer

Maximum Power Transfer
ECGR 2156 Logic and Networks Laboratory
UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE
Department of Electrical and Computer Engineering
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
OBJECTIVES
In this experiment the student will investigate the circuit requirements for the transfer of
maximum power from the power source to the load in DC circuits with only real impedances.
MATERIALS/EQUIPMENT NEEDED
DC Voltage Source (capable of 10 Vdc)
Resistors: 100Ω, 1kΩ, 10kΩ, 100kΩ
Decade Resistor Box
Multimeter
INTRODUCTION
The circuit shown in Figure 1-1 uses an ideal voltage source in series with a sourcing resistance
to approximate a practical voltage source in which the terminal voltage drops with increasing
load current. In a resistive circuit like this, the resistive load receives maximum power when the
load resistance is equal to the source resistance (R L =R S ). The maximum power can be calculated
using the expression
pmax =
Vs2
4 Rs
The laboratory experiment will verify, for several sourcing resistors, that maximum power
transfer is achieved when the load resistance is selected as established above.
Rs
10VDC
RL
Figure 1-1 Lab circuit setup
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
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ECGR 2156 Logic and Networks Laboratory
PRELAB
1. For the circuit shown in Figure 1-1, determine the theoretical value of the load voltage and
load power for a 100Ω source resistance and load resistances in Table 1-1.
2. For the circuit shown in Figure 1-1, determine the theoretical value of the load voltage and
load power for a 1kΩ source resistance and load resistances in Table 1-2.
3. For the circuit shown in Figure 1-1, determine the theoretical value of the load voltage and
load power for a 10kΩ source resistance and load resistances in Table 1-3.
4. For the circuit shown in Figure 1-1, determine the theoretical value of the load voltage and
load power for a 100kΩ source resistance and load resistances in Table 1-4.
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
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ECGR 2156 Logic and Networks Laboratory
PROCEDURE
1. Construct the circuit shown in Figure 1-1 using a variable voltage source, a fixed resistor for
the sourcing resistance and a decade box for the load resistance.
2. Be careful that your voltage source is set to a value that will not cause the power ratings of
the selected sourcing resistor or the decade box to be exceeded.
3. Additionally, the selected decade box must cover the range of values presented in Tables 1-1
to 1-4 so the plot of power vs. load resistance will show a clear maximum.
4. To determine load power, measure the load voltage and calculate the load power. Complete
these measurements and calculations for sourcing resistances of 100Ω, 1kΩ, 10kΩ, and
100kΩ. Record your results in the tables.
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
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ECGR 2156 Logic and Networks Laboratory
DATA/OBSERVATIONS
Table 1-1: Values for 100 Ω Source Resistance and Variable Load Resistance
Theoretical
RS
RL
100 Ω
10
VL
Measurements
VL
PL =
(V L )2/R L
PL =
(V L )2/R L
50
75
90
95
100
105
110
125
500
1K
5K
10K
50K
75K
100K
INSTRUCTOR'S INITIALS:
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
DATE:
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ECGR 2156 Logic and Networks Laboratory
Table 1-2: Values for 1K Ω Source Resistance and Variable Load Resistance
Theoretical
RS
RL
1K Ω
10
VL
Measured
VL
PL =
(V L )2/R L
PL =
(V L )2/R L
50
100
500
900
950
975
1K
1.25K
1.5K
1.75K
5K
10K
50K
75K
100K
INSTRUCTOR'S INITIALS:
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
DATE:
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ECGR 2156 Logic and Networks Laboratory
Table 1-3: Values for 10K Ω Source Resistance and Variable Load Resistance
Theoretical
RS
RL
10K Ω
10
VL
Measured
VL
PL =
(V L )2/R L
PL =
(V L )2/R L
50
100
500
1K
5K
7K
9K
9.5K
9.75K
10K
10.25K
10.5K
11K
12K
25K
50K
75K
100K
INSTRUCTOR'S INITIALS:
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
DATE:
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ECGR 2156 Logic and Networks Laboratory
Table 1-4: Values for 100K Ω Source Resistance and Variable Load Resistance
Theoretical
RS
RL
100K Ω
10
VL
Measurement
VL
PL =
(V L )2/R L
PL =
(V L )2/R L
50
100
500
1K
5K
10K
50K
75K
90K
95K
97K
99K
100K
101K
103K
105K
110K
INSTRUCTOR'S INITIALS:
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
DATE:
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ECGR 2156 Logic and Networks Laboratory
POST-LAB
Post-Lab questions must be answered in each experiment’s laboratory report.
1. Create Table 1-5 in Excel or similar software for import into your write-up. Use the values
from the Pre-Lab to calculate theoretical maximum power.
% error =
meas − theo
×100
theo
Table 1-5: Maximum Power Transfer for Source Resistors
Source
Resistance
RS
Load
Resistance
Measured
Load
Voltage
VL
RL
Maximum
Power
Maximum
Power
(Measured)
(Theoretical)
PL
=(V L )2/R L
P=(V S )2/4R S
Percent
Error
100 Ω
1000 Ω
10K Ω
100K Ω
2. For each of the four sourcing resistors, create a plot of output power vs. load resistance.
Format axis to show bell curve.
3. Explain how resistor tolerances can cause errors in the experimentally determined maximum
power.
Be sure to include all items from the post-lab exercise above in your written lab report.
EXPERIMENT 1 – MAXIMUM POWER TRANSFER
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