Description
I would like to have a lab report for this experiment. All the instructions and lab data are attached. No need for a methodology section in the report.
Unformatted Attachment Preview
ELEC 201
Lab 05 – Thevenin Equivalent Circuit
1
LAB 5: Thévenin Equivalent Circuits
OBJECTIVES
After completing this lab, you should be able to do the following:
• Explain the idea of a Thévenin equivalent circuit and its usefulness for circuit analysis.
• Replace an unknown linear electrical network with its Thévenin equivalent.
• Demonstrate two experimental methods for determining the Thévenin equivalent circuit of
a resistive network.
• Experimentally demonstrate the maximum power transfer theorem.
• Correctly combine power supplies to provide DC power to a circuit.
• Use a decade resistor box appropriately.
INTRODUCTION
Replacing a complicated circuit by its electrical equivalent is a powerful tool used in electrical
engineering. We already used this idea when we replaced resistor combinations with an equivalent
resistance. Thévenin’s theorem provides a means of reducing a complicated linear network into
an equivalent circuit when there are two terminals of special interest (a and b in Figure 1). This
equivalent Thévenin circuit is composed of a voltage source and a resistor in series. If either the
original network or its Thévenin equivalent is connected to another electrical network, the response
(i.e. voltage and current) at the terminals a and b will be identical. In other words, one could not
tell the difference between the original network and its Thévenin equivalent.
Circuit with
• dependent sources
• independent
sources
• resistors
• linear elements
a
a
Rth
Vth
+
–
b
b
Figure 1 – Replacing a “Black Box Circuit” with its Thévenin Equivalent
To determine the Thévenin equivalent of a linear electrical network, we need the value of the
voltage source, VTh, and the resistor, RTh. (Note that since RTh appears at the output of the circuit,
it is sometimes called the output resistance, Rout.) VTh can be determined by measuring the voltage
at the terminals of the network when the terminals are open-circuited (no load connected).
Determining the Thévenin resistance value is more difficult.
If the terminals of the network are shorted together and the current measured through the short,
the Thévenin resistance can be determined as:
Open – Circuit Voltage Voc VTh
.
=
=
Short – Circuit Current I sc I N
______________________________________________________________________________
ThéveninResistance= RTh =
Based on a lab by Dr. T. Schubert and adopted from Dr. S. Lord
1
ELEC 201
Lab 05 – Thevenin Equivalent Circuit
2
However, sometimes it is not possible to measure either the open-circuit voltage and/or the shortcircuit current without damaging the original circuit. Hence, one can plot the terminal voltage
(Vab) vs. current (Iab = Iload) with varying load resistances and use this to determine RTh and VTh.
PROCEDURE
Obtain a black box from your instructor. This box contains a circuit whose parameters you will
determine analytically. Note that you do NOT need to know what is inside to do the analysis.
YOUR TASK: Determine the Thévenin equivalent circuit for what is inside the black box.
Connect +28V to the + Input Terminal (orange) and ground to the Grd Input Terminal (black).
A. Modeling the “Black Box” (Experimental Determination of VTh and RTh (Rout))
Method 1 (can only be used if it is safe to short circuit the output)
• Measure the open-circuit voltage between the two output terminals (yellow and black) with a
DMM.
• Measure the short-circuit current between the two output terminals.
• Determine the experimental Thévenin equivalent circuit for your black box.
Method 2 (always safe to use)
• Connect a decade resistor between the two output terminals. Note that the decade resistor is
acting as a load.
• For several values of the load resistance, determine the load voltage, VL, and the load current,
Iload. Plot the load voltage as a function of the load current.
• Extrapolate your graph to obtain the open-circuit voltage and short-circuit current. Compute
the Thévenin equivalent circuit.
• Compare this Thévenin equivalent circuit to that obtained using the method of Part A.
• Calculate the slope of your V-I curve. What is the significance of this value?
• Plot the power dissipated in the load as a function of load resistance. At what value of load
resistance is the load power maximum (i.e. maximum power transfer)? How does this
compare to Rth?
B. What’s inside the “Black Box”?
• Draw a circuit diagram for what you think is inside your black box.
• Now draw another circuit diagram for another possible circuit that would have the same
Thévenin equivalent circuit as the one in your black box.
• Explain these circuits to your instructor.
______________________________________________________________________________
Based on a lab by Dr. T. Schubert and adopted from Dr. S. Lord
2
Part A:
Voltage (volts): Current (mA)
Open-Circuit:
17.94
–
Short-Circuit:
–
14.85
Thévenin Equivalent Circuit:
1.208080808 (ohms)
(R=V/I)
Vth =17.94
V
+
–
R (ohms):
V(load): (volts) I (load): (mA)
50
0.728
14.2
250
3.1
12.271
500
5.26
10.48
750
6.87
9.09
1000
8.11
8.078
2500
11.77
5.46
5000
14.45
2.86
7500
15.45
2.04
10000
15.98
1.59
20000
16.9
0.84
30000
17.23
0.57
40000
17.39
0.43
50000
17.49
0.35
Vth = 17.9 V
Isc = 14.79 mA
Power Max: 65.51w at 1000ohms
Power (watts) vs. R
70
60
Power (watts)
Rth = 1.2 ohms
50
40
30
20
10
0
0
20000
Power (watts)
Load voltage (v) as function of load current (mA)
10.3376
20
38.0401
18
55.1248
16
65.51258
14
64.2642
41.327
31.518
25.4082
14.196
V(load) (volts)
62.4483
9.8211
12
10
Series1
8
Linear (Series1)
6
7.4777
4
6.1215
2
y = -1.2093x + 17.944
0
0
5
10
I (load) (mA)
w at 1000ohms
Power (watts) vs. R (ohms):
Series1
20000
40000
R (ohms):
60000
15
Linear (Series1)
Purchase answer to see full
attachment
