Download EXPERIMENT 4 THEVENIN AND NORTON EQUIVALENT CIRCUITS

EE209 Circuit Laboratory I
2016-2017
EXPERIMENT 4
THEVENIN AND NORTON EQUIVALENT CIRCUITS
4.1 Objective
The objective of this experiment is to study Thevenin's and Norton's theorems and their
application in circuit analysis.
4.2 Equipment List
1.
2.
3.
4.
5.
Function/Arbitrary Waveform Generator (AATech AWG 1020A)
Multi-meters
Breadboard
Resistors: 1.2 k, 1.8 k, 2.7 k, 4.7 k, 5.6 k, 2x10 k
Potentiometer: 10 k
4.3 Preliminary Work
1. Research the intended purpose of Thevenin’s and Norton’s theorems.
2. Research how Thevenin voltage and Norton current can be determined in a circuit.
3. Construct the Figure 4.1 on any of circuit design programs (PSpice, Multisim, etc.).
Follow the experiment steps (from 1 to 10) on the circuit design program you have
chosen and note the observed results to your pre-lab report which will be submitted.
4.4 Theory
Thevenin’s Theorem
Thevenin’s Theorem is a very powerful tool for simplifying a linear two-terminal
network of fixed resistances and voltage sources by replacing the network with a single
voltage source in series with single resistor. When the circuit is simplified, the single voltage
source is called the Thevenin voltage source (providing Thevenin voltage (VT)) and VT is
equal to the open circuit voltage (VOC) at the terminals (a-b) of the original network. The
single resistor is called the Thevenin resistance (RTH) and is equal to the open circuit voltage
(VOC) at the terminals divided by the short circuit current (ISC) between the terminals of the
original network.
Therefore,
VTH = VOC
and
RTH=VOC/ISC
The short circuit current (ISC) is measured by connecting an ampermeter between the
terminals (a-b) of the original network and recording the current reading. The short circuit
current (ISC) is calculated by drawing a short between the terminals of the original network
and calculating the current in the short.
EE209 Circuit Laboratory I
2016-2017
An alternate method of determining the Thevenin resistance (RTH) is by replacing all
voltage sources with a short circuit and all current sources with an open in the original
network and determining the equivalent resistance is equal to the Thevenin resistance (RTH).
The strength of the Thevenin theorem lies in the fact that, although the Thevenin
equivalent circuit is not the original circuit, it acts like the original circuit in terms of the
voltage and current at the terminals.
Norton’s Theorem
Norton’s Theorem states that any linear two-terminal network of fixed resistances and
voltage sources may be replaced with a single current source in parallel with a single resistor.
The single current source is called the Norton current source (providing Norton current (IN))
and IN is equal to the short circuit current (ISC) between the terminals of the original network.
The single resistor is called the Norton resistance (RN) and is equal to the Thevenin resistance
in the Thevenin equivalent circuit. It is found by following the same procedure that was used
to find Thevenin resistance (RTH).
When a resistance RLoad is connected between the terminals a-b of the original
network, the voltage across the terminals (VAB) will be the same as the voltage across the
terminals of the Thevenin equivalent circuit if the same value resistance (RLoad) is connected
across the terminals of Thevenin equivalent circuit. The same statement can be made for the
Norton equivalent circuit.
4.5 Experimental Work
1. Set up the circuit in Fig. 4.1:
R1 = 1.2 k Ω
R2 = 10 k Ω
R3 = 5.6 k Ω
R4 = 10 k Ω
R5 = 2.7 k Ω
R6= 4.7 k Ω
Rload = 1.8 k Ω
VS1 =10 V
VS2 = 6V
Figure 4.1. Linear Circuit to Study Thevenin and Norton
2. Measure the current (IL ), through RLoad and the voltage (VL ), across RLoad.
3. Find the Thevenin equivalent circuit seen by RLoad (i.e. the equivalent circuit between
nodes A & B, with RLoad removed from the circuit). To get the equivalent circuit,
follow these steps:
EE209 Circuit Laboratory I
2016-2017
a. Remove RLoad from the circuit.
b. Measure VAB (open circuit voltage = Thevenin Voltage = VT ).
c. Set all the voltage sources to zero volts, and use the ohmmeter to measure the
equivalent resistance between nodes A & B (This is the Thevenin Resistance=RT).
d. Can RT be determined using only the measurements in (2) and (3b)? How?
4. Find the Norton equivalent circuit seen by RLoad. For this part, DO NOT physically
apply a short to measure ISC =IN . Instead, use the load line method to measure ISC =IN.
This works as follows:
a. Set the potentiometer to the original load value and connect it between nodes
A&B.
b. Vary the potentiometer, and measure the voltage (VP) across it, and the current (IP)
through it.
c. Obtain five data points (preferably having uniform voltage spacing between them)
and plot VP vs. IP.
d. From the plot in (c), find IN , VT , and RT . Or, you can measure IP and RP instead
of IP and VP. This can be easier to handle in lab. Why?
5. Compare the results from part (4) to the results from part (3).
6. Set VS1 to zero, and measure the Thevenin equivalent voltage (VT1 ) seen by RLoad.
7. Set VS2 to zero (restore VS1) and measure VT2.
8. What is the relationship between VT1 , VT2 , and VT . Why?
9. Set up the circuit in Fig. 3.4, and measure the voltage VRL , and the current IRL .(Use
the values measured in step 3 for VT and RT ).
10. Compare VRL and IRL to those measured in step 2.
Figure 3.4
4.6 Post Lab Questions
1.
2.
3.
4.
Discuss your results and compare ALL your lab data to the calculated results.
Explain any deviations that you found.
Comment on Thevenin and Norton equivalent circuits.
Discuss the superposition theorem. Why does it work?