UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE
Department of Electrical and Computer Engineering
Experiment No. 9 - Thevenin and Norton Circuits
Overview:
This lab will use Thevenin and Norton Theorems to calculate the current through (or voltage
across) any one of several resistors in a circuit, and verify the results by measurement. The
student will develop the Thevenin constant voltage and Norton constant current equivalent
circuits, and verify their validity by measurement.
Thevenin’s Theorem
Thevenin’s Theorem can be used for two purposes:
1. to calculate the current through (or voltage across) a component in any circuit, or
2. to develop a constant voltage equivalent circuit which may be used to simplify the analysis of
a complex circuit.
Any combination of sources and resistances with two terminals can be replaced by the series
combination of a single voltage source e and a single resistor r. The value of e (the Thevenin
voltage) is the open circuit voltage at the output terminals, and the value of r (the Thevenin
resistance) is the equivalent resistance looking back into the network at the output terminals with
all voltage sources replaced by a short and all current sources replaced by an open.
Figure 1. A circuit converted to its Thevenin equivalent
In Figure 2 a particular driving circuit with output terminals a and b has been replaced by its
Thevenin equivalent circuit, consisting of a Thevenin voltage source Eth in series with the
Thevenin resistance Rth.
Figure 2. Thevenin equivalent circuit
To find and apply the Thevenin equivalent circuit, follow the steps below:
Step 1
Remove the resistor R (often referred to as the load resistor) for which you wish to
calculate the current and/or voltage. Label these terminals (where the resistor was
removed) “a” and “b”. Calculate the voltage across these open terminals. This is
Eth.
Step 2
From the open terminals, (“a” and “b”) calculate the resistance “looking back” into
the circuit with all voltage sources removed and replaced by a short and all current
sources removed and replaced by an open. This is done because the internal
resistance of an ideal voltage source is zero and the internal resistance of an ideal
current source is infinite. The resistance so obtained is Rth.
Step 3
Now, the current through R is: I = Eth/( Rth + R), and
the voltage across R is: VR = REth /( Rth + R).
Norton’s Theorem
Norton’s Theorem can be used for two purposes:
1. to calculate the voltage across (or current through) a component in any circuit, or
2. to develop a constant current equivalent circuit which may be used to simplify the analysis of
a complex circuit.
Any combination of sources and resistances with two terminals can be replaced by the parallel
combination of a single current source i and a single resistor r. The value of i (the Norton
current) is the short circuit current at the output terminals, and the value of r (the Norton
resistance) is the equivalent resistance looking back into the network from the output terminals
with all voltage sources replaced by a short and all current sources replaced by an open. It should
be clear that the Norton and Thevenin resistances are defined in the same manner. In fact, for the
same network they will always have the same value.
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Figure 3. A circuit converted to its Norton equivalent
In Figure 4 a particular driving circuit with output terminals a and b has been replaced by its
Norton equivalent circuit, consisting of a Norton current source In in parallel with the Norton
resistance Rn.
Figure 4. Norton equivalent circuit
One method for finding the Norton equivalent circuit is to first find the Thevenin equivalent
current, and then, find the Norton current given by In = Eth/Rth and the Norton resistance which
is simply equal to Rth.
To find and apply the Norton equivalent circuit directly, follow the steps listed below:
Step 1
Remove the resistor R for which you desire to calculate the voltage and/or
current. Label these terminals “a” and “b”. Short these terminals together and
determine the current that flows through this short. This short circuit current is In.
Step 2
From the open terminals, (“a” and “b”) calculate the resistance “looking back”
into the circuit with all voltage sources removed and replaced by a short and all
current sources removed and replaced by an open. The resistance so obtained is
Rn .
Step 3
The current through R is: I = In Rn/(R + Rn), and
the voltage across R is: E = RIn Rn/(R + Rn).
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Pre Lab – Thevenin and Norton
Thevenin
1. In the circuit of Figure 5, the 3.3 k resistor of Figure 10 has been removed. Use the steps
of Thevenin’s theorem, previously given, to calculate Eth and Rth. Show all work in the space
provided.
Step 1: Determine Eth , the open circuit output voltage in Figure 5.
Eth = _______________________
R3 = 3.3 k
Figure 5. Circuit for Thevenin analysis with load resistor R3 removed.
Step 2: In Figure 5, replace the voltage source with a short and determine Rth.
Rth = _________________________
Using your calculated values for Eth and Rth, draw in the space below the Thevenin equivalent
circuit.
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Step 3: Using your Thevenin equivalent circuit, calculate the value of IR3.
IR3 =
ETh
= ________________
(RTh + R3 )
2. Use Thevenin’s theorem to find the current through R3 in the bridge circuit of Figure 6.
Do all of Thevenin’s Theorem steps showing all
calculations and diagrams, properly labeled.
Step 1: Solve for Eth____________________
Figure 6. Circuit for Thevenin calculation
Step 2: Solve for Rth____________________
Draw the Thevenin equivalent circuit:
Step 3: Calculate IR3 using the Thevenin equivalent circuit. IR3________________
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Norton
3. Use Norton’s theorem to determine In and Rn for the circuit of Figure 7.
Figure 7. Circuit for Norton analysis
Step 1: With R3 replaced by a short circuit, calculate (do not measure) the short-circuit
current In.
In = _____________________
Step 2: In Figure 8, with R3 removed and the 12V source replaced by a short circuit,
calculate Rn.
Rn = ___________________
Figure 8. Circuit of Figure 7 with R3 removed and the voltage source replaced by a short
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4. Determine In and Rn for the circuit Figure 6.
Step 1: With R3 removed and replaced by a short, calculate and record the current through
the short. This is In. Show all work.
In = _________________
Step 2: Referring to Figure 9, calculate and record Rn. Show all work.
Rn = _______________________
Figure 9. Circuit of Figure 6 with R3 removed and the voltage source replaced by a short
(INSTRUCTOR’S SIGNATURE_____________________________DATE
7
)
Lab Session— Thevenin and Norton
1. Show your pre-lab work to the instructor at the beginning of the lab session.
2. The purpose of this procedure is to experimentally determine Eth and Rth for the circuit
of Figure 5, and measure the current through and voltage across resistor R3. Calculated and
measured values will be compared.
a. Connect the circuit in Figure 10; measure and record the current through and
voltage across R3.
Figure 10. Circuit for Thevenin analysis
IR3 = __________
VR3 = ________
b. Verify Step 1 of Thevenin’s procedure by measurement: Connect the circuit of
Figure 10 with R3 removed; measure and record Eth (the voltage across open
terminals a and b).
Eth = ________
c. Verify Step 2 by measurement: Connect the circuit of Figure 10 with R3 removed
and the voltage source replaced by a short; measure and record Rth (the resistance
between terminals a and b).
Rth = __________
3. The purpose of this procedure is to compare currents and voltages generated by the
Thevenin equivalent circuit to those generated by the original circuit. Build the circuit of
Figure 6 using the Thevenin equivalent circuit determined in the pre-lab to replace the
network external to resistor R3. Obtain a resistor for Rth as close as possible to its
calculated value, or use a potentiometer whose value you may set equal to Rth.
a. Measure the current through and voltage across R3 in your Thevenin equivalent
circuit. Record these values.
IR3 = __________
VR3 = __________
INSTRUCTOR'
S INITIALS
DATE:
8
b. Connect the original circuit of Figure 6 (with all five resistors); measure the
current through and voltage across R3. Record these values.
IR3 = ________________
VR3 = ________________
NORTON
4. The purpose of this procedure is to experimentally determine In and Rn for the circuit of
Figure 7, and measure the current through and voltage across R3. Calculated and measured
values will be compared.
a. Connect the circuit in Figure 7; measure and record the current through and
voltage across R3.
IR3 = __________
VR3 = __________
Figure 11. Circuit for Norton analysis with R3 replaced by an ammeter
b. Verify Step 1 of Norton’s procedure by measurement: Connect the circuit of
Figure 11; be sure to use a current range higher than the calculated value of In.
This measurement provides the “short circuit” current or Norton current In.
Record this value.
In = ___________
c. Verify Step 2 of Norton’s procedure by measurement: Connect the circuit of
Figure 8, and use the DMM to measure the resistance between terminals a and b.
This is the measured value of Rn. Record this value.
Rn = __________
INSTRUCTOR'
S INITIALS
DATE:
9
5. In this procedure, the student will connect the bridge circuit of Figure 6, measure the
current through and voltage across R3, and determine the Norton values, In and Rn.
a. Record the measured values of IR3 and VR3.
IR3 = ________________ VR3 = ________________
b. Connect the circuit of Figure 6 with R3 replaced by the ammeter. Measure and
record In.
In = __________
c. With R3 removed and the voltage source replaced by a short measure and record
the value of Rn.
Rn = __________________
INSTRUCTOR'
S INITIALS
DATE:
10
Post Lab – Thevenin and Norton
1. Compare the value of the calculate current through resistor R3 in pre-lab procedure 3 with
its measured value in lab-session procedure 2a.
2. Compare the calculated values of Eth and Rth in pre-lab procedure 1 with the measured
values in lab-session procedures 2b and 2c.
3. Compare the measured values of current and voltage in lab-session procedure 3a with
those in lab-session procedure 3b.
4. Compare the calculated values of In and Rn in pre-lab procedure 5 with the measured
values in lab-session procedures 4b and 4c.
5. Use Norton’s Theorem and Ohm’s Law to calculate the voltage across R3 in the circuit of
Figure 7. Compare this value with its measured value in lab-session procedure 4a.
VR3 = I n
Rn R3
Rn + R3
6. Compare the calculated values of In and Rn in pre-lab procedure 6 with the measured
values in lab-session procedures 5b and 5c.
7. Be sure to comment on the differences observed between calculated and measured values
in steps 1 through 6 above. If significant differences (not explainable by resistor
tolerances and expected measurement errors) are observed, make your best effort to
explain.
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