Nodal Analysis Lab
Name _______________________________________ Section __________________
Prelab (Must be completed before lab.)
Nodal analysis is a method of solving for the node voltages in a circuit. A node voltage is the
voltage of a node with respect to ground. In other words, it is the voltage between that node and
ground. Nodal analysis can be used even when all other circuit solution methods will not work.
Once node voltages are found, the voltages across each circuit element are found easily.
1.
Use nodal analysis to calculate the node voltages V1 and V2 in Figure 1. Record to
datasheet.
2.
Use nodal analysis to calculate the node voltages V1, V2, and V3 in Figure 2. Record to
datasheet.
3.
Use a MULTISIM simulation to find the node voltages V1 and V2 in Figure 1. Include a
printoff of your simulation circuit. Record values to datasheet.
4.
Use a MULTISIM simulation to find the node voltages V1, V2, and V3 in Figure 2.
Include a printoff of your simulation circuit. Record values to datasheet. Note: most circuit
simulation software does not like two voltage sources connected together directly, as in
Figure 2. Most circuit simulators use nodal analysis at their core and ideal voltage sources
have an indeterminate current through them, subject only to the nature of the circuit to
which they are connected. You can fool the software by connecting the voltage sources
together using a VERY small resistor, on the order of 1 milliohm. This value is small
enough to not perturb the simulation but large enough to be non-zero.
5.
Compare your simulation results with your calculated values for both circuits.
R1
11k
R2
V1
R3
2
1
6.2k
3
V2
9.1k
V1
DC = 7.5V
R4
3k
R5
1.1k
0
Figure 1
1
R1
2
V1
5.1K
R4
2k
DC = 5V
R2
3
V2
0
R6
20K
6.2K
R5
9.1K
DC = 8V
4
R3
4.7K
5
V3
Figure 2
Lab Session A
Measure the actual values for the resistors in Figure 1, and record them in the Data Sheet.
Use these values to calculate the nodal voltages V1 and V2. Use the Multimeter to measure V1
and V2 for this circuit.
Compare your measured values with your calculated values. Explain any discrepancies.
Use your measured node voltages to calculate the voltage drops across each resistor. See Figure
3.
Figure 3
Lab Session B
Measure the actual values for the resistors for the circuit of Figure 2, and use these to calculate
the nodal voltages. Use the Multimeter to measure V1, V2 and V3 for this circuit.
Compare your measured values with your calculated values. Explain any discrepancies.
Calculate the resistor voltage drops using the measured nodal voltages. See Figure 3.
Figure 4
Now, we will measure the node voltages, using the superposition principle. Zero the 8V power
supply by setting it to 0V. Measure the voltages V1’, V2’ and V3’ in Figure 5 and record these
into the data sheet.
R1
V1'
1
5.1K
DC = 5V
R4
2k
R2
V2'
0
6.2K
R5
9.1K
R3
4.7K
Figure 5
Now, measure the voltages V1”, V2” and V3” in Figure 6.
V3'
R6
20K
R1
V1''
1
5.1K
R4
2k
R2
V2''
0
R6
20K
6.2K
R5
9.1K
DC = 8V
R3
4.7K
V3''
Figure 6
The superposition principle states that the system response to all sources can be determined by
summing the systems response to each source acting alone, with all other sources “zeroed.” This
strategy only works for linear systems. Calculate the node voltages V1, V2, V3, by zeroing all
but one source and calculating V1, V2, and V3. Repeat this process until all sources have had
been accounted for and then sum each response. Remember that you must be consistent in your
choices of polarity.
Compare the superposition results to the measurement results. Is there any difference?
Post lab
1.
Can
these
circuits
be
solved
by
2.
What was the easiest/hardest part of this lab?
other
Hand in:
•
•
•
•
•
•
Datasheet
Prelab calculations
Prelab simulations
Lab calculations
Answered questions from prelab, lab and postlab.
NO LAB REPORT required for this lab.
methods
than
nodal
analysis?
Datasheet: Nodal Analysis Lab
Name: _______________________
Section: _________________________
Prelab
Fig 1 Calculated:
V1 _______________ V2 _______________
Fig 2 Calculated:
V1 _______________ V2 _______________ V3 _______________
Fig 1 Simulated:
V1 _______________ V2 _______________
Fig 2 Simulated:
V1 _______________ V2 _______________ V3 _______________
Lab Session A
Actual Resistor
Values:
Resistor voltages:
Calculated node voltages:
V1: ____________
R1:____________ VR1:____________
R2:____________ VR2:____________
R3:____________ VR3:____________
R4:____________ VR4:____________
V2: ____________
Measured node voltages:
V1: ____________
V2: ____________
R5:____________ VR5:____________
Lab Session B
Actual Resistor
Values:
Resistor voltages:
R1:____________ VR1:____________
R2:____________ VR2:____________
R3:____________ VR3:____________
R4:____________ VR4:____________
R5:____________ VR5:____________
R6:____________ VR6:____________
Calculated node voltages:
V1: __________ V2: __________ V3: __________
Measured node voltages:
V1: __________ V2: __________ V3: __________
Superposition:
V1’: _________ V2’: _________ V3’: _________
V1”: _________ V2”: _________ V3”: _________
V1: __________ V2: __________ V3: _________