ECE 211 Electrical Circuits Lab I
LAB #6
Fall 2014
Name ___________________
Section ______________
Node-Voltage Analysis
OBJECTIVE:
1. Solve a circuit using nodal analysis.
COMPONENTS AND EQUIPMENT:
1. Variable DC supply
2. Digital multimeter
3. Leads
4. Resistors of various values
THEORY
Nodes
A node is a section of a circuit which connects components to each other. All of the current entering a
node must leave a node, according to Kirchoff's Current Law(KCL). Every point on the node is at the
same voltage; no matter how close it is to each component, because the connections between
components regarded as perfect conductors. This voltage is called the node voltage, and is the voltage
difference between the node and an arbitrary reference, the ground point. The ground point is a node
which is defined as having zero voltage. The ground node should be chosen carefully for convenience.
Note that the ground node does not necessarily represent an actual connection to ground. For example,
if a node has a voltage of 5 Volts, then the voltage drop between that node and the ground node will be
5 Volts.
Nodal Analysis
Nodal analysis is a formalized procedure based on KCL equations.
Steps:
1. Identify all nodes.
2. Choose a reference node. Identify it with reference (ground) symbol. A good choice is the node
with the most branches, or a node which can immediately give you another node voltage (e.g.,
below a voltage source).
3. Assign voltage variables to the other nodes (these are node voltages.)
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ECE 211 Electrical Circuits Lab I
LAB #6
Fall 2014
4. Write a KCL equation for each node (sum the currents leaving the node and set equal to zero).
Rearrange these equations into the form A*V1+B*V2=C (or similar for equations with more
voltage variables.)
5. Solve the system of equations from step 4. There are a number of techniques that can be used:
simple substitution, Cramer's rule, the adjoint matrix method, etc.
Example
Given the Circuit below, find the voltages at all nodes.
node 0:
node 1:
(defined as ground node)
(free node voltage)
node 2:
node 3:
which results in the following system of linear equations:
therefore, the solution is:
Another solution with KCL would be to solve node in terms of node 2;
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ECE 211 Electrical Circuits Lab I
LAB #6
Fall 2014
PROCEDURE:
1. Connect the circuit as shown in Figure 1
Figure 1 - Circuit #1
2. Pick different resistors value for Ra, Rb, and Rc. Choose these resistors at random. Record
the resistor values. Then calculate Ia, Ib, Ic.
3. Measure and record the values of Ia, Ib, Ic, Va, Vb, and Vc. Make a table for the calculated
and recorded value
4.
Calculate the measured value error % for Ia, Ib, and Ic
5. Does Ia = Ib + Ic ? Measure V1.
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ECE 211 Electrical Circuits Lab I
LAB #6
Fall 2014
Figure 2 - Circuit #2
6. Connect the circuit as shown in Figure 2
7. Calculate Ia, Ib, Ic, and Id.
8. Record the values of Ia, Ib, Ic, Id, Va, Vb, Vc, and Vd. Record resistor values.
9. Find error % of Ia, Ib, Ic, and Id.
10. Measure V1 . Does Ib + Ic = Id?
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ECE 211 Electrical Circuits Lab I
LAB #6
Fall 2014
REPORT:
1. Calculate V1 and then Ia, Ib, Ic, Va, Vb, and Vc in the circuits shown in Figure 1 using nodal
analysis. Show all work.
2. Calculate Ia, Ib, Ic, Va, Vb, Vc and Vd in the circuits shown in Figure 2 using nodal analysis.
Show all work.
3. Compare between the measured and calculated values for both circuits.
4. Repeat the measurements calculation of Circuit #2, but with the reference node moved to
the node N1.
5. Is there a difference in Va, Vb, Vc, and Vc? If so, write down the new value for each voltage.
6. Write a conclusion for this experiment.
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