ECE 211 Electrical Circuits Lab I
LAB #6
Name
Section
Circuit Analysis Using Node Voltage Method
OBJECTIVE:
1. Solve a circuit using nodal analysis.
COMPONENTS AND EQUIPMENT:
1. Variable DC supply
2. Digital multimeters (2)
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 point. The reference point is a node which is
defined as having zero voltage. The ground node should be chosen carefully for convenience. Note that
the reference 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 reference node will be 5 Volts.
Nodal Analysis
Nodal analysis is a formalized procedure based on KCL equations.
Steps:
1.
2.
3.
Identify all nodes.
Choose a reference node. Identify it with reference 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).
Assign voltage variables to the other nodes (these are node voltages.)
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ECE 211 Electrical Circuits Lab I
LAB #6
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.
The solution can be obtained by applying KCL at node 1(the only non-reference
essential node) in terms of the voltage of that node, as follows:
−9
+
+
=0
1
3
4
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ECE 211 Electrical Circuits Lab I
LAB #6
PROCEDURE:
Experiment 1:
1. Connect the circuit as shown in Figure 1
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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 V1. Compare between the calculated and measured values.
4. Measure the values of Ia, Ib, Ic. Compare the calculated and measured values.
Does Ia = Ib + Ic?
5.
Calculate the measured value error % for Ia, Ib, Ic and V1.
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ECE 211 Electrical Circuits Lab I
LAB #6
Experiment 2:
a
b
c
Figure 2 - Circuit #2
1. Connect the circuit as shown in Figure 2
2. Pick different resistors value for Ra, Rb, R c and Rd. Choose these resistors at random.
Record the resistor values.
3. Calculate Ia, Ib, Ic, and Id.
4. Measure the values of Ia, Ib, Ic, Id, Va, Vb, and Vc. Then compare with calculated.
5. Find error % of Ia, Ib, Ic, and Id.
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ECE 211 Electrical Circuits Lab I
LAB #6
REPORT: (solve it during the Lab)
Repeat the calculations of Circuit #2 (by applying the Node Voltage Method), but
with the reference node moved to the node (b).
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