Chapter 4-1
•Terminology and rules
•Node Voltage
•Review Matrix
representation of a systems
of equations
Planar circuit: a circuit that can be drawn on a plane with
no crossing branches
Identify essential nodes and meshes
Need n equations to solve for n unknowns
Let be represent number of essential branches
Let ne represent number of essential nodes
Node-Voltage method: allows us to solve a circuit
using
(ne – 1) equations
Mesh-Current method: allows us to solve a circuit
using
be – (ne -1) equations
Node-Voltage method
1. Draw circuit with no branches crossing
Node-Voltage method
2. Count the number of essential nodes (ne ), you will need
(ne -1) equations to describe the circuit,
Node-Voltage method
3. This circuit has three essential nodes
4. Choose one as a reference node, typically the node with the
most branches
5. Assign remaining essential nodes with node voltages, in this
case, nodes 1 and 2.
A Node Voltage is defined as the voltage rise from the reference node to a
non-reference node
6. Label the nodes and label currents as leaving the nodes, one node at a time
apply KCL, using ohms law to write in terms of voltages summed to zero at the
node
7. Repeat step 6 for the other nodes
𝑣𝑎 − 10 𝑣𝑎 𝑣𝑎 − 𝑣𝑏
+ +
=0
1
5
2
𝑣𝑏 − 𝑣𝑎 𝑣𝑏
+
−2=0
2
10
Things to remember: work on one node at a time.
Define currents as leaving the node, based on node voltage definition
If a current exist in the circuit that enters the node, it is assigned a minus sign
Matrix representation for a system of equations
2𝑖1 + 3𝑖2 = 6
2𝑖1 + 2𝑖2 = 10
𝑖1 + 2𝑖2 − 3𝑖3 = 4
2𝑖1 − 𝑖2 + 2𝑖3 = 3
𝑖1 + 𝑖2 + 𝑖3 = 6
You Do
𝑖1 − 3𝑖3 = 4 − 2𝑖2
2𝑖1 − 𝑖2 + 3 = 0
𝑖3 = 6 − (𝑖1 + 𝑖2 )
1
1
2
1 0
3 2
2 1
𝑖1
2
𝑖2 = 4
𝑖3
1
Find 𝑖2
CoolMath.com
What you should know
1.
2.
3.
Basic circuit definitions required for node-voltage
method.
Application of node-voltage
Have a method to solve a system of equations