Node & Mesh AnalysisNode & Mesh Analysis

OutlineOutline Nodal AnalysisNodal Analysis

• Define a symbol for all unknown node voltages.Define a symbol for all unknown node voltages.• Write KCL at each node where variables occurWrite KCL at each node where variables occur• Using Ohm’s Law, solve resulting equations.Using Ohm’s Law, solve resulting equations.

Mesh CurrentsMesh Currents• Set up the currentsSet up the currents• Use KVLUse KVL

Methods to solve linear equationsMethods to solve linear equations• SubstitutionSubstitution• DeterminantsDeterminants• CalculatorCalculator• Method from Numerical MethodsMethod from Numerical Methods

Node analysis:Node analysis: Node analysis is more powerful method than Node analysis is more powerful method than

mesh analysis.mesh analysis.

This method is based on the application of KCL on This method is based on the application of KCL on different nodes of the circuit.different nodes of the circuit.

In this metode,instead of assuming the mesh In this metode,instead of assuming the mesh current,we assume node volteges with respect to current,we assume node volteges with respect to some reference node and write KCL equations for some reference node and write KCL equations for all the nodes.all the nodes.

Definition of node:Definition of node: The point at which two or more elements are connected The point at which two or more elements are connected

together is called node.together is called node. Two types of nodeTwo types of node1. Principal node:1. Principal node:o If three or more elements are common to a node,that node If three or more elements are common to a node,that node

is called principle node. is called principle node. 2. Reference node: 2. Reference node: o The node , we assume to zero potential is called reference The node , we assume to zero potential is called reference

node. node.

stepssteps Step 1 : identify a reference node .Step 1 : identify a reference node .

Step 2 : “kill” sources and identify independent nodes.Step 2 : “kill” sources and identify independent nodes.

Step 3 : replace sources and label “ constrained “ voltages .Step 3 : replace sources and label “ constrained “ voltages .

Step 4 : apply KCL at each independent node .Step 4 : apply KCL at each independent node .

step 5 : use ohms law to write the KCL equations in trems of step 5 : use ohms law to write the KCL equations in trems of node voltages .node voltages .

Step 6 : solve the system of equations to determine the Step 6 : solve the system of equations to determine the node voltages .node voltages .

Nodal Analysis Example 1Nodal Analysis Example 1Find all voltages and currents.

Nodal Analysis Example 2Nodal Analysis Example 2Find Vo

+ Vo -

Mesh analysisMesh analysis

Definition of mesh Definition of mesh “ “Mesh is defined as a loop which is not contain any other Mesh is defined as a loop which is not contain any other

loops with in it .”loops with in it .”

Mesh analysis is important techniques which are useful to Mesh analysis is important techniques which are useful to find solution of network.find solution of network.

If network has large number of voltage sources , it is useful If network has large number of voltage sources , it is useful to use mesh analysis.to use mesh analysis.

Sign:Sign:

+ve sign :+ve sign : Both current pass through common Both current pass through common

resistance in the same direction. resistance in the same direction.

-ve sign:-ve sign: Both the current pass through the Both the current pass through the

common resistance in opposite common resistance in opposite direction.direction.

Mesh CurrentsMesh Currents Steps:Steps:

• Label each unknown current in each mesh, going Label each unknown current in each mesh, going clockwise.clockwise.

A mesh is a loop which does not contain any other loops A mesh is a loop which does not contain any other loops within it.within it.

Also, write down the polarities of the currents as they go Also, write down the polarities of the currents as they go through each resistor.through each resistor.

• Write KVL equations for each mesh. In this case, use Write KVL equations for each mesh. In this case, use V=I*R. When resistors are in both meshes, I=(IV=I*R. When resistors are in both meshes, I=(I11-I-I22).).

• Use Ohm’s Law to express the voltages in terms of the Use Ohm’s Law to express the voltages in terms of the mesh currents.mesh currents.

• Again, you may need extra equations if there are other Again, you may need extra equations if there are other current/voltage sources.current/voltage sources.

• Solve for the unknown currents.Solve for the unknown currents.

Mesh Current Example - 1Mesh Current Example - 1Calculate the mesh currents.

Mesh Current Example - 2Mesh Current Example - 2Find the current through the 1 ohm R

Methods of Solving Sets of Methods of Solving Sets of EquationsEquations

CalculatorCalculator• rref functionrref function• solve functionsolve function

Linear AlgebraLinear Algebra SubstitutionSubstitution GraphingGraphing Euclid’s MethodEuclid’s Method

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