1. Methods of Analysis Circuits 1 Fall 2005 Harding University Jonathan White

2. Outline Nodal Analysis Nodal 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 Currents Mesh Currents Set up the currentsSet up the currents Use KVLUse KVL Methods to solve linear equations Methods to solve linear equations SubstitutionSubstitution DeterminantsDeterminants CalculatorCalculator Method from Numerical MethodsMethod from Numerical Methods

3. Nodal Analysis Steps: Steps: Define a voltage at every node in the circuitDefine a voltage at every node in the circuit Note: Some may be known, such as the source and ground Note: Some may be known, such as the source and ground Write KCL at the nodes where the unknown voltages existWrite KCL at the nodes where the unknown voltages exist Now, plug into these KCL equations with the unknown voltages, remembering how Ohm’s Law works. In this case, I = (V H – V L )/R, because we are writing voltages for nodes, not just resistors. Since current flows from a higher potential to a lower potential, the voltage over a resistor that is connected to 2 nodes is just V H – V LNow, plug into these KCL equations with the unknown voltages, remembering how Ohm’s Law works. In this case, I = (V H – V L )/R, because we are writing voltages for nodes, not just resistors. Since current flows from a higher potential to a lower potential, the voltage over a resistor that is connected to 2 nodes is just V H – V L Other current and voltage sources must be factored in to either the KCL equations or the unknown voltages. They sometimes actually make the equations easier.Other current and voltage sources must be factored in to either the KCL equations or the unknown voltages. They sometimes actually make the equations easier. Solve for the unknown voltages.Solve for the unknown voltages.

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

5. Nodal Analysis Example 2 Find Vo + Vo -

6. Mesh Currents Steps: Steps: Label each unknown current in each mesh, going clockwise.Label each unknown current in each mesh, going clockwise. A mesh is a loop which does not contain any other loops within it. A mesh is a loop which does not contain any other loops within it. Also, write down the polarities of the currents as they go through each resistor. Also, write down the polarities of the currents as they go through each resistor. Write KVL equations for each mesh. In this case, use V=I*R. When resistors are in both meshes, I=(I 1 -I 2 ).Write KVL equations for each mesh. In this case, use V=I*R. When resistors are in both meshes, I=(I 1 -I 2 ). Use Ohm’s Law to express the voltages in terms of the mesh currents.Use Ohm’s Law to express the voltages in terms of the mesh currents. Again, you may need extra equations if there are other current/voltage sources.Again, you may need extra equations if there are other current/voltage sources. Solve for the unknown currents.Solve for the unknown currents.

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

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

9. Methods of Solving Sets of Equations Calculator Calculator rref functionrref function solve functionsolve function Linear Algebra Linear Algebra Substitution Substitution Graphing Graphing Euclid’s Method Euclid’s Method