Methods of Analysis

Circuits 1 Fall 2005 Harding University Jonathan White

Outline

   Nodal Analysis • Define a symbol for all unknown node voltages.

• Write KCL at each node where variables occur • Using Ohm’s Law, solve resulting equations.

Mesh Currents • Set up the currents • Use KVL Methods to solve linear equations • Substitution • Determinants • Calculator • Method from Numerical Methods

Nodal Analysis

 Steps: • Define a voltage at every node in the circuit  Note: Some may be known, such as the source and ground • Write 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 • Solve for the unknown voltages.

H sometimes actually make the equations easier.

– V L • Other current and voltage sources must be factored in to either the KCL equations or the unknown voltages. They

Nodal Analysis Example 1

Find all voltages and currents.

Nodal Analysis Example 2

Find Vo + Vo -

Mesh Currents

 Steps: • Label each unknown current in each mesh, going clockwise.

  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.

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

current/voltage sources.

• Solve for the unknown currents.

1 -I 2 ).

• Use Ohm’s Law to express the voltages in terms of the • Again, you may need extra equations if there are other

Mesh Current Example - 1

Calculate the mesh currents.

Mesh Current Example - 2

Find the current through the 1 ohm R

Methods of Solving Sets of Equations

     Calculator • rref function • solve function Linear Algebra Substitution Graphing Euclid’s Method