EENG 2610: Circuits AnalysisClass 5: Loop Analysis

Oluwayomi AdamoDepartment of Electrical EngineeringCollege of Engineering, University of North Texas

Loop Analysis Loop analysis uses KVL to determine a set of loop currents. In general, there are (B-M+1) linearly independent KVL equations.

B: number of branches, M: number of nodes The number of “window panes” tells us how many equations we need !

All the circuits in this course will be planar Planar means we can draw the circuit on a sheet of paper in such a way

that no conductor crosses another conductor. A mesh is a special kind of loop that does not contain any loops within it.

Loop current is also called mesh current, and loop analysis is called mesh analysis.

Write KVL Equations (or mesh equations)

Loop current: 21 , ii

In loop analysis, the unknown parameters are loop currents. The current in a branch equals to the algebraic sum of all the loop

currents passing through that branch.

Example 3.12: Find current I0

An alternative selection of loop currents

The presence of a current source simplifies loop analysis Define one loop through each current source, The remaining loop currents must pass through elements not covered by the

previous equations, and cannot pass through the current sources.

Example 3.15: Find V0

Example 3.16: Find I0Current sources shared by meshes – The General Loop Approach

3I

Determine how many equations we need from the number of “window panes” Define one loop through each current source, Additional loop currents are defined to pass through elements not covered by the

previous equations, and cannot pass through current sources. Write KVL for meshes and general loops using loop currents that we have defined.

First, we treat dependent source as though it were an independent source when writing KVL equations.

Then we write the controlling equation for the dependent sources.

Example 3.20: Find V0Circuits containing Dependent Sources

1I2I

3I4I

Problem Solving Strategyfor Loop Analysis Step 1: Define independent loops and loop current

One loop current is assigned to each independent loop in a circuit that contains N independent loops

Find N by counting the number of “window panes” Step 2: If only contains voltage sources

If only independent voltage sources are present, write N linearly independent KVL equations, one for each loop.

If dependent voltage sources are present, write KVL equations as what is done for circuits with only

independent voltage sources; Then write control equations for the dependent voltage sources

Step 3: If current sources are present,

Use the General Loop Approach Define one loop through each current source, Additional loop currents are defined to pass through elements not

covered by the previous equations, and cannot pass through current sources.

Write KVL for meshes and general loops using loop currents that we have defined.