EENG 2610: Circuits Analysis Class 5: Loop Analysis Oluwayomi Adamo Department of Electrical Engineering College 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.

In loop analysis, the unknown parameters are loop currents. Write KVL Equations (or mesh equations) Loop current: 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 Example 3.15: Find V0 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 3.16: Find I0 Current sources shared by meshes – The General Loop Approach 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.

Example 3.20: Find V0 Circuits containing Dependent Sources 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.

Problem Solving Strategy for 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.