Lecture 4: Mesh Current Analysis & Source Transformation Nilsson ENG17 : Circuits I Spring April 9, 2015

Overview Mesh-Currents Mesh-Current w/Dependent Source Special Cases Node-Voltage vs. Mesh-Current Source Transformations 2

Go Mesh or Go Home Mesh = loop with no other loops inside it Mesh-Current Method needs [b e – (n e – 1)] equations Planar circuits only Mesh current = current that exist only in the perimeter of a mesh Mesh current ≠ Branch current –maybe 3

Mesh Currents 4

Evolution 5 Branch Currents Mesh Currents

Strategy for Mesh-Current Analysis 1.Assign mesh currents. 2.Apply KVL to each mesh. –Use Ohm’s law to express voltages in terms of mesh currents 3.Solve the resulting simultaneous equations to get mesh currents. 4.Use mesh currents to find branch currents and/or any other parameter. 6

Example 7

Overview Mesh-Currents Mesh-Current w/Dependent Source Special Cases Node-Voltage vs. Mesh-Current Source Transformations 8

(Don’t) Mesh It Up 9

Overview Mesh-Currents Mesh-Current w/Dependent Source Special Cases Node-Voltage vs. Mesh-Current Source Transformations 10

Mesh with Current Source 11

Supermesh…Super Cool 12

Example 13

Example 14

Overview Mesh-Currents Mesh-Current w/Dependent Source Special Cases Node-Voltage vs. Mesh-Current Source Transformations 15

Node…Mesh…and all the rest Why are we here? Difficult answer Try to make life easier Supernodes or supermeshes? 16

Comparison 17

Overview Mesh-Currents Mesh-Current w/Dependent Source Special Cases Node-Voltage vs. Mesh-Current Source Transformations 18

Source Transformations Akin to series / parallel reductions and delta-to-wye transformation Allows a voltage source with resistor in series to be replaced by current source in parallel with same resistor 19

Additional Elements 20

Recap Mesh-Currents Mesh-Current w/Dependent Source Special Cases Node-Voltage vs. Mesh-Current Source Transformations 21

Example 22

Example 23

Example 24