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Lecture 4: Mesh Current Analysis & Source Transformation Nilsson 4.5-4.9 ENG17 : Circuits I Spring 2015 1 April 9, 2015

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

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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

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Mesh Currents 4

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Evolution 5 Branch Currents Mesh Currents

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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

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Example 7

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

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(Don’t) Mesh It Up 9

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

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Mesh with Current Source 11

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Supermesh…Super Cool 12

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Example 13

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Example 14

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

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

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Comparison 17

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

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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

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Additional Elements 20

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

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Example 22

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Example 23

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Example 24

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