EE201 Circuit Theory

March 9, 2015Seung-Tak Ryu

Electrical Engineering, KAIST

Ch 3. Nodal and Loop Analysis

Ch.3 Outline 3.1. Nodal analysis

– Node voltage with respect to a common point (ground)– Circuits with current sources– Circuits with voltage sources (supernode)

3.2. Loop analysis (mesh analysis)– Circuits with voltage sources – Circuits with current sources (supermesh)

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Nodal analysis Find each node voltage by applying KCL

– 5 nodes (variables) with 5 homogeneous equations • Solution to A[V] = 0: Null space with infinitely many solutions

– Voltage: node voltages are defined with respective to a common point.

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Ground as a common node Set node 5 to be the ground as a reference point, and apply KCL

– N-node circuit with N-1 linearly independent KCL equations.

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CKT with only independent current sources Find KCL equations for v1 and v2.

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CKT with only independent current sources

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Node 1:

Node 2:

Node 3:

CKT with dependent current sources Determine the set of linearly independent equations that finds

v1, v2, and v3.

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CKT with independent voltage sources Determine all node voltages and branch currents.

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CKT with independent voltage sources Independent voltage source between two nonreference nodes.

– Branch current through 6-V source?

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CKT with independent voltage sources Supernode

– KCL holds for a surface

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CKT with independent voltage sources Determine Io.

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CKT with dependent voltage sources Find Io.

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Node analysis? How many node equations?

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Mesh analysis How about KVL?

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Loop1:

Loop2:

Mesh analysis How about KVL?

Different choice of loops?

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Loop1:

Loop2:

CKT with independent current sources Find Vo and V1.

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CKT with independent current sources Independent current source between two loops.

– How to choose I3 loop?

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CKT with independent current sources Supermesh

– Created by removing the 4-mA current source

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Supermesh

CKT with independent current sources Find Vo.

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CKT with dependent sources Find Vo

– Why large loop for I2?

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Concluding remark Node or Loop analysis?

Examine the circuit carefully before selecting an analysis approach.

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