Lecture 4+5_v2

Lecture 4+5_v2 - Similar for node voltage: Rule: (# eq.) =...

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Spring 2011 ECE 2100, A. Molnar, Cornell University 1 Lectures 4+5 Node voltage and mesh current analysis

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Spring 2011 ECE 2100, A. Molnar, Cornell University 2 Node voltage analysis 1. Set one node = 0 (ground) 2. Name other nodes 3. Collapse trivial nodes: 4. Solve KCL for remaining nodes (1 eq/node) Write currents in terms of node voltages: 2 1 2 2 1 1 4 R R R V R V V + + = R1 R2 R3 R4 R5 R6 Pick this as ground Collapse: V4 V2 V1 V3 6 3 4 3 1 3 3 2 3 5 2 3 2 3 1 2 2 1 2 4 1 3 1 2 1 2 1 0 : 0 : 0 : R V R V V R V V V R V R V V R R V V V R V V R R V V I V in - - + - = - - + + - = - + + - + - = Note that in a given eq. a given voltage always has the same sign Iin
Spring 2011 ECE 2100, A. Molnar, Cornell University 3 Mesh Current analysis 1. Identify Meshes 2. Choose mesh current polarities 3. Collapse trivial nodes/meshes 4. Solve KVL for remaining meshes (1 eq/mesh) 1. Write voltages in terms of currents: R1 R2 R3 R4 R5 R6 Collapse: ( 29 ( 29 ( 29 ( 29 ( 29 in I I I R I I R I R I I I R I I R I I R R I I = + - - + - = + - - + + - = 3 3 6 2 3 5 2 3 1 2 2 3 1 2 4 1 3 1 2 1 1 : but defined not is Iin across voltage : problem : 0 : 0 : Note that in a given eq. a given current always has the same sign Iin I 1 I 2 I 3 Rule: (# eq.) = (# meshes) – (# of I-sources)

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Unformatted text preview: Similar for node voltage: Rule: (# eq.) = (# nodes) (# of V-sources) Spring 2011 ECE 2100, A. Molnar, Cornell University 4 Node-V/ mesh-I w/dep. sources ( 29 ( 29 2 1 1 1 2 1 1 I I r I I gm gmV r I R I r I I in o f in + =-= = +-- V1 V2 R F I in r gmV1 r o 1 2 2 1 2 1 1 =---=---gmV r V R V V R V V r V I o f f in I1 I2 Node voltage: two nodes, 2 eq. Dep. Sources violate same sign rule Mesh current: only one real mesh for KVL: But add in KCL for dep. Source to get two Challenge: show these give the same answer! Spring 2011 ECE 2100, A. Molnar, Cornell University 5 A useful transformation R1 R2 R3 RC RB RA 1 3 1 3 2 2 1 1 R R R R R R R R R R R R R R A C B A C B + + = + + = Spring 2011 ECE 2100, A. Molnar, Cornell University 6 Using this + V-+ V-+ V-+ V- b Y Y Collapse series...
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This note was uploaded on 06/10/2011 for the course ECE 2100 taught by Professor Kelley/seyler during the Spring '05 term at Cornell University (Engineering School).

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Lecture 4+5_v2 - Similar for node voltage: Rule: (# eq.) =...

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