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ECE 2100 Lectures 3+4_rev2

ECE 2100 Lectures 3+4_rev2 - Iin Mesh Current analysis 1...

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ECE 2100 Lectures 3+4 Professor Alyosha Molnar

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Voltage, Current dividers 2 1 2 R R R V V in out + = 2 1 1 2 2 1 R R R V R V V out + + = + Vin - + Vout - R1 R2 Iin Iout R1 R2 V1 V2 R1 R2 V1, V2 measured relative to ground 2 1 1 2 1 2 1 1 1 R R R I R R R I I in in out + = + =
More annoying symbols Dependant Voltage source: Dependant Current source: + + V in V out =AV in - - + V in I out =g m Vin - + I in V out =r t I in - I in I out =AI in Voltage amp: A is unitless transresistor : r t is in Ohms Current amp: A is unitless transconductor : gm is in Siemens

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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) 1. Write currents in terms of node voltages: 2 1 1 4 2 1 2 R R R V R V V + + = R1 R2 R3 R4 R5 R6 Pick this as ground Collapse: V2 V4 V1 V3 5 4 3 4 3 1 2 4 1 4 6 3 4 3 1 3 3 4 3 4 1 3 1 2 1 4 1 0 : 0 : 0 : R V R V V R R V V V R V R V V R V V V R V V R R V V I V in - - + + - = - - + - = - + + - + - = Note that in a given eq. a give voltage always has the same sign
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Unformatted text preview: Iin 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 : : : 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) Similar for node voltage: Rule: (# eq.) = (# nodes) – (# of V-sources)...
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