Lecture 01 - Node Voltage Analysis

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Presentation transcript:

Lecture 01 - Node Voltage Analysis EE 2415 Lecture 01 - Node Voltage Analysis

Introduction to the Node Voltage Method More direct than branch equations Fewer equations to solve Choose one node as reference Express all variables in terms of node voltages Solution is set of node voltages w.r.t. chosen reference node Solution completely defines the circuit

Node Voltage Example 1 (1/4) Apply KCL at Node 1: Use Ohm’s Law:

Node Voltage Example 1 (2/4) Apply KCL at Node 2: Use Ohm’s Law:

Node Voltage Example 1 (3/4) KCL for Node 1: KCL for Node 2:

Node Voltage Example 1 (4/4)

Node Voltage Example 1a (1/2)

Node Voltage Example 1a (2/2)

Node Voltage Example 2 (1/2) KCL for Node 1: KCL for Node 2:

Node Voltage Example 2 (2/2) Substitute: into KCL equations Node 1: Node 2:

Node Voltage Example 2a (1/2) Substituting for ix:

Node Voltage Example 2a (2/2)

Node Voltage Example 3 (1/2) KCL for Node 1: KCL for Node 2:

Node Voltage Example 3 (2/2) Substitute: into KCL equations Node 1: Node 2:

Node Voltage Example 3a (1/2) After Substitution:

Node Voltage Example 3a (2/2) Substitute and solve:

Node Voltage Example 4 (1/3) No KCL equation possible at node 1 or at node 2. KCL can be applied at the supernode.

Node Voltage Example 4 (2/3) KCL @ Supernode: Other relationships: and

Node Voltage Example 4 (3/3)

Node Voltage Example 4a (1/2)

Node Voltage Example 4a (2/2) Substitute and solve:

Alternative to Supernode (1/2) KCL @ Node 1: KCL @ Node 2:

Alternative to Supernode (2/2) Use Ix to get same info as Supernode: