EE 2315

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## EE 2315

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**EE 2315**Lecture 04 - Wye/Delta & Delta/Wye Conversions and Node Voltage Analysis**Wye/Delta Conversion (1/2)**Wye Delta**Effects of D-Y & Y-D Conversions**• D-Y Conversion eliminates a loop but adds a node. • Y-D Conversion eliminates a node but adds a loop.**Y-D Conversion Example**Find Rab Several Methods: We choose to eliminate node c, then simplify.**Introduction to 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 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 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 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: