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Lecture 3: Resistive Circuits & Nodal Analysis Nilsson 3.3, 3.4, 3.7, 4.1-4.4 ENG17 (Sec. 1): Circuits I Summer 1 2014 June 25, 2014 1 Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases 2 Voltage Divider • One voltage supply, multiple voltage levels 3 Load • RL = load = 1+ circuit elements that draw power from circuit – May alter voltage across parallel element – But not if RL >> R2 4 Example 5 Example • Wheatstone Bridge – 2 voltage dividers in parallel 6 Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases 7 Current Divider • One current supply, multiple current levels 8 Example 9 Example • Similar analysis 10 Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases 11 Voltage Division • Generalization of voltage divider circuit 12 Current Division • Generalization of current divider circuit 13 Example 14 Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases 15 Unable to get Req • For example, Wheatstone bridge circuit (below) cannot be simplified with standard parallel/series rules • Must use circuit transformation 16 Defining Delta/Pi and Y/T Δ π Y T 17 Delta-to-Wye Circuit Transformation • Equivalent resistance between nodes • Note: resistor values are NOT THE SAME 18 Apply to Wheatstone Bridge 19 Recap • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases 20 Planar Circuit Planar Not Planar Nodal good for either Mesh good for planar 21 Identify • • • • • • • Node Essential Node Path Branch Essential Branch Loop Mesh 22 Simultaneous Equations • How many unknown currents? • How many equations needed? 23 Node Voltage Method – Setting Up • Identify essential nodes • Define reference node • Apply KCL to each non-reference node, express current in terms of node voltages • Solve simultaneous equations 24 Node Equations 25 Example 26 Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases 27 Dependent Sources • Only need to add equation to describe relationship of the dependent source 28 Example 29 Overview • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases 30 Source Between Essential Nodes 31 w/Dependent Source 32 Supernode 33 Example 34 Recap • Voltage Divider • Current Divider • Voltage / Current Division • Δ-to-Y Equivalent Circuits • Node Voltage Method • NVM w/Dependent Sources • NVM Special Cases 35