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EEE 302 Electrical Networks II. Dr. Keith E. Holbert Summer 2001. Circuit Analysis Techniques. While Obeying Passive Sign Convention Ohm’s Law; KCL; KVL Voltage and Current Division Series/Parallel Impedance combinations. Kirchoff’s Current Law ( KCL ). i 1 (t). i 5 (t).
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EEE 302Electrical Networks II Dr. Keith E. Holbert Summer 2001 Lecture 2
Circuit Analysis Techniques • While Obeying Passive Sign Convention • Ohm’s Law; KCL; KVL • Voltage and Current Division • Series/Parallel Impedance combinations Lecture 2
Kirchoff’s Current Law (KCL) i1(t) i5(t) The sum of currents entering the node is zero: Analogy: mass flow at pipe junction i2(t) i4(t) i3(t) Lecture 2
+ - + v(t)2 + v(t)1 v(t)3 - - Kirchoff’s Voltage Law (KVL) • The sum of voltages around a loop is zero: • Analogy: pressure drop thru pipe loop Lecture 2
In General: Voltage Division Consider N impedances in series: Source voltage(s) are divided between the resistors in direct proportion to their resistances Lecture 2
In General: Current Division Consider N impedances in parallel: Special Case (2 resistors in parallel) Lecture 2
Class Example • Extension Exercise E8.12 Lecture 2
Steps of Nodal Analysis 1. Choose a reference node. 2. Assign node voltages to the other nodes. 3. Apply KCL to each node other than the reference node; express currents in terms of node voltages. 4. Solve the resulting system of linear equations. Lecture 2
Class Example • Extension Exercise E8.13 Lecture 2
Steps of Mesh/Loop Analysis 1. Identify mesh (loops). 2. Assign a current to each mesh. 3. Apply KVL around each loop to get an equation in terms of the loop currents. 4. Solve the resulting system of linear equations. Lecture 2
Class Example • Extension Exercise E8.14 Lecture 2
Nodal Analysis Recipe 1&2) Identify and label N nodal voltages plus the ground node (V=0) 3) Apply KCL at N nodes (supernode makes constraint eq.) 4) Solve for the nodal voltages Loop Analysis Recipe 1&2) Identify and label N mesh currents 3) Apply KVL at the N meshes 4) Solve for the mesh currents Nodal and Loop Analyses Lecture 2