Download Nodal Analysis and Thevenin & Norton Equivalents in Circuit Analysis and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! L Haken ECE110 transparencies – set 4 page 1 ECE 110 Transparencies Set 4 for Noon Lecture Lippold Haken Nodal Analysis................................................................................ 2 Thevenin and Norton Equivalents.............................................. 10 These transparencies include material by Prof. Tim Trick and Prof. Marie-Christine Brunet L Haken ECE110 transparencies – set 4 page 2 Nodal Analysis Nodal analysis is a particular method of solving circuits. You write equations in terms of node voltages, and then solve those equations. 1) Label every node in the circuit, and label currents through each voltage source and current source. 2) Write down any “known” voltage: Ground is 0 volts Use node voltage constraints across voltage sources 3) Write KCL equations in terms of the node voltages. For n nodes, you have n-1 equations. 4) Solve the equations to get the unknown node voltages. 5) Solve for currents through each element (if you are asked to do so) using the node voltages. 6) Solve for power (if you are asked to do so). Elements supplying energy: Negative power Elements absorbing energy: Positive power L Haken ECE110 transparencies – set 4 page 5 Quiz LH15 Solve for the node voltages. Verify your answers. L Haken ECE110 transparencies – set 4 page 6 Floating Voltage Source L Haken ECE110 transparencies – set 4 page 7 Examples L Haken ECE110 transparencies – set 4 page 10 Thevenin and Norton Equivalents The Thevenin circuit is a linear circuit that has one resistor and one voltage source: The Norton circuit is a linear circuit using one resistor and one current source: We often simplify linear circuits to their Thevenin or Norton equivalents (the Thevenin or Norton circuit with the identical IV characteristic). Exercise: Show that the same equivalent resistance REQ works for both Thevenin and Norton: REQ = RTH = RN VTH = IN * RN L Haken ECE110 transparencies – set 4 page 11 Computing REQ Compute the open-circuit voltage, the short-circuit current, and use ohm’s law: REQ = |VOC / ISC| Be sure you understand why this works. Be sure you use the proper direction of current and voltage polarity. Be sure you know how to read VOC and ISC on an IV chacacteristic: L Haken ECE110 transparencies – set 4 page 12 Shortcut for Computing REQ: Compute REQ with voltage sources shorted, current sources open. Exercise 1 Find VOC, ISC, and REQ two ways: (1) Using REQ shortcut (redraw) (2) Without shortcut, using Thevenin-Norton conversions.
