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These transparencies present a method for solving circuits using nodal analysis and the concept of thevenin and norton equivalents. Examples, exercises, and quizzes for practice. It also covers the process of computing req and its shortcut method.
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Nodal Analysis................................................................................ 2 Thevenin and Norton Equivalents.............................................. 10
These transparencies include material by Prof. Tim Trick and Prof. Marie-Christine Brunet
Nodal analysis is a particular method of solving circuits. You write equations in terms of node voltages, and then solve those equations.
Label every node in the circuit, and label currents through each voltage source and current source.
Write down any “known” voltage: Æ Ground is 0 volts Æ Use node voltage constraints across voltage sources
Write KCL equations in terms of the node voltages. For n nodes, you have n-1 equations.
Solve the equations to get the unknown node voltages.
Solve for currents through each element (if you are asked to do so) using the node voltages.
Solve for power (if you are asked to do so). Elements supplying energy: Negative power Elements absorbing energy: Positive power
Exercise
Solve for the node voltages. Verify your answers.
Quiz LH
Solve for the node voltages. Verify your answers.
Examples
Exercise
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 R (^) EQ works for both Thevenin and Norton:
Computing R (^) EQ
Compute the open-circuit voltage, the short-circuit current, and use ohm’s law:
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 V (^) OC and I (^) SC on an IV chacacteristic:
Exercise 2
Find V (^) OC , I (^) SC , and R (^) EQ any way you can. Here are possible three ways you might do it: (1) Use R (^) EQ shortcut, then find V (^) OC or I (^) SC (whichever is easier), then remaining values. (2) Use Node Voltage method at node C. (3) Use current divider equation.
Exercise 3
Find V (^) OC , I (^) SC , and R (^) EQ two ways: (3) Using R (^) EQ shortcut, then superposition to find V (^) OC , then I (^) SC. (4) Without shortcut, using Thevenin-Norton conversions.
