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Superposition Principle in Linear Circuits

Learn about the superposition principle in linear circuits, where the current or voltage at any point can be calculated as the sum of individual contributions of each source acting alone. Discover how to calculate Thévenin equivalent and equivalent resistance in linear circuits.

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Superposition Principle in Linear Circuits

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  1. Slides from Lecture 6 with clearer markups 16 Sept. 2004

  2. Superposition A linear circuit is one constructed only of linear elements (linear resistors, and linear capacitors and inductors,linear dependent sources) and independent sources. Linear means I-V charcteristic of elements/sources are straight lines when plotted. Principle of Superposition: • In any linear circuit containing multiple independent sources, the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone.

  3. Superposition • Procedure: • Determine contribution due to one independent source • Set all other sources to 0: Replace independent voltage • source by short circuit, independent current source by open • circuit • Repeat for each independent source • Sum individual contributions to obtain desired voltage • or current

  4. Superposition Example • Find Vo 4 V 2 W + – + Vo – – + 24 V 4 A 4 W

  5. Calculating a Thévenin Equivalent • Calculate the open-circuit voltage, voc • Calculate the short-circuit current, isc • Note that isc is in the direction of the open-circuit voltage drop across the terminals a,b ! a network of sources and resistors + voc – b a network of sources and resistors isc b

  6. Thévenin Equivalent Example Find the Thevenin equivalent with respect to the terminals a,b:

  7. Thévenin Equivalent Example Find the Thevenin equivalent with respect to the terminals a,b:

  8. Alternative Method of Calculating RTh For a network containing only independent sources and linear resistors: • Set all independent sources to zero voltage source  short circuit current source  open circuit • Find equivalent resistance Req between the terminals by inspection Or, set all independent sources to zero • Apply a test voltage source VTEST • Calculate ITEST network of independent sources and resistors, with each source set to zero Req ITEST network of independent sources and resistors, with each source set to zero – + VTEST

  9. RTh Calculation Example #1 Set all independent sources to 0:

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