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DC Circuit Theorems

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Superposition
3 Superposition In this lecture, you will: Learn the principle of superposition Learn how to apply the principle of superposition to solve  DC circuits Understand the tradeoffs in applying superposition versus  other circuit analysis approaches

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4 Linearity Linear operators: Add and subtract Multiply and divide by constants Differentiate and integrate Nonlinear operators: Exponents other than 1 For example, squares and square roots Logarithms and many other functions.
5 Linear Circuit Elements Resistors are linear circuit elements: V = IR  is clearly a straight line. Ideal capacitors and inductors are linear. Independent sources are linear. Dependent sources are linear provided that the output voltage  or current is proportional to the first power of a specified  voltage or current (or a sum of these).

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6 Nonlinear Circuit Elements Semiconductor devices are nonlinear. Diodes Transistors Devices using ferromagnetic materials are nonlinear. Iron core inductors. Many other real world devices are nonlinear  although their response may be approximately linear  over a limited range.
7 Linear Circuits linear circuit  is a circuit composed exclusively of  linear circuit elements. 3 A 10  40  + 50 V -

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8 Superposition Superposition is a property of all  linear systems: [ ] [ ] ) ( ) ( ) ( y f b x f a by ax f + = +
9 Superposition Definition :  Any linear system obeys the principle of  superposition , which states that whenever a  linear system is excited or driven by more than one  independent source of energy, the total response is the  sum of the individual responses that result from each  independent source acting alone.

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10 What does this mean? Since we are dealing with linear circuits, we can  determine the response of the circuit to each  independent source acting alone and then sum the  results. Of course, superposition only makes sense when there is  more than one independent source.
11 Superposition Example IR V = 2A - + V R 3A 10 Ω ( 29 ( 29 ( 29 ( 29 ( 29 V A V A V Total V V A V V A V R R R R R 0 . 10 30 20 3 2 0 . 30 10 3 3 0 . 20 10 2 2 - = - = + = - = × - = = × =

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12 Superposition in Circuits The response in a linear circuit having more than one  independent source can be obtained by adding the  responses caused by the separate independent sources  acting alone.  How do I find the response of the circuit to one source  acting alone?
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