Lecture_6 - ECE103 Spring 2008 Lecture 6 Circuit Theorems...

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ECE103 Spring 2008 Lecture 6 Circuit Theorems Linearity Property Linearity is the property of one element describing a linear relationship between cause and effect. The linearity property is a combination of the scaling property and the additivity property The homogeneity property requires that if the input or excitation is multiplied by a constant factor, the output or response will be multiplied by the same constant factor. For a resistor in an electric circuit, we can easily check that Ohm’s law relates the current through and the voltage across a resistor linearly. To corroborate that we observe that the scaling property applies: vR i k k i =→ = When we increase the current by a constant factor k the voltage increases by the same factor. The other property is the additivity: the voltage across a resistor is related to the current by the Ohm’s law 11 2 2 vi R R == If we apply a current 12 ii + , the voltage is calculated () 1 2 1 2 i R i R i R v v =+ = + = + So we can conclude that a resistor is a linear element because the voltage-current relationship fulfills both the homogeneity and additivity properties. A linear circuit is one whose output is linearly related (or directly proportional) to its input Superposition The superposition principle rests on the linearity property. In a circuit with two or more
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This note was uploaded on 10/28/2008 for the course ECE 103 taught by Professor Marconi during the Spring '08 term at Colorado State.

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Lecture_6 - ECE103 Spring 2008 Lecture 6 Circuit Theorems...

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