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ECE201_Lecture10

ECE201_Lecture10 - (i.e circuit with resistors dep sources...

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1 ECE201 Linear Circuit Analysis I Lecture 10. Topics: Superposition and Linearity 1. Mathematical definition of linearity linearity = proportionality + superposition For function f(u) = y input output Proportionality: f( α u) = α y ( α : scalar) Superposition: f(u 1 + u 2 ) = f(u 1 ) + f(u 2 ) Linearity: f( α u 1 + β u 2 ) = α f(u 1 ) + β f(u 2 ) ( α ⋅ β : scalers) Obviously, linearity can be extended to multiple inputs. 2. Linear resistive circuit General linear relationship: sn n s sm m s i i v v y β α + + + + + = 1 1 1 1 scalers) : , ( 1 1 n m What does α 1 v s1 mean? • Output due to v s1 alone; and • Output when v s2 … v sm , i s1 … is sn are “dead” Linear Circuit containing no indep. sources
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Unformatted text preview: (i.e,, circuit with resistors, dep. sources, etc.) ↑ ↑ +-+-v s1 v sm i si i sn … + v – or → i output or variable of interest: y (i.e., v or i) 2 A “dead” voltage source: (v = 0) A “dead” current source: (i = 0) 3. Linear resistive circuit analysis (examples) (1) Find I o Question: Does linearity apply to the power absorbed by the 60 ohm resistor? ⇒ + – + v – short circuit ⇒ i open circuit → 3 (2) Find α 1 and α 2 , so that V o = α 1 V s1 + α 2 V s2 . 4 (3) Find i x in the circuit below 5 ( cont .) Exercise: Find α 1 , β 1 , β 2...
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ECE201_Lecture10 - (i.e circuit with resistors dep sources...

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