lecture08

lecture08 - EE 205 Coifman Linear functions f(Kx)=Kf(x)...

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EE 205 Coifman 8-1 Linear functions f(K · x)=K · f(x) f(x 1 +x 2 )=f(x 1 )+f(x 2 ) Linear circuits - part 1: proportionality property y=K · x K x y = Kx Input Output
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EE 205 Coifman 8-2 e.g., i S = x R 1 K R 2 i O = y But how do you use this? 1) implicit in time varying i/o 2) unit output method 3) will pop up in subsequent engineering courses
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EE 205 Coifman 8-3 + - 5 V 15 20 10 10 + v O - ΩΩ How do you find v o ? Unit output method- one more tool for your toolbox For circuits with one input, First, turn the problem around, given a chosen output, what is the required input? Then use the proportionality property to find K and solve the circuit 1) A unit output is assumed; i.e., v o =1V or i o =1A 2) Solve for the input using the tools we have already developed 3) K = output / input = 1 / input_for_unit_output
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EE 205 Coifman 8-4 A B 15 20 10 10 + v S - i 3 i 1 + v 3 - + v 1 - i 2 L1 L2 i O v O = 1 V (Assumed) - + + v 2 - ΩΩ (this may seem like a trivial case, but trust me, you will appreciate this technique later in more complicated analysis)
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EE 205 Coifman 8-5 Linear circuits - part 2: additivity property y=K 1 · x 1 +K 2 · x 2 +K 3 · x 3 +... K 1 K 2 K 3 . . . x 1 x 2 x 3 y + + + + K 1 x 1 K 2 x 2 K 3 x 3
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EE 205
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lecture08 - EE 205 Coifman Linear functions f(Kx)=Kf(x)...

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