Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6EE201 Lecture 20 P. 1Linearity, superposition, response classificationsSuperposition can be applied to RL or RC circuits with voltage or current sources (excitations). When applying superposition:1) Find response due to each excitation without initial conditions.2) Find response due to initial conditions (one at a time) when all independent sources are deactivated.3) Sum all responses.Example: Using superposition, determine iL(t) for t 0 given iL(0-) = -1 A.2 H 10 u(t) V(20/3)10 EE201 Lecture 20 P. 2+_ 2 u(t) AStep 1: Find response due to initial conditions.2 H4iLiL d iL(t) dt+ RTHLiL(t) = 0 (RTH/L) = 2 s-1iL1(t) = [e-(R/L)(t-to)] iL(to) = -e-2t AEE201 Lecture 20 P. 3Step 2: Find response from voltage source.iL2(t) = iL2() + [iL2(to+) - iL2()]e-(RTH/L)(t-to)2 H 10 u(t) V(20/3)10 +_iLiL2(0+) = 0; iL2() = 1 ARTH = 4 ; RTH/L = 2 s-1iL2(t) = (1 - e-2t) AEE201 Lecture 20 P. 4Step 3: Find response from current source.2 H(20/3)10 2 u(t) AiLiL3(t) = iL3() + [iL3(to+) – iL3()]e-(RTH/L)(t-to)iL3(0+) = 0; iL3() = 2 ARTH = 4 ; RTH/L = 2 s-1iL3(t) = 2(1 - e-2t) AEE201 Lecture 20 P. 5Step 4: Sum individual contributions.iL (t) = iL1(t) + iL2(t) + iL3(t)iL(t) = [- e-2t + (1 - e-2t) + 2(1 - e-2t)] AiL(t) = [(3 - 4e-2t)] AAdvantage of superposition: superposition allows the effect of changing a single input or initial condition on the total response to be determined. Example: For the example above, change voltage source to 5 u(t) V.Voltage is cut by a factor of two. Scale result of step 2.iL2(t) = 0.5 (1 - e-2t) AiL(t) = [(2.5 – 3.5e-2t)] AEE201 Lecture 20 P. 6Response classificationsZero-input response: response to initial conditions when input is set to zero.Zero-state response: response to a specified input signal or set of input signals when all initial conditions are zero.Complete response: sum of the zero-input and zero-state responses.Natural response: portion of complete response which has the same exponent as zero-input response.Forced response: portion of complete response which has same exponent as the input
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