EE201 Lecture 20 P 1 Linearity superposition response classifications Superposition 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 EE201 Lecture 20 P 2 Example Using superposition determine iL t for t 0 given iL 0 1 A 10 iL 10 u t V 2H 20 3 2 u t A Step 1 Find response due to initial conditions iL RTH d iL t iL t 0 L 4 2H dt R L 2 s 1 TH iL1 t e R L t to iL to e 2t A EE201 Lecture 20 P 3 Step 2 Find response from voltage source 10 iL 10 u t V 2H 20 3 iL2 0 0 iL2 1 A RTH 4 RTH L 2 s 1 iL2 t iL2 iL2 to iL2 e RTH L t to iL2 t 1 e 2t A EE201 Lecture 20 P 4 Step 3 Find response from current source 10 iL 2H 20 3 iL3 0 0 iL3 2 A RTH 4 RTH L 2 s 1 2 u t A iL3 t iL3 iL3 to iL3 e RTH L t to iL3 t 2 1 e 2t A EE201 Lecture 20 P 5 Step 4 Sum individual contributions iL t iL1 t iL2 t iL3 t iL t e 2t 1 e 2t 2 1 e 2t A iL t 3 4e 2t A Advantage 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 A iL t 2 5 3 5e 2t A EE201 Lecture 20 P 6 Response classifications Zero 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 zeroinput response Forced response portion of complete response which has same exponent as the input excitation
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