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ECE201_Lecture20

# ECE201_Lecture20 - form for t t e x t x x t x t t ≥ ∞...

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1 ECE201 Linear Circuit Analysis I Lecture 20 Topic: Linearity/Response Classification 1. Linearity = Proportionality & Superposition 2. Superposition still works for circuits with linear inductors, linear capacitors, linear resistors, dependent sources and independent sources, PROVIDED that initial conditions are properly accounted for. 3. General Linear Relationship: response input zero ) ( response state - zero ) ( ) ( 0 01 1 1 1 1 1 + + + + + + + + = k k Sn n S Sm m S x x i i v v y γ γ β β α α α , β , γ : constants v s : independent voltage source i s : independent current source x o : initial conditions 4. To compute zero-state response, set all initial conditions for capacitors and inductors to zero. Compute the response (y) due to each input source (v s or i s ), one at a time. 5. To compute zero-input response, deactivate all independent sources, compute the response (y) due to each initial condition, one at a time. 6. For RC or RL circuits with constant or step input sources, any variable of interest has the

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Unformatted text preview: form: for )] ( ) ( [ ) ( ) ( t t e x t x x t x t t ≥ ∞ − + ∞ = − − + τ τ = L R or τ = RC 2 Example 1 Consider the circuit below in which v c (0 – ) = 5 V . Use superposition to find the response v c (t) for t ≥ 0. Step 1 Determine the zero-input response. Step 2 Determine the zero-state response due to v s . 3 Step 3 Determine the zero-state response due to i s . Step 4 Find v c (t) for t ≥ 0 by superposition: 4 Example 2 Repeat the above example when v c new (0 – ) = − 10 V v s new (t) = − 15 u(t) V i s new (t) = 24 u(t) A 5 Example 3 Consider the circuit below. Find v c (t) for t ≥ 0 using linearity. (a) Find zero-input response if v c (0 – ) = 5 V (b) Find zero-state (zero I.C.) response due to only the V-source. 6 (c) Find zero-state (zero I.C.) response due to the I-source (d) Compute total response v c (t) for t ≥ 0....
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ECE201_Lecture20 - form for t t e x t x x t x t t ≥ ∞...

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