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3.LaplaceCircuitsx4 - Overview of Laplace Transforms for...

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Example 1: Circuit Analysis We can use the Laplace transform for circuit analysis if we can define the circuit behavior in terms of a linear ODE. For example, solve for v ( t ) . Check your answer using the first-order response methods discussed in ECE 221. 10 u(t) v ( t ) - + 5 mH i (0-) = -2 mA 5 k Ω J. McNames Portland State University ECE 222 Laplace Circuits Ver. 1.64 3 Overview of Laplace Transforms for Circuit Analysis Passive element equivalents Review of ECE 221 methods in s domain Examples J. McNames Portland State University ECE 222 Laplace Circuits Ver. 1.64 1 Example 1:Workspace Hint: [r,p,k] = residue([-2e-3 2e3],[1 1e6 0]) r = -0.0040, 0.0020, p = -1000000, 0 k = [] J. McNames Portland State University ECE 222 Laplace Circuits Ver. 1.64 4 Prerequisite and New Knowledge Prerequisite knowledge Ability to find Laplace transforms of signals Ability to find inverse Laplace transforms Ability to perform DC circuit analysis using all of the standard methods New knowledge Ability to solve for any current or voltage in a circuit with the basic linear elements (resistors, capacitors, inductors, op amps, switches, and sources) No longer restricted to DC or sinusoidal steady-state analysis J. McNames Portland State University ECE 222 Laplace Circuits Ver. 1.64 2
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Kirchhoff’s Laws N k =1 v k ( t ) = 0 N k =1 V k ( s ) = 0 M k =1 i k ( t ) = 0 M k =1 I k ( s ) = 0 Kirchhoff’s laws are the foundation of circuit analysis KVL: The sum of voltages around a closed path is zero KCL: The sum of currents entering a node is equal to the sum of currents leaving a node If Kirchhoff’s laws apply in the s domain, we can use the same techniques that you learned last term (ECE 221) Apply the LPT to both sides of the time domain expression for these laws The laws hold in the s domain J. McNames Portland State University ECE 222 Laplace Circuits Ver. 1.64 7 Example 1:Workspace J. McNames Portland State University ECE 222 Laplace Circuits Ver. 1.64 5 Defining s Domain Equations: Resistors R v ( t ) - + i ( t
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