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Unformatted text preview: 1 1 Summary of Lecture #2 8/25/2010 Introduction to Laplace transform approach Laplace transform domain circuits Basic signals Unit step function, u(t) Ramp function, r(t) Pulse function, p(t) Delta function , (t) Example Laplace transform, F(s) = L (f(t)) Definition Region of convergence (ROC) Abscissa of convergence Pole or poles of F(s) Tables 12.1 and 12.2 4 Time domain approach to circuit problems Use KCL and KVL to set up a dif. eq. Identify the initial and final conditons Solve the dif. eq. Laplace transform approach to circuit problems Laplace transform of the input signals, V in (s) = L [v in (t)] Transfer function of the circuit, H(s) Output signal in s-domain, V out (s) = H(s) V in (s) Inverse Laplace trasnform, output signal in time-domain, v out (t) = L- 1 [V out (s)] 5 Input Signal circuit Output Signal Laplace transform of input signal Laplace transform of circuit Laplace transform of output signal Figure 12.2 Tables 12.1 and 12.2 Circuit problems and Laplace transform 6 Resistors Inductors Capacitors Time domain representation Frequency domain representation V =j L I V = R I v = Ri di v L dt = dv i C dt = 1 V I j C = In Laplace transform domain V = RI V = sL I 1 V I sC = j s 7 Unit step function < = t , 1 t , ) t ( u < =- o o o t t , 1 t t , ) t t ( u t u(t) 1 t u(t - t o ) 1 t o t u(t + + + t 1 ) 1 t 1 t 1 > 0 t o > 0 Unit step function Shifted step functions - - < = + 1 1 1 t t , 1 t t , ) t t ( u =- 2 2 2 t t , t t , 1 ) t t ( u t u(t 2- t)...
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- Spring '06