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Unformatted text preview: 1 1 Summary of Lecture #6 9/03/2010 Passive circuit elements with zero initial condition in time and frequency domains R R, L Ls, C 1/(Cs) Impedance Z(s) and admittance Y(s) Series and parallel comb. of Z(s) and Y(s) . Voltage and current divisions Source transformation L and C with initial conditions i(t) L (i(t)) = I(s) v(t) L L L L (v(t)) = V(s) 2 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 3 Time domain representation VI characteristic of a resistor VI characteristic of an inductor VI characteristic of a capacitor v R (t) i R (t) + _ i L (t) v L (t) + _ dt ) t ( di L ) t ( v L L = + = = - t t L o L t L L o ' dt ) ' t ( v L 1 ) t ( i ' dt ) ' t ( v L 1 ) t ( i R R v (t) Ri (t) = i L (- ) = 0 i C (t) v C (t) + _ C dt ) t ( dv C ) t ( i C C = + = = - t t C o C t C C o ' dt ) ' t ( i C 1 ) t ( v ' dt ) ' t ( i C 1 ) t ( v c v ( )- = 4 Frequency shift L [e- at f (t)] = F (s+a) 1st- and 2nd- order time differentiation Nth-order time differentiation See Eq. 13.45- =---- =-...
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This document was uploaded on 01/13/2012.
- Spring '06