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lecture 7

# lecture 7 - Summary of Lecture#7 L and C with zero initial...

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1 Summary of Lecture #7 9/08/2010 L and C with zero initial conditions in frequency domain L Ls, C 1/(Cs) L and C with non-zero initial conditions Eq. voltage source in series Eq. current source in parallel Transfer functions Cramer’s rule and matrix inversion Nodal analysis Loop or mesh analysis Thevenin and Norton equivalents Superposition Examples 2 Frequency shift L [e - at f (t)] = F (s+a) 1st- and 2nd- order time differentiation Nth-order time differentiation See Eq. 13.45 - = - - - - = - = 0 t 2 2 2 dt ) t ( df ) 0 ( sf ) s ( F s ] dt f d [ ) 0 ( f ) s ( sF ] dt df [ L L initial value initial derivative 3 Cap. with non-zero initial voltage v C (0 - ) Eq. voltage source in series Eq. current source in parallel s ) 0 ( v ) s ( I Cs 1 ) s ( V c C C - + = ) s ( CsV ) 0 ( Cv ) s ( I C c C = + - )] 0 ( v ) s ( sV [ C ) s ( I , dt ) t ( dv C ) t ( i c C C C C - - = = 4 Ind. with non-zero initial current i L (0 - ) Eq. current source in parallel Eq. voltage source in series s ) 0 ( i ) s ( V Ls 1 ) s ( I L L L - + = ) 0 ( Li ) s ( LsI ) s ( V L L L - - = )] 0 ( i ) s ( sI [ L ) s ( V , dt ) t ( di L ) t ( v L L L L L - - = = 5 C v c (t) i c (t) + - v c (0 - ) Cv c (0 - ) I c (s) V c (s) + - I c (s) V c (s) + - + - Cs 1 v c (0 - ) s i L (t) v L (t) + - L i L (0 - ) I L (s) V L (s) + - Ls i L (0 - ) s + - Ls I L (s) V L (s) + - Li L (0 - ) Cs 1 Circuit elements having non-zero initial conditions in time and frequency domains Current source in parallel Voltage source in series 6 Transfer function of two-port circuits Assumptions: No independent source Zero initial conditions where F j (s) and G i (s) stand for V 1 (s), I 1 (s) V 2 (s) or I 2 (s) . Subscripts i and

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lecture 7 - Summary of Lecture#7 L and C with zero initial...

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