Unformatted text preview: t 0 y (t ) = [ y (0) y ( )]e
t • 0 t/ + y ( ) for t 0 (with y ( ) = X S ) y (t ) = [ y (0) y ( )]e •
• t/ + y ( ) for t 0 •
y (t ) = [ y (0) y ( )]e t/
+ y ( ) for t y transient (t ) = [ y (0) y ( )]e y (t ) = [ y (0) y ( )]e t/ for t / 0 (with y ( ) = X S ) 0 (with y ( ) = X S ) + y ( ) for t 0 (with y ( ) = X S ) y (t ) = y transient + y steady for t state y transient = [ y (0) y ( )]e
y steady state = y ( ) 0 t/ for t 0 • y transient = y (0)e t/ y ( )e •
y steady state = y( ) = XS t/ for t 0 VS = Ri (t ) + L i (t ) = VS
+ I0
R di (t )
for t
dt
VS
e
R t/ 0 for t VS u (t ) = Ri (t ) + L 0 di (t )
dt i (t ) = VS
VS
e
+ I0
R
R t/ for t 0 i (t ) = VS
VS
e
+ I0
R
R v (t ) = L di (t )
= (VS
dt t/ for t 0 t/ for t I 0 R)e 0 C vC (t ) = I S R + (V0 I S R)e iC (t ) = C dvC
= (I S
dt t/ V0
)e
R for t t/ for t 0 0 dvC vC
+ = I S for t
dt
R 0 C dvC vC
+ = I S u (t )
dt
R vC (t ) = I S R + (V0 I S R)e iC (t ) = C dvC
= (I S
dt t/ V0
)e
R for t t/ for t 0 0 • • • •
• •
• •
•
•
• • v aux
10K
v
i = aux
20K
i aux = 7i + i
i aux = v aux
10K 6 v aux
= v aux (0.1 10
20 K
v aux
= 5K
i aux 3 0.3 10 3 ) • iC = i R i
v O (t ) = R i (t )
dv (t )
i (t ) = C I
dt dv I (t )
vO (t ) = RC
dt •
• • • iC = i R i
v (t )
i (t ) = I
R
dv (t )
i (t ) = C O
dt 1t
vO (t ) =
v I (t ) dt + vO (0)
RC 0 •
• • vO (t ) = VI
t + vO (0)
RC •
dvO (t )
VI
=
dt
RC
• •
• •
• 1t
vO (t ) =
v I (t ) dt + vO (0)
RC 0 •
• •
•...
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 Fall '14

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