Diode with an LC Load No initial conditions.
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Transcript Diode with an LC Load No initial conditions.
Diode with an LC Load
No initial conditions.
Close the switch @ t = 0.
Solve for the current i.
ECE 442 Power Electronics
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Solution
t
di 1
Vs L idt vC (t 0)
dt C t0
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t
di 1
Vs L idt vC (t 0)
dt C t0
Vs
1
LsI ( s )
I (s)
s
Cs
1
2
Vs Ls I ( s ) I ( s )
C
I ( s)
Vs
1
Ls
C
2
i (t ) Vs
Vs
2 1
L s
LC
1
Vs
LC
1
2 1
L s
LC
LC
C
sin 0t
L
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i (t ) Vs
C
sin 0t
L
di
C
0Vs
cos 0t
dt
L
di Vs
cos 0t
dt L
Vs
di
t 0
dt
L
1
C
Vs
cos 0t
L
LC
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Capacitor Voltage
t
t
1
1
C
vC (t ) idt Vs
sin 0t
C0
C0
L
t
Vs
1
C
vC (t ) Vs
sin 0t
C
L0
LC
vC (t ) Vs cos 0t cos(0)
t
1
cos 0t
1
LC
0
vC (t ) Vs 1 cos 0t
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What happens at time t1=π√LC?
t t1 LC
C
C
1
i (t1 ) Vs
sin 0t1 Vs
sin
LC 0
L
L
LC
1
vC (t1 ) Vs 1 cos 0t1 Vs 1 cos(
LC 2Vs
LC
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Waveforms of Current and Voltage
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