1
11
Capacitor and Current Drive
r
S
d ( )q t
( )Cv t
C
( )Ci t
● Current drive: Excitation of capacitor with current Source
( )Ci t
SI ( )Cv t
( )LV t
( )Ci t
t
tInd
uct
or
and
its
Cir
cuit
Pro
pe
rtie
s
2
22
Capacitive Switching Circuit #1
CSI
( )Ci t
( )Cv t
Open
Closed
( )Cv t
( )Ci t
Ca
pac
itor
and
its
Circ
uit
Pro
pe
rtie
s
3
33
Capacitive Switching Circuit #2
SI( )Ci t
( )Cv t
Open
Closed Closed
( )Ci t
( )Cv t
Open
Ca
pac
itor
and
its
Circ
uit
Pro
pe
rtie
s
4
44
Charge Balance Condition: Amp-sec Balance Condition
● Consider an excitation of capacitor with periodic ac current
● Change in charge q(t)=C vC(t)
( )Ci t
1T
2T1I
2I
0A
( )Cv t
( )q t ( )Ci t
( )q t
Ca
pac
itor
and
its
Circ
uit
Pro
pe
rtie
s
5
55
Generalization of Amp-sec Balance Condition
( )Ci tAverage { ( )} 0Ci t
( )Ci t
Ca
pac
itor
and
its
Circ
uit
Pro
pe
rtie
s
6
66
Implication
● Whenever possible, a switching circuit establishes a steady-state equilibrium by adjusting the circuit variables to satisfy the amp-sec balance condition on the capacitor in the circuit.
● A circuit that violates the amp-sec balance condition can be easily devised, but the circuit eventually destroys itself by an over-voltage condition on the capacitor
SI
( )Ci t
( )Cv t
Open
Closed Closed
Open
Ca
pac
itor
and
its
Circ
uit
Pro
pe
rtie
s
7
77
Capacitive Switching Circuit #3
1SI
Closed
Open
( )Ci t
( )Cv t
2SI
Q D
( )Ci t
( )Cv t Open
Case #1: IS1=25A IS2=25A
Ca
pac
itor
and
its
Circ
uit
Pro
pe
rtie
s
8
88
( )Ci t
( )Cv t
( )Ci t
( )Cv t
Closed
Open OpenClosed
Open Open
Case #2: IS1=30A IS2=20A Case #3: IS1=20A IS2=30A
Capacitive Switching Circuit #3C
ap
acito
r a
nd it
s C
ircu
it P
rop
ert
ies