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