
12-6 Power Electronics and Motor Drives
current i
DC
are practically constant in each conguration; they are equal, respectively, to v
0
and i
s
during
d
1
T
S
, where d
1
denotes the duty cycle of switch Q
1
, and to (−v
0
) and (−i
s
) during the rest of the switching
period. Applying the circuit averaging technique to the converter signies replacing the instantaneous
values of v
AB
and i
DC
by their average value calculated over the switching period T
S
(Figure 12.5). It yields
v d v
i d i
AB
dc s
#( )
( )
2 1
2 1
1 0
1
−
−#
(12.3)
Replacing the averaged expressions (12.3) of v
AB
and i
DC
into Equation 12.2 yields a one-input-two-
outputs bilinear system represented ...