3
CALCULATIONS OF VOLTAGE CONVERSION RATIO
BUCK CONVERTER (cont’d
)
• Via energy balance
sOO
T
OOout
oninin
T
ininin
TiVdtiVE
TiVdtiVE
s
s
=
==
==
==
=
=
==
==
==
=
∫
∫∫
∫
∫
∫∫
∫
0
0
Assuming 100% efficiency, i.e.,
outin
EE
• Via flux (volt-sec) balance on L
F
D
T
T
V
V
M
s
on
in
o
=
==
==
==
==
==
=
ˆ
D -- duty cycle
on
oinL
T
N
VV
t
N
V −
−−
−
=
==
=∆
∆∆
∆=
==
=∆Φ
∆Φ∆Φ
∆Φ
+
++
+
off
oL
T
N
V
t
N
V
=
==
=∆
∆∆
∆=
==
=∆Φ
∆Φ∆Φ
∆Φ
−
−−
−
−
−−
−+
++
+
D
T
T
V
V
M
s
on
in
o
=
==
==
==
==
==
=
ˆ
• Since average voltage across L
F
during switching cycle must
be zero, output voltage is average of voltage at input of
output filter, i.e., average of V
D
∆Φ
∆Φ∆Φ
∆Φ
T
on
T
off
Hl
m
= NI
d
Φ
ΦΦ
Φ
dt
V
L
= N
Φ
Φ Φ
Φ
=BS
