Advanced Analog Technology, Inc
.
May 2008
AAT1168/1168A/1168B
2
P
= I
(
.r
C
)
ESR
Lpeak
+
+
ESR: Equivalent Series Resistance
−
−
r
Example 2:COUT = 38µF,
= 20m Ω
C
VRIPPLE(COUT
)
=
=
4mV
V
(ESR)
22mV
RIPPLE
β
−
V
=
26mV
+
RIPPLE
PESR = 0.023W or 0.6% power loss
Boost Converter Power loss
Figure 5. Block Diagram of Boost Converter with
Peak Current Mode (PCM)
The largest portions of power loss in the boost
converter are the internal power MOSFET, the inductor,
the Schottky diode, and the output capacitor. If the
boost converter has 90% efficiency, there is
approximately 3.3% power loss in the internal MOSFET,
1% power loss in the inductor, 5.1% power loss in the
Schottky diode, and 0.6% power loss in the output
capacitor.
Power Stage Transfer Functions
The duty to output voltage transfer function
T
is
:
p
V
(s + w )(s − w
esr
)
z2
2
n
O
T (s) =
p
= T
p0
2
d
s + 2ξw s + w
n
−r
1
C
Where
And
T
= V
,
w
=
esr
p0
O
1−D R + r
)
Cr
C
(
(
)
L
C
Loop Compensation Design
The voltage-loop gain with current loop closed sets the
stability of steady state response and dynamic
performance of transient response. The loop
compensation design is as follows:
2
1−D R + r
RL
1
−
D 2
− r
(
)
LC R + r
L
wz2
=
,
w =
n
L
(
)
L
C
2
C[r R + r + R r 1−D ] + L
(
)
(
)
L
C
L c
ξ =
,
2
2 LC R + r [r + 1−D R ]
(
)
(
)
L
C
L
β
r
=
rL
+
DrDS
+
(1
−
D)RF
rL is the inductor equivalent series resistance,
r is
C
capacitor ESR, RL is the converter load resistance,
C
is output filter capacitor, rDS is the transistor turn on
resistance, and RF is the diode forward resistance.
The duty to inductor current transfer function Tpi is:
il
s + wzi
Tpi(s)
=
=
Tpi0
2
s2
+
2ξwns
+
wn
d
V
R
+ 2r
(
1
O
L
C
Where
T
=
,
w
=
pi0
zi
Figure 4. Closed-current Loop for Boost with PCM
L R + r
L
C R / 2 + r
L C
)
(
)
C
–
–
–
Advanced Analog Technology, Inc
. –
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