Datasheet

ADP1877 Data Sheet
Rev. D | Page 22 of 32
Then the power loss in the low-side MOSFET is
BODYDIODECLSLS
PPP +=
Note that MOSFET, R
DSON
, increases with increasing
temperature with a typical temperature coefficient of 0.4%/
o
C.
The MOSFET junction temperature rise over the ambient
temperature is
T
J
= T
A
+ θ
JA
× P
D
where:
θ
JA
is the thermal resistance of the MOSFET package.
T
A
is the ambient temperature.
P
D
is the total power dissipated in the MOSFET.
LOOP COMPENSATION
As with most current mode step-down controller, a transcon-
ductance error amplifier is used to stabilize the external voltage
loop. Compensating the ADP1877 is fairly easy; an RC
compensator is needed between COMP and AGND. Figure 34
shows the configuration of the compensation components:
R
COMP
, C
COMP
, and CC2. Because C
C2
is very small compared to
C
COMP
, to simplify calculation, C
C2
is ignored for the stability
compensation analysis.
COMPx
ADP1877
AGND
C
COMP
R
COMP
C
C2
0.6V
FBx
G
m
08299-011
Figure 34. Compensation Components
The open loop gain transfer function at angular frequency, s, is
given by
)()()( sZsZ
V
V
GGsH
FILTER
COMP
OUT
REF
CS
m
××××=
(1)
where:
G
m
is the transconductance of the error amplifer, 500 µs.
G
CS
is the tranconductance of the current sense amplifier.
Z
COMP
is the impedance of the compensation network.
Z
FILTER
is the impedance of the output filter.
V
REF
= 0.6 V
G
CS
with units of A/V is given by
MINDSONCS
CS
RA
G
_
1
×
=
(2)
where:
A
CS
is the current sense gain of either 3 V/V, 6 V/V, 12 V/V, or
24 V/V set by the gain resistor between DL and PGND.
R
DSON_MIN
is the the low-side MOSFET minimum on resistance.
Because the zero produced by the ESR of the output capacitor is
not needed to stabilize the control loop, the ESR is ignored for
analysis. Then Z
FILTER
is given by
OUT
FILTER
sC
Z
1
=
(3)
Because C
C2
is very small relative to C
COMP
, Z
COMP
can be written as
COMP
COMPCOMP
COMP
COMPCOMP
sC
CsR
sC
RZ
×+
=+=
1
1
(4)
At the crossover frequency, the open loop transfer function is
unity of 0 dB, H (f
CROSS
) = 1. Combining Equation 1 and
Equation 3, Z
COMP
at the crossover frequency can be written as
))(
2
()(
REF
OUTOUT
CS
m
CROSS
CROSSCOMP
V
VC
GG
f
fZ
×
×
×
π
=
(5)
The zero produced by R
COMP
and C
COMP
is
COMPCOMP
ZERO
CR
f
×π
=
2
1
(6)
At the crossover frequency, Equation 4 can be shown as
CROSS
ZERO
CROSS
COMPCROSSCOMP
f
ff
RfZ
+
×=)(
(7)
Combining Equation 5 and Equation 7 and solving for R
COMP
gives
)()
2
(
REF
OUTOUT
CS
m
CROSS
ZERO
CROSS
CROSS
COMP
V
VC
GG
f
ff
f
R
×
×
×
×π
×
+
=
(8)
Choose the crossover and zero frequencies as follows:
13
SW
CROSS
f
f =
(9)
655
SWCROSS
ZERO
ff
f ==
(10)
Substituting Equation 2, Equation 9, and Equation 10 into
Equation 8 yields
)()
2
(83.0
REF
OUTOUT
m
CROSS
DSONCSCOMP
V
VC
G
f
RAR
×
×
×π
××=
(11)
where:
G
m
is the transconductance of the error amplifer, 500 µs.
A
CS
is the current sense gain of 3 V/V, 6 V/V, 12 V/V or 24 V/V.
R
DSON
is on resistance of the low-side MOSFET.
V
REF
= 0.6 V
And combining Equation 6 and Equation 10 yields
CROSSCOMP
COMP
fR
C
×π
=
2
(12)
And lastly set C
C2
to
COMPCCOMP
CCC ×≤≤×
10
1
20
1
2
(13)