Datasheet

ADP1874/ADP1875 Data Sheet
Rev. A | Page 28 of 44
Ceramic capacitors are known to have low ESR. However, there
is a trade-off in using the popular X5R capacitor technology
because up to 80% of its capacitance may be lost due to derating
as the voltage applied across the capacitor is increased (see
Figure 86). Although X7R series capacitors can also be used, the
available selection is limited to 22 µF maximum.
20
10
0
–10
–20
–30
–40
–50
–60
–70
–80
–90
–100
0 5 10 15 20 25
30
CAPACITANCE CHARGE (%)
DC VOLTAGE (V
DC
)
X7R (50V)
X5R (25V)
X5R (16V)
10µF TDK 25V, X7R, 1210 C3225X7R1E106M
22µF MURATA 25V, X7R, 1210 GRM32ER71E226KE15L
47µF MURATA 16V, X5R, 1210 GRM32ER61C476KE15L
09347-078
Figure 86. Capacitance vs. DC Voltage Characteristics for Ceramic Capacitors
Electrolytic capacitors satisfy the bulk capacitance requirements
for most high current applications. However, because the ESR
of electrolytic capacitors is much higher than that of ceramic
capacitors, several MLCCs should be mounted in parallel with
the electrolytic capacitors to reduce the overall series resistance.
COMPENSATION NETWORK
Due to its current-mode architecture, the ADP1874/ADP1875
require Type II compensation. To determine the component
values needed for compensation (resistance and capacitance
values), it is necessary to examine the converters overall loop
gain (H) at the unity gain frequency (f
SW
/10) when H = 1 V/V.
FILT
COMP
OUT
REF
CS
M
ZZ
V
V
GGH ××××== V/V1
Examining each variable at high frequency enables the unity-
gain transfer function to be simplified to provide expressions
for the R
COMP
and C
COMP
component values.
Output Filter Impedance (Z
FILT
)
Examining the filter’s transfer function at high frequencies
simplifies to
OUT
L
OUT
L
FILTER
CESRRs
CESRs
RZ
)(1
1
++
××+
×=
at the crossover frequency (s = 2πf
CROSS
). ESR is the equivalent
series resistance of the output capacitors.
Error Amplifier Output Impedance (Z
COMP
)
Assuming that C
C2
is significantly smaller than C
COMP
, C
C2
can
be omitted from the output impedance equation of the error
amplifier. The transfer function simplifies to
22
ZERO
CROSS
CROSS
COMP
COMP
ff
f
R
Z +×=
and
SWCROSS
ff ×=
12
1
where f
ZERO
, the zero frequency, is set to be 1/4 the crossover
frequency for the ADP1874.
Error Amplifier Gain (G
m
)
The error amplifier gain (transconductance) is
G
m
= 500 µA/V (µs)
Current-Sense Loop Gain (G
CS
)
The current-sense loop-gain is
ONCS
CS
RA
G
×
=
1
(A/V)
where:
A
CS
(V/V) is programmable for 3 V/V, 6 V/V, 12 V / V, and 24 V/V
(see the Programming Resistor (RES) Detect Circuit and Valley
Current-Limit Setting sections).
R
ON
is the channel impedance of the lower side MOSFET.
Crossover Frequency
The crossover frequency is the frequency at which the overall
loop (system) gain is 0 dB (H = 1 V/V). It is recommended for
current-mode converters, such as the ADP1874, that the user
set the crossover frequency between 1/10 and 1/15 the
switching frequency.
SWCROSS
ff
12
1
=
The relationship between C
COMP
and f
ZERO
(zero frequency) is as
follows:
COMPCOMP
ZERO
CR
f
××π
=
2
1
The zero frequency is set to 1/4 the crossover frequency.
Combining all of the above parameters results in
( )
( )
CS
MREF
OUT
L
OUT
OUT
L
ZERO
CROSS
CROSS
COMP
GGV
V
R
CESRs
CESRRs
ff
f
R
11
1
)(1
2
2
2
2
22
×××
××+
++
×
+
=
where ESR is the equivalent series resistance of the output
capacitors.
ZERO
COMP
COMP
fR
C
××π×
=
2
1