Datasheet

Data Sheet ADP1870/ADP1871
Rev. B | Page 25 of 44
Ceramic capacitors are known to have low ESR. However, the
trade-off of using X5R technology is that up to 80% of its capaci-
tance might be lost due to derating as the voltage applied across
the capacitor is increased (see Figure 80). Although X7R series
capacitors can also be used, the available selection is limited to
only up to 22 µF.
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
08730-078
Figure 80. Capacitance vs. DC Voltage Characteristics for Ceramic Capacitors
Electrolytic capacitors satisfy the bulk capacitance requirements
for most high current applications. Because the ESR of electrolytic
capacitors is much higher than that of ceramic capacitors, when
using electrolytic capacitors, several MLCCs should be mounted
in parallel to reduce the overall series resistance.
COMPENSATION NETWORK
Due to their current-mode architecture, the ADP1870/ADP1871
require Type II compensation. To determine the component
values needed for compensation (resistance and capacitance
values), it is necessary to examine the converter’s overall loop
gain (H) at the unity gain frequency (f
SW
/10) when H = 1 V/V:
FILT
COMP
REF
OUT
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
FILTER
sC
Z
1
=
at the crossover frequency (s = 2πf
CROSS
).
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
CROSS
ZERO
CROSSCOMP
COMP
f
ffR
Z
)( +
=
and
SWCROSS
ff ×=
12
1
where f
ZERO
, the zero frequency, is set to be 1/4
th
of the crossover
frequency for the ADP1870.
Error Amplifier Gain (G
M
)
The error amplifier gain (transconductance) is
G
M
= 500 µA/V
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). For current-mode
converters, such as the ADP1870, it is recommended that the
user set the crossover frequency between 1/10
th
and 1/15
th
of 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
th
of the crossover frequency.
Combining all of the above parameters results in
REF
OUT
CS
M
OUT
CROSS
ZERO
CROSS
CROSS
COMP
V
V
GG
Cf
ff
f
R ×
π
×
+
=
2
ZERO
COMP
COMP
fR
C
××π×
=
2
1