Datasheet
Data Sheet ADP1878/ADP1879
Rev. B | Page 25 of 40
Ceramic capacitors are known to have low ESR. However, there
is a trade-off in using the popular X5R capacitor technology
because as much as 80% of its capacitance may be lost due to
derating as the voltage applied across the capacitor is increased
(see Figure 82). Although X7R series capacitors can also be
used, the available selection is limited to 22 µF maximum.
Figure 82. 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 capaci-
tors, mount several MLCCs in parallel with the electrolytic
capacitors to reduce the overall series resistance.
COMPENSATION NETWORK
Due to its current-mode architecture, the ADP1878/ADP1879
require Type II compensation. To determine the component
values needed for compensation (resistance and capacitance
values), it is necessary to examine the overall loop gain (H) of the
converter at the unity-gain frequency (f
SW
/10) when H = 1 V/V:
= 1 V V
=
×
×
×
×
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 transfer function of the filter at high frequencies
simplifies to
=
×
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 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
=
×
+
and
=
1
12
×
where f
ZERO
, the zero frequency, is set to be 1/4
th
of the crossover
frequency for the ADP1878.
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
=
1
×
(
)
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 low-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 ADP1878
, that the user set
the crossover frequency between 1/10
th
and 1/15
th
of the switching
frequency.
=
1
12
The relationship between C
COMP
and f
ZERO
(zero frequency) is as
follows:
=
1
2 ×
×
The zero frequency is set to 1/4
th
of the crossover frequency.
Combining all of the above parameters results in
=
+
×
1
+ (
(
+
)
)
1
+ ( × ×
)
×
1
×
×
1
where ESR is the equivalent series resistance of the output
capacitors.
=
1
2 × ×
×
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
09441-082