ADP1875 Analog Devices, ADP1875 Datasheet - Page 28

• Manufacturer Part Number: ADP1875
• Description: Synchronous Buck Controller with Constant On-Time, Valley Current Mode, and Power Saving Mode
• Manufacturer: Analog Devices

ADP1874/ADP1875
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.
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 converter’s overall loop
gain (H) at the unity gain frequency (f
Examining each variable at high frequency enables the unity-
gain transfer function to be simplified to provide expressions
for the R
Output Filter Impedance (Z
Examining the filter’s transfer function at high frequencies
simplifies to
at the crossover frequency (s = 2πf
series resistance of the output capacitors.
Figure 86. Capacitance vs. DC Voltage Characteristics for Ceramic Capacitors
–100
H
Z
–10
–20
–30
–40
–50
–60
–70
–80
–90
20
10
FILTER
0
= V/V
COMP
0
1
=
10µF TDK 25V, X7R, 1210 C3225X7R1E106M
22µF MURATA 25V, X7R, 1210 GRM32ER71E226KE15L
47µF MURATA 16V, X5R, 1210 GRM32ER61C476KE15L
and C
R
L
=
5
×
G
1
COMP
M
1
+
X5R (16V)
×
+
s
G
(
s
10
component values.
R
CS
×
DC VOLTAGE (V
L
ESR
×
+
V
V
ESR
X7R (50V)
X5R (25V)
FILT
OUT
REF
×
15
C
)
)
C
CROSS
OUT
×
OUT
Z
DC
SW
COMP
). ESR is the equivalent
)
20
/10) when H = 1 V/V.
×
Z
FILT
25
30
Rev. 0 | Page 28 of 44
Error Amplifier Output Impedance (Z
Assuming that C
be omitted from the output impedance equation of the error
amplifier. The transfer function simplifies to
and
where f
frequency for the ADP1874.
Error Amplifier Gain (G
The error amplifier gain (transconductance) is
G
Current-Sense Loop Gain (G
The current-sense loop-gain is
where:
A
(see the Programming Resistor (RES) Detect Circuit and Valley
Current-Limit Setting sections).
R
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.
The relationship between C
follows:
The zero frequency is set to 1/4 the crossover frequency.
Combining all of the above parameters results in
where ESR is the equivalent series resistance of the output
capacitors.
R
CS
ON
m
COMP
f
CROSS
= 500 μA/V (μs)
(V/V) is programmable for 3 V/V, 6 V/V, 12 V/V, and 24 V/V
is the channel impedance of the lower-side MOSFET.
G
C
Z
f
f
f
CROSS
CROSS
ZERO
f
COMP
=
CS
COMP
CROSS
ZERO
2
+
=
, the zero frequency, is set to be 1/4 the crossover
f
=
=
=
ZERO
=
A
=
2
12
CS
12
R
1
1
π
2
f
CROSS
COMP
2
×
×
×
1
×
C2
f
×
R
SW
π
R
f
is significantly smaller than C
COMP
×
ON
SW
1
×
R
2
1
1
2
COMP
+
(A/V)
+
×
1
(
f
s
CROSS
(
C
(
s
m
R
COMP
COMP
×
×
)
L
ESR
+
f
2
ZERO
+
CS
ESR
and f
×
)
f
ZERO
C
)
C
OUT
ZERO
OUT
2
)
2
)
(zero frequency) is as
2
COMP
×
R
1
L
)
×
COMP
V
V
OUT
REF
, C
×
C2
G
can
M
1
G
CS