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NCP5322A
http://onsemi.com
19
This formula assumes steadystate conditions with no
more than one phase on at any time. The second term in
Equation 4 is the total ripple current seen by the output
capacitors. The total output ripple current is the “time
summation” of the two individual phase currents that are
180 degrees outofphase. As the inductor current in one
phase ramps upward, current in the other phase ramps
downward and provides a canceling of currents during part
of the switching cycle. Therefore, the total output ripple
current and voltage are reduced in a multiphase converter.
3. Input Capacitor Selection
The choice and number of input capacitors is primarily
determined by their voltage and ripple current ratings. The
designer must choose capacitors that will support the worst
case input voltage with adequate margin. To calculate the
number of input capacitors one must first determine the total
RMS input ripple current. To this end, begin by calculating
the average input current to the converter:
IIN,AVG
IO,MAX
D
(5)
where:
D is the duty cycle of the converter, D = V
OUT
/V
IN
.
η
is the specified minimum efficiency.
I
O,MAX
is the maximum converter output current.
The input capacitors will discharge when the control FET
is ON and charge when the control FET is OFF as shown in
Figure 15.
I
C,MAX
I
C,MIN
0 A
I
IN,AVG
FET On,
Caps Discharging
FET Off,
Caps Charging
t
ON
T/2
I
C,IN
= I
C,MAX
I
C,MIN
Figure 15. Input Capacitor Current for a
TwoPhase Converter
The following equations will determine the maximum and
minimum currents delivered by the input capacitors:
IC,MAX
ILo,MAX
IIN,AVG
(6)
IC,MIN
ILo,MIN
IIN,AVG
(7)
I
Lo,MAX
is the maximum output inductor current:
ILo,MAX
IO,MAX2
ILo2
(8)
I
Lo,MIN
is the minimum output inductor current:
ILo,MIN
IO,MAX2
ILo2
(9)
I
Lo
is the peaktopeak ripple current in the output
inductor of value Lo:
ILo
(VIN
VOUT)
D (Lo
fSW)
(10)
For the twophase converter, the input capacitor(s) RMS
current is then:
ICIN,RMS
[2D
(IC,MIN2
IC,MIN
IC,IN
IC,IN23)
IIN,AVG2
(1
2D)]1 2
(11)
Select the number of input capacitors (N
IN
) to provide the
RMS input current (I
CIN,RMS
) based on the RMS ripple
current rating per capacitor (I
RMS,RATED
):
NIN
ICIN,RMSIRMS,RATED
(12)
For a twophase converter with perfect efficiency (
η
= 1),
the worst case input ripplecurrent will occur when the
converter is operating at a 25% duty cycle. At this operating
point, the parallel combination of input capacitors must
support an RMS ripple current equal to 25% of the
converter’s DC output current. At other duty cycles, the
ripplecurrent will be less. For example, at a duty cycle of
either 10% or 40%, the twophase input ripplecurrent will
be approximately 20% of the converter’s DC output current.
In general, capacitor manufacturers require derating to the
specified ripplecurrent based on the ambient temperature.
More capacitors will be required because of the current
derating. The designer should be cognizant of the ESR of the
input capacitors. The input capacitor power loss can be
calculated from:
PCIN
ICIN,RMS2
ESR_per_capacitor NIN
(13)
Low ESR capacitors are recommended to minimize losses
and reduce capacitor heating. The life of an electrolytic
capacitor is reduced 50% for every 10
°
C rise in the
capacitor’s temperature.
4. Input Inductor Selection
The use of an inductor between the input capacitors and
the power source will accomplish two objectives. First, it
will isolate the voltage source and the system from the noise
generated in the switching supply. Second, it will limit the
inrush current into the input capacitors at power up. Large
inrush currents will reduce the expected life of the input
capacitors. The inductor’s limiting effect on the input
current slew rate becomes increasingly beneficial during
load transients.
The worst case input current slew rate will occur during
the first few PWM cycles immediately after a stepload
change is applied as shown in Figure 16. When the load is
applied, the output voltage is pulled down very quickly.
Current through the output inductors will not change
instantaneously so the initial transient load current must be
conducted by the output capacitors. The output voltage will
step downward depending on the magnitude of the output