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NCP5314
http://onsemi.com
20
I
C,MAX
I
C,MIN
0 A
I
IN,AVG
FET On,
Caps Discharging
FET Off,
Caps Charging
t
ON
T/4
Δ
I
C,IN
= I
C,MAX
I
C,MIN
Figure 24. Input Capacitor Current for a
FourPhase Converter
Δ
I
Lo
is the peaktopeak ripple current in the output
inductor of value Lo:
ILo
(VIN
VOUT)
D (Lo
fSW)
(10)
For the fourphase converter, the input capacitor(s) RMS
current is then:
ICIN,RMS
[4D
(IC,MIN2
IC,MIN
IC,IN
IC,IN23)
IIN,AVG2
(1
4D)]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 fourphase converter with perfect efficiency (
η
= 1),
the worst case input ripplecurrent will occur when the
converter is operating at a 12.5% duty cycle. At this
operating point, the parallel combination of input capacitors
must support an RMS ripple current equal to 12.5% of the
converter’s DC output current. At other duty cycles, the
ripplecurrent will be less. For example, at a duty cycle of
either 6% or 19%, the fourphase input ripplecurrent will
be approximately 10% 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 know 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.
5. 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 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 25. 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
current (I
O,MAX
), the per capacitor ESR of the output
capacitors (ESR
OUT
) and the number of the output
capacitors (N
OUT
) as shown in Figure 25. Assuming the load
current is shared equally between all phases, the output
voltage at full transient load will be:
VOUT,FULLLOAD
VOUT,NOLOAD
(14)
(IO,MAX
)
ESROUTNOUT
When the control MOSFET (Q1 in Figure 25) turns ON,
the input voltage will be applied to the opposite terminal of
the output inductor (the SWNODE). At that instant, the
voltage across the output inductor can be calculated as:
VLo
VIN
VIN
VOUT,FULLLOAD
VOUT,NOLOAD
(IO,MAX
)
(15)
ESROUTNOUT
The differential voltage across the output inductor will
cause its current to increase linearly with time. The slew rate
of this current can be calculated from:
dILodt
VLoLo
(16)
Current changes slowly in the input inductor so the input
capacitors must initially deliver the vast majority of the
input current. The amount of voltage drop across the input
capacitors (
Δ
V
Ci
) is determined by the number of input
capacitors (N
IN
), their per capacitor ESR (ESR
IN
) and the
current in the output inductor according to:
VCi
ESRINNIN
ESRINNIN
dILodt
dILodt
tON
D fSW
(17)
Before the load is applied, the voltage across the input
inductor (V
Li
) is very small and the input capacitors charge
to the input voltage V
IN
. After the load is applied, the voltage
drop across the input capacitors,
Δ
V
Ci
, appears across the
input inductor as well. Knowing this, the minimum value of
the input inductor can be calculated from:
LiMIN
VLi
VCi
dIINdtMAX
dIINdtMAX
(18)
dI
IN
/dt
MAX
is the maximum allowable input current slew
rate.