CS51311
Application Information: continued
their high saturation flux density and have low loss at high
frequencies, a distributed gap and exhibit very low EMI.
The inductor value can be determined by:
L=
(V
IN
−
V
OUT
)
×
t
TR
∆Ι
,
where I
L(VALLEY)
= inductor valley current.
Given the requirements of an application such as a buck
converter, it is found that a toroid powdered iron core is
quite suitable due to its low cost, low core losses at the
switching frequency, and low EMI.
Step 5: Selection of the Input Capacitors
These components must be selected and placed carefully to
yield optimal results. Capacitors should be chosen to pro-
vide acceptable ripple on the input supply lines. A key
specification for input capacitors is their ripple current rat-
ing. The input capacitor should also be able to handle the
input RMS current I
IN(RMS)
.
The combination of the input capacitors C
IN
discharges
during the on-time.
The input capacitor discharge current is given by:
I
CINDIS(RMS)
=
(I
L(PEAK)2
+ (I
L(PEAK)
×
I
L(VALLEY)
) + I
L(VALLEY)2
×
D
3
where
I
CINDIS(RMS)
= input capacitor discharge current;
I
L(PEAK)
= inductor peak current;
I
L(VALLEY)
= inductor valley current.
C
IN
charges during the off-time, the average current
through the capacitor over one switching cycle is zero:
I
CIN(CH)
= I
CIN(DIS)
×
,
D
1
−
D
,
,
where
V
IN
= input voltage;
V
OUT
= output voltage;
t
TR
= output voltage transient response time (assigned
by the designer);
∆I
= load transient.
The inductor ripple current can then be determined:
∆I
L
=
V
OUT
×
T
OFF
L
,
where
∆I
L
= inductor ripple current;
V
OUT
= output voltage;
T
OFF
= switch Off-Time;
L = inductor value.
The designer can now verify if the number of output
capacitors from step 2 will provide an acceptable output
voltage ripple (1% of output voltage is common). The for-
mula below is used:
∆I
L
=
Rearranging we have:
ESR
MAX
=
∆V
OUT
∆I
L
∆V
OUT
ESR
MAX
,
where
ESR
MAX
= maximum allowable ESR;
∆V
OUT
= 1%
×
V
OUT
= maximum allowable output volt-
age ripple ( budgeted by the designer );
∆I
L
= inductor ripple current;
V
OUT
= output voltage.
The number of output capacitors is determined by:
ESR
CAP
Number of capacitors =
,
ESR
MAX
where ESR
CAP
= maximum ESR per capacitor (specified in
manufacturer’s data sheet).
The designer must also verify that the inductor value
yields reasonable inductor peak and valley currents (the
inductor current is a triangular waveform):
I
L(PEAK)
= I
OUT
+
where
I
L(PEAK)
= inductor peak current;
I
OUT
= load current;
∆I
L
= inductor ripple current.
I
L(VALLEY)
= I
OUT
−
∆I
L
2
,
12
∆I
L
2
,
where
I
CIN(CH)
= input capacitor charge current;
I
CIN(DIS)
= input capacitor discharge current;
D = Duty Cycle.
The total Input RMS current is:
I
CIN(RMS)
=
(I
CIN(DIS)2
×
D) + (I
CIN(CH)2
×
(1
−
D))
The number of input capacitors required is then deter-
mined by:
N
CIN
=
I
CIN(RMS)
,
I
RIPPLE
where
N
CIN
= number of input capacitors;
I
CIN(RMS)
= total input RMS current;
I
RIPPLE
= input capacitor ripple current rating (specified
in manufacturer’s data sheets).
The total input capacitor ESR needs to be determined in
order to calculate the power dissipation of the input capac-
itors:
ESR
CIN
=
ESR
CAP
,
N
CIN
where
ESR
CIN
= total input capacitor ESR;
ESR
CAP
= maximum ESR per capacitor (specified in
manufacturer’s data sheets);
N
CIN
= number of input capacitors.
CHERRY [ CHERRY SEMICONDUCTOR CORPORATION ]
