NCP3102C
http://onsemi.com
13
I
RMS
= I
OUT
*1+
ra
2
12
→
(eq. 7)
10.03 A = 10 A * 1 +
26%
2
12
I
OUT
= Output current
I
RMS
= Inductor RMS current
ra = Ripple current ratio
I
PK
= I
OUT
*
1 +
ra
2
→ 11.3 A = 10 A *
1 +
26%
2
(eq. 8)
I
OUT
= Output current
I
PK
= Inductor peak current
ra = Ripple current ratio
A standard inductor should be found so the inductor will
be rounded to 3.3 mH. The inductor should support an RMS
current of 10.03 A and a peak current of 11.3 A.
The final selection of an output inductor has both
mechanical and electrical considerations. From a
mechanical perspective, smaller inductor values generally
correspond to smaller physical size. Since the inductor is
often one of the largest components in the regulation system,
a minimum inductor value is particularly important in space
constrained applications. From an electrical perspective, the
maximum current slew rate through the output inductor for
a buck regulator is given by Equation 9.
SlewRate
LOUT
=
V
CC
− V
OUT
L
OUT
→ 2.64 A∕ms =
12 V − 3.3 V
3.3 mH
(eq. 9)
L
OUT
= Output inductance
V
CC
= Input voltage
V
OUT
= Output voltage
Equation 9 implies that larger inductor values limit the
regulator’s ability to slew current through the output
inductor in response to outputload transients. Consequently,
output capacitors must supply the load current until the
inductor current reaches the output load current level.
Reduced inductance to increase slew rates results in larger
values of output capacitance to maintain tight output voltage
regulation. In contrast, smaller values of inductance
increase the regulator’s maximum achievable slew rate and
decrease the necessary capacitance at the expense of higher
ripple current. The peak--to--peak ripple current is given by
the following equation:
I
PP
=
V
OUT
1 − D
L
OUT
*F
SW
→
(eq. 10)
2.64 A =
3.3 V
1 − 27.5%
3.3 mH*275kHz
D = Duty ratio
F
SW
= Switching frequency
I
PP
= Peak--to--peak current of the inductor
L
OUT
= Output inductance
V
OUT
= Output voltage
From Equation 10 the ripple current increases as L
OUT
decreases, emphasizing the trade--off between dynamic
response and ripple current.
The power dissipation of an inductor falls into two
categories: copper and core losses. Copper losses can be
further categorized into DC losses and AC losses. A good
first order approximation of the inductor losses can be made
using the DC resistance as shown below:
LP
CU_DC
= I
RMS
2
* DCR → 171 mW = 10.03
2
*1.69mΩ
(eq. 11)
I
RMS
= Inductor RMS current
DCR = Inductor DC resistance
LP
CU_DC
= Inductor DC power dissipation
The core losses and AC copper losses will depend on the
geometry of the selected core, core material, and wire used.
Most vendors will provide the appropriate information to
make accurate calculations of the power dissipation, at
which point the total inductor losses can be captured by the
equation below:
LP
tot
= LP
CU_DC
+ LP
CU_AC
+ LP
Core
→
(eq. 12)
352 mW = 171 mW + 19 mW + 162 mW
LP
CU_DC
= Inductor DC power dissipation
LP
CU_AC
= Inductor AC power dissipation
LP
Core
= Inductor core power dissipation
Output Capacitor Selection
The important factors to consider when selecting an
output capacitor are DC voltage rating, ripple current rating,
output ripple voltage requirements, and transient response
requirements.
The output capacitor must be rated to handle the ripple
current at full load with proper derating. The RMS ratings
given in datasheets are generally for lower switching
frequency than used in switch mode power supplies, but a
multiplier is usually given for higher frequency operation.
The RMS current for the output capacitor can be calculated
below:
CO
RMS
= I
OUT
ra
12
→ 0.75 A = 10 A
26%
12
(eq. 13)
Co
RMS
= Output capacitor RMS current
I
OUT
= Output current
ra = Ripple current ratio
The maximum allowable output voltage ripple is a
combination of the ripple current selected, the output
capacitance selected, the Equivalent Series Inductance
(ESL), and Equivalent Series Resistance (ESR).
The main component of the ripple voltage is usually due
to the ESR of the output capacitor and the capacitance
selected, which can be calculated as shown in Equation 14:
