### FAIRCHILD AB-12

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Application Bulletin AB-12
Insight into Inductor Current
Introduction
The design of the main power inductor in a switching power
supply provides many challenges to the engineer. Not only
must an inductance value be chosen, but also how much current the inductor can handle, the winding resistance,
mechanical factors, etc. This Application Bulletin looks at
one of these considerations: understanding the effects of DC
current on an inductor. This will provide some of the background necessary to making an informed selection of an
inductor.
Understanding the Function of the
Inductor
An inductor is often described as being part of an LC filter at
the output of a switching power supply (with the “C” being
the output capacitors). Although this is correct, for the purposes of understanding the design of an inductor it is necessary to have deeper insight into the inductor’s operation.
In a buck converter (the type used by all Fairchild switching
controllers), one end of the inductor is attached to the output
voltage, which is DC. The other end is alternately attached to
the input voltage or ground, the alternation occurring at the
switching frequency (see Figure 1):
controller being used, this may be done in one of two ways:
the connection to ground can be made with a diode, or with
another (“low-side”) MOSFET. In the latter case, the converter is called “synchronous”.
Now consider what happens to the inductor’s current during
these two states. In State 1, the input voltage is being applied
to one side of the inductor, and the output voltage to the
other side. For a buck converter, the input voltage is necessarily larger than the output voltage, and so there is a net positive voltage across the inductor. Conversely, in State 2,
ground is applied to the side of the inductor that was previously attached to the input voltage. For a buck converter, the
output voltage is necessarily positive, and so there is a net
negative voltage across the inductor.
We recall that the current through an inductor changes
according to
dI
V = L ----dt
Thus when the voltage across the inductor is positive
(State 1), the inductor current increases; when the voltage
across the inductor is negative (State 2), the inductor current
decreases. The net current through the inductor is shown in
Figure 2:
VIN
State 1
DC Output Voltage
+
IDC
IPP
State 2
Figure 1. Basic Switching Action of a Converter
State 1
In State 1, the connection is made to the input voltage: this is
done by turning on a (“high-side”) MOSFET. In State 2,
the connection is made to ground. Depending on the type of
State 2
Figure 2. Inductor Current
Rev 1.0.0.
AB-12
Inspection of this figure shows that the maximum current
that the inductor ever sees consists of the DC current, plus
half of the peak-to-peak current due to the switching. This
latter is called the ripple current. Using the equation above,
we can calculate this peak current as:
I PP
1 ( V in – V out ) ´ t on
I PK = I DC + ------ = I DC + --- ------------------------------------------- =
L
2
2
1 ( V in – V out ) ´ T ´ DC
I DC + --- ------------------------------------------------------L
2
where ton is the time that the converter is in State 1, T is the
switching period (one over the switching frequency) and DC
is the Duty Cycle, that is, the percentage of time that the converter is in State 1.
APPLICATION BULLETIN
Inductor Core Saturation
Having now calculated the peak inductor current, we can
look at what this does to the inductor. The fundamental fact
to know is that as the current through an inductor increases,
its inductance decreases. This is due to the underlying physics of the core material. How much the inductance decreases
is the important question: if it decreases too much, the converter may not work properly any more. The current at which
the inductor does not function properly in the circuit any
more is called the “saturation current”, and is a fundamental
parameter of the inductor.
In practice, the switching power inductors used for converters always have a “soft” saturation. What this means can be
understood by viewing a plot of actually measured inductance vs. DC current:
9
Synchronous Converter:
I PK
1 ( V in – V out – I ´ R ) ( V out + I ´ R )
= I DC + --- ------------------------------------------------ ----------------------------------T
L
V in
2
8
7
Inductance (mH)
Caveat: This calculation has assumed that the voltage drops
due to the various components (such as the resistive drop of
the MOSFETs and inductor or current sense resistor, or the
forward voltage of a schottky in a non-synchronous converter) are negligible compared to the input and output voltages. If they are not, use these more accurate equations
6
5
4
3
2
1
0
Nonsynchronous Converter:
1 ( V in – V out – I ´ R ) ( V out + I ´ R S + V f )
I PK = I DC + --- ------------------------------------------------ -------------------------------------------------- T
L
( V in – I ´ R M + V f )
2
where Rs is the sum of the sense resistor’s resistance and the
winding resistance of the inductor, Vf is the forward drop of
the schottky, and R is the sum of the resistance of Rs and the
on-resistance of the MOSFET, R = Rs + RM.
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Current (A)
This inductor has a “soft” saturation characteristic because
its inductance doesn’t radically decrease at some particular
current: as the current increases, the inductance very gradually tails off.
NOTE: The relatively large drop in inductance shown in this
curve is typical of most inductors such as toroids, gapped Ecores, etc. However, rod core inductors show almost no
change in inductance at almost any current.
Given this soft saturation characteristic, it is apparent that in
most converters, it is adequate to specify the inductor’s minimum inductance at the DC output current; adding a little bit
of extra current due to the ripple doesn’t greatly affect the
inductance. In most applications, ripple current will be relatively small anyway, since it directly impacts output ripple
voltage. Thus it is common practice in the industry to specify
inductance at the DC output current, and to ignore the ripple
current in the spec.
2
APPLICATION BULLETIN
AB-12
Notes:
3
AB-12
APPLICATION BULLETIN
LIFE SUPPORT POLICY
FAIRCHILD’S PRODUCTS ARE NOT AUTHORIZED FOR USE AS CRITICAL COMPONENTS IN LIFE SUPPORT DEVICES
OR SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF THE PRESIDENT OF FAIRCHILD SEMICONDUCTOR
CORPORATION. As used herein:
1. Life support devices or systems are devices or systems
which, (a) are intended for surgical implant into the body,
or (b) support or sustain life, and (c) whose failure to
perform when properly used in accordance with
instructions for use provided in the labeling, can be
reasonably expected to result in a significant injury of the
user.
2. A critical component in any component of a life support
device or system whose failure to perform can be
reasonably expected to cause the failure of the life support
device or system, or to affect its safety or effectiveness.
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Ó 1998 Fairchild Semiconductor Corporation
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