lm27213mtd National Semiconductor Corporation, lm27213mtd Datasheet - Page 16

• Manufacturer Part Number: lm27213mtd
• Description: Single Phase Hysteretic Buck Controller
• Manufacturer: National Semiconductor Corporation

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Component Selection
L = 0.60 µH
If the switching frequency is pushed up a bit the inductor
value may be reduced accordingly. In general for a 12A, low
voltage CPU, a value between 0.56 µH and 0.7 µH works out
well. The inductor chosen should be capable of handling the
full load current continuously. It must not hard saturate under
fault conditions. The saturation specifications for most induc-
tors indicate when the inductance has fallen off by a given
percentage. This percentage will vary by manufacturer and
is not standardized. As such, it’s best to look at the published
curves of inductance vs. DC current. If the inductor main-
tains more than 1/3 of it’s specified no load inductance under
short circuit conditions, it will probably work just fine. There
will also most likely be an RMS current rating for the inductor
as well. This relates to the heating to be expected at the
rated DC current. In most processor applications it’s safe to
assume the average DC current for thermal analysis pur-
poses will be approximately 80% of the specified maximum
load current. The inductor should be specified for at least this
value of continuous current.
OUTPUT CAPACITOR SELECTION
Once an inductor value is chosen it’s time to look at the
output capacitors. There are several possible basic ap-
proaches to take with regards to output de-coupling. It’s
possible to use ceramic capacitors exclusively. This will re-
quire a rather large number of small case size capacitors. It
is also possible to use primarily aluminum-polymer type
devices for the bulk decoupling with a relatively small num-
ber of ceramic capacitors for high frequency bypassing. The
third approach is something that’s more a combination of the
two approaches, using a moderate number of ceramic ca-
pacitor and a couple of large bulk caps. The design criteria
will be slightly different with the various approaches.
The controlling factor in a CPU core voltage regulator is
generally the load-off transient. When the processor load
drops dramatically, all the energy stored in the inductor will
get transferred into the output capacitors. The energy stored
in an inductor is L x I
tor is C x V
Where:
C
fied voltage limits.
L is the inductor value
I
occurs
I
V
condition
V
It’s recommended that the current used for I
the full load output current plus
current
From the example being examined earlier, if we assume a
12A full load, a 0.56µH inductor, an initial voltage of 1.144V,
a minimum current of 3.5A and a maximum voltage of
1.197V, the minimum allowable output capacitance is calcu-
lated as:
Since ripple current is approximately 6A,
I
max
min
max
min
max
init
C
min
is the load current after the transient has settled
is the initial output voltage at the time of the load step
= 12A + 3A = 15A
is the peak inductor current at the time the load step
is the minimum capacitance required to meet the speci-
is the maximum allowed output voltage at the low load
= 0.56µH(15A
2
C
/2. So:
min
= L(I
2
2
/2 while the energy stored in a capaci-
max
- 3.5A
2
- I
2
min
)/1.197V
1
2
⁄
2
)/(V
the estimated pk-pk ripple
max2
2
(Continued)
-1.144V
-V
init
max
2
)
2
) = 960µF
be equal to
16
This calculation assumes perfect capacitors (ESR = 0) and is
a reasonable assumption for an all ceramic solution only.
More capacitance will be required if aluminum-poly type
capacitors are used due to their higher ESR. However, that
will generally not be a problem since they tend to have large
capacitance values. If using 22 µF, 1206 case ceramic ca-
pacitors, this design would require approximately 44 capaci-
tors distributed around the processor. Only capacitors with
either X5R or X7R dielectrics should be considered. Lower
cost devices have voltage and temperature coefficients that
make them unusable in these applications. Using a small
number of physically large ceramic capacitors is not recom-
mended since the lead inductance will be excessive. They
tend not to provide adequate high frequency bypassing.
A reasonable way to reduce the capacitor count is through
the addition of several aluminum-poly type capacitors. A
typical example may be the Panasonic SP series. A 330µF,
2.5V device is available with an ESR of only 5mΩ. Adding a
pair of these will permit reducing the number of ceramic
capacitors considerably.
A reasonable estimate of the soar voltage when the load is
suddenly reduced when using primarily alminum-poly type
capacitors can be obtained from the following equation:
Where:
V(T) is the instantaneous capacitor voltage increase above
the initial DC voltage at the instant the load is reduced
C is output capacitance in µF.
Io is the inductor current at the instant the load is decreased
ESR is the output capacitor ESR
m is the inductor current down slope equal to Vout/L
The maxima occurs at :
Simply solve for Tmax and substitute into the equation for
V(T) to calculate the maximum output voltage rise. This
equation accounts for the decrease in voltage across the
ESR as the capacitors are being charged by the decreasing
inductor current.
Using numbers from the previous example:
And V
This is just a bit higher than the specification allows but does
not account for improvements expected as a result of having
a number of ceramic output capacitors on the board. The
performance of combinations of capacitors is best examined
using a circuit simulator as the mathematics gets unwieldy. A
simple model would be an inductor connected in parallel with
the output capacitors. Set the initial conditions for the peak
inductor current at full load and the capacitor voltage to the
lowest point on the load line. A current source in parallel with
the output that is set for the minimum load current will allow
the simulation of load steps that are less than 100% of full
load.
T
max
max
= (12A-2.043A/µs*0.0025Ω*660µF)/2.043A/µs =
= 0.058V
4.22µs