FAN5182_08 Datasheet, PDF (16/19 Pages) Fairchild Semiconductor – Adjustable Output, 1-, 2-, or 3-Phase Synchronous Buck Controller

Input Capacitor Selection and Input
Current di/dt Reduction
In continuous inductor current mode, the source current
of the high-side MOSFET is approximately a square
wave with a duty ratio equal to D × VOUT/VIN and an
amplitude equal to the output current. To prevent large
voltage variation, a low-ESR input capacitor, sized for
the maximum rms current, must be used. The maximum
rms capacitor current is given by:
I_CRMS = D × I_O ×
1 _−1
n×D
(30)
I_CRMS = 0.15 × 55A ×
1 _{−1 = 9.1A}
3 × 0.15
(31)
Note that manufacturers often specify capacitor ripple
current rating based on only 2,000 hours of life.
Therefore, it is advisable to further derate the capacitor
or to choose a capacitor rated at a higher temperature
than required. Several capacitors may be placed in
parallel to meet size or height requirements in the
design. In this example, the input capacitor bank is
formed by two 2,700µF, 16V aluminum electrolytic
capacitors and three 4.7µF ceramic capacitors.
To reduce the input current di/dt to a level below the
system requirement, in this example 0.1A/µs, an
additional small inductor (L > 370nH at 10A) can be
inserted between the converter and the supply bus. This
inductor serves as a filter between the converter and
the primary power source.
WARNING: During start-up with a pre-charged output
capacitor the capacitor, is discharged prior to the
converter starting. The energy that was stored in the
output capacitor is transferred to the input voltage
through the upper FET. This can cause a momentary
increase in VIN that could exceed the VIN maximum
specification for the controller or driver if there is
insufficient capacitance on VIN.
To ensure that this does not happen, use the following
equation to calculate a minimum value of CIN:
CIN COUT⋅
VO⁶
2
2
VIN_Max − VIN_Norm
(32)
Inductor DCR Temperature Correction
With the inductor's DCR being used as the sense
element, its necessary to compensate for temperature
changes in the inductor's winding if an accurate current-
limit set point is desired. Fortunately, copper has a well-
known temperature coefficient (TC) of 0.39%/°C.
If RCS is designed to have an opposite and equal
percentage of change in resistance to that of the
inductor wire, it cancels the temperature variation of the
inductor's DCR. Due to the nonlinear nature of NTC
thermistors, resistors RCS1 and RCS2 are needed. See
Figure 11 for instructions on how to linearize the NTC
and produce the desired temperature coefficient.
Figure 11. Temperature Compensation Circuit
Follow the procedures and expressions shown below
for calculation of RCS1, RCS2, and RTH (the thermistor
value at 25°C) based on a given RCS value.
1. Select an NTC according to type and value. With no
value yet, start with a thermistor with a value close
to RCS. The NTC should also have an initial
tolerance of better than 5%.
2. Based on the NTC type, find its relative resistance
value at two temperatures. The temperatures that
work well are 50°C and 90°C. These resistance
values are called A (RTH(50°C)/RTH(25°C)) and
B(RTH(90°C)/RTH(25°C)). Note that the NTC's
relative value is always 1 at 25°C.
3. Find the relative value of RCS required for each of
these temperatures. This is based on the
percentage of change needed, which, in this
example, is initially 0.39%/°C. These are called r1
(1/ (1 + TC × (T1 - 25))) and r2 (1/ (1 + TC × (T2 -
25))), where TC = 0.0039 for copper. T1 = 50°C and
T2 = 90°C are chosen. From this, calculate that r1 =
0.9112 and r2 = 0.7978.
4. Compute the relative values for RCS1, RCS2, and RTH
using Equations 33, 34, and 35.
r_CS2
=
(A
− B) × r₁ × r₂ − A × (1− B) × r₂ + B × (1− A) × r₁
A × (1 − B) × r₁ − B × (1− A) × r₂ − (A − B)
r_CS1
=
(1 −
⎜⎜⎝⎛ _1−
1
r_CS2
⎟⎟⎠⎞
−
A)
⎜⎜⎝⎛ _r1
A
− r_CS2
⎟⎟⎠⎞
r_TH
=
⎜⎜⎝⎛
1
−
1
r_CS2
1
⎟⎟⎠⎞ ^− ⎜⎜⎝⎛ _r1
1
− r_CS1
⎟⎟⎠⎞
(33)
(34)
(35)
5. Calculate RTH = rTH x RCS, then select the closest
thermistor value available. Also, compute a scaling
factor k based on the ratio of the actual thermistor
value used relative to the computed one:
k = ^RTH(ACTUAL)
R _{TH(CALCULATED)}
(36)
6. Calculate values for RCS1 and RCS2 using:
R_CS1 = R _CS × k × r_CS1
(37)
R_CS2 = R_CS × ((1 − k) + (k × r_CS2 ))
(38)
© 2005 Fairchild Semiconductor Corporation
FAN5182 • Rev. 1.1.3
16
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