LTC3866 Datasheet, PDF (29/36 Pages) Linear Technology – Current Mode Synchronous Controller for Sub Milliohm DCR Sensing

LTC3866
Applications Information
This design will require 0.33µH. The Würth 744301033,
0.32µH inductor is chosen. At the nominal input voltage
(12V), the ripple current will be:
∆I_L(NOM)
=
V_OUT
f•L
⎛
⎝⎜⎜^1−
V_OUT
V_IN(NOM)
⎞
⎠⎟⎟
It will have 10A (33%) ripple. The peak inductor current
will be the maximum DC value plus one-half the ripple
current, or 35A.
The minimum on-time occurs at the maximum V_IN, and
should not be less than 90ns:
t_ON(MIN)
=
V_OUT
V_{IN(MAX )}f
=
1.5V
20V(400kHz)
=
187ns
DCR sensing is used in this circuit. If C1 and C2 are chosen
to be 220nF, based on the chosen 0.33µH inductor with
0.32mΩ DCR, R1 and R2 can be calculated as:
R1= ^L = 4.69k
DCR • C1
R2
=
DCR
L
• C2
•
5
=
937Ω
Choose R1 = 4.64k and R2 = 931Ω.
The maximum DCR of the inductor is 0.34Ω. The
V_SENSE(MAX) is calculated as:
V_SENSE(MAX) = I_PEAK • DCR_MAX = 12mV
The current limit is chosen to be 15mV. If temperature
variation is considered, please refer to Inductor DCR
Sensing Temperature Compensation with NTC Thermistor.
The power dissipation on the topside MOSFET can be
easily estimated. Choosing an Infineon BSC050NE2LS
MOSFET results in: R_DS(ON) = 7.1mΩ (max), V_MILLER =
2.8V, C_MILLER ≅ 35pF. At maximum input voltage with T_J
(estimated) = 75°C:
P_MAIN
=
1.5V
20V
(^30A)²
[¹⁺
(0.005)(75°C
–
25°C)_]
•
(^0.0071Ω)
+
(^20V
)²
⎛
⎝⎜
30A
2
⎞⎠⎟_(2Ω)
(^35pF)
•
⎡
⎣⎢5.5V
1
–
2.8V
+
1
2.8V
⎤⎦⎥_(400kHz)
= 599mW + 122mW
= 721mW
For a 0.32mΩ DCR, a short-circuit to ground will result
in a folded back current of:
I_SC
=
(^{1/ 3})^15mV
0.0032Ω
–
1^⎛
2
⎜
⎝
90ns(20V) ^⎞
0.33µH
⎟
⎠
=
12.9 A
An Infineon BSC010NE2LS, R_DS(ON) = 1.1mΩ, is chosen
for the bottom FET. The resulting power loss is:
P_SYNC
=
20V – 1.5V
20V
(^30A
)²
•
⎡⎣_{1+ (0.005) • (75°C – 25°C)}⎤⎦ _{• 0.0011Ω}
P_SYNC = 1.14W
C_IN is chosen for an equivalent RMS current rating of at
least 13.7A. C_OUT is chosen with an equivalent ESR of
4.5mΩ for low output ripple. The output ripple in continu-
ous mode will be highest at the maximum input voltage.
The output voltage ripple due to ESR is approximately:
V_ORIPPLE = R_ESR (∆I_L) = 0.0045Ω • 10A = 45mV_P-P
Further reductions in output voltage ripple can be made
by placing a 100µF ceramic capacitor across C_OUT.
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