LTC3862_15 Datasheet, PDF (31/42 Pages) Linear Technology – Multi-Phase Current Mode Step-Up DC/DC Controller

LTC3862
Applications Information
in high duty cycle applications. Figure 25 illustrates the
normalized input ripple current, where:
I_NORM
=
V_IN
L•f
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0
0
1-PHASE
2-PHASE
0.2
0.4
0.6
0.8
1.0
DUTY CYCLE
3862 F25
Figure 25. Normalized Input Peak-to-Peak Ripple Current
A Design Example
Consider the LTC3862 application circuit is shown in Fig-
ure 26a. The output voltage is 48V and the input voltage
range is 5V to 36V. The maximum output current is 5A
when the input voltage is 24V to 36V. Below 24V, current
limit will linearly reduce the maximum load to 1A at 5V
in (see Figure 26b).
1. The duty cycle range (where 5A is available at the
output) is:
D_MAX
=


V_O + V_F
V_O +
– V_IN 
V_{F }
=


48V + 0.5V – 24V 
48V + 0.5V 
=
50.5%
D_MIN

=


48V + 0.5V – 36V 
48V + 0.5V 
=
25.8%
2. The operating frequency is chosen to be 300kHz so
the period is 3.33μs. From Figure 6, the resistor from
the FREQ pin to ground is 45.3k.
3. The minimum on-time for this application operating
in CCM is:

t_ON(MIN)
=
1
f
•


V_O
+
V_F – V_IN(MAX) 
V_O + V_F

=
1
300kHz
•


48V + 0.5V – 36V 
48V + 0.5V 
=
859ns
The maximum DC input current is:
I_IN(MAX) =
I_O(MAX)
1– D_MAX
=
5A
1– 0.505
= 10.1A
4. A ripple current of 40% is chosen so the peak current
in each inductor is:
I_IN(PK)
=
1
n
•


1–
χ
2 
•
I_O(MAX)
1– D_MAX

=
1
2
•


1+
0.4
2 
•
1–
5A
0.505
=
6.06A
5. The inductor ripple current is:
∆I_L

=
χ
n
• ^IO(MAX)
1– D_MAX
=
0.4 _• 5A
2 1– 0.505
= 2.02A
6. The inductor value is therefore:
L
=
V_IN(MIN)
∆I_L • f
• D_MAX
=
24V
2.02A • 300kHz
•
0.505
^{= 20µH}
7. For a current limit value 30% higher than the maximum
load current:
I_O(CL) = 1.3 • I_O(MAX) = 1.3 • 5A = 6.5A
For more information www.linear.com/LTC3862
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