LTC3786 LINER [Linear Technology], LTC3786 Datasheet - Page 26

• Manufacturer Part Number: LTC3786
• Description: Multi-Phase Current Mode Step-Up DC/DC Controller
• Manufacturer: LINER [Linear Technology]

applicaTions inForMaTion
LTC3862-2
Maximum Duty Cycle Limitations
Another operating extreme occurs at high duty cycle,
when the input voltage is low and the output voltage is
high. In this case:
A single-ended boost converter needs a minimum off-time
every cycle in order to allow energy transfer from the input
inductor to the output capacitor. This minimum off-time
translates to a maximum duty cycle for the converter. The
equation above can be rearranged to obtain the maximum
output voltage for a given minimum input or maximum
duty cycle.
The equation for D
guideline for determining the maximum duty cycle of
the application circuit. However, losses in the inductor,
input and output capacitors, the power MOSFETs, the
sense resistors and the controller (gate drive losses) all
contribute to an increasing of the duty cycle. The effect
of these losses will be to decrease the maximum output
voltage for a given minimum input voltage.
After the initial calculations have been completed for an
application circuit, it is important to build a prototype of
the circuit and measure it over the entire input voltage
range, from light load to full load, and over temperature,
in order to verify proper operation of the circuit.
Peak and Average Input Currents
The control circuit in the LTC3862-2 measures the input
current (by means of resistors in the sources of the power
MOSFETs), so the output current needs to be reflected back
to the input in order to dimension the power MOSFETs
26
D
V
O(MAX)
MAX
=

 
=
V
1– D
O
+ V
V
IN
V
MAX
O
F
MAX
– V
+ V
– V
IN(MIN)
above can be used as an initial
F
F

 
properly. Based on the fact that, ideally, the output power
is equal to the input power, the maximum average input
current is:
The peak current in each inductor is:
where n represents the number of phases and χ represents
the percentage peak-to-peak ripple current in the inductor.
For example, if the design goal is to have 30% ripple cur-
rent in the inductor, then χ = 0.30, and the peak current
is 15% greater than the average.
Inductor Selection
Given an input voltage range, operating frequency and
ripple current, the inductor value can be determined using
the following equation:
where:
Choosing a larger value of ∆I
value inductor but results in higher output voltage ripple,
greater core losses, and higher ripple current ratings for
the input and output capacitors. A reasonable starting
point is 30% ripple current in the inductor (χ = 0.3), or:
I
I
L =
∆I
∆I
IN(MAX)
IN(PK)
L
L
V
=
=
∆I
IN(MIN)
χ
n
0.3
=
L
n
=
•
n
1
• f
1– D
•
1– D
I
• 1+
I
O(MAX)
O(MAX)
1– D

 
• D
I
O(MAX)
MAX
MAX
MAX
MAX
χ
2

 
•
1– D
I
O(MAX)
MAX
L
allows the use of a lower
38622f