LT3988
11
3988f
should be at least 30% higher. For highest efficiency, the
series resistance (DCR) should be less than 0.1Ω. Table 1
lists several vendors and types that are suitable.
The current in the inductor is a triangle wave with an
average value equal to the load current. The peak switch
current is equal to the output current plus half the peak-to-
peak inductor ripple current. The LT3988 limits its switch
current in order to protect itself and the system from
overload faults. Therefore, the maximum output current
that the LT3988 will deliver depends on the switch current
limit, the inductor value and the input and output voltages.
When the switch is off, the potential across the inductor
is the output voltage plus the catch diode drop. This gives
the peak-to-peak ripple current in the inductor:
∆I
L
= 1–DC
( )
•
V
OUT
+ V
F
where f is the switching frequency of the LT3988 and L is
the value of the inductor. In continuous mode, the peak
inductor and switch current is:
I
SWPK
=I
LPK
=
L
+I
L
To maintain output regulation, this peak current must
be less than the LT3988’s switch current limit, I
LIM
. For
both switches, I
LIM
is at least 1.5A at low duty cycle and
decreases linearly to 1.1A at DC = 90%. (See chart in the
Typical Performance Characteristics section).
The minimum inductance can now be calculated as:
L
MIN
=
1–DC
MIN
2 • f
•
V
OUT
+ V
F
I
LIM
–I
OUT
However, it’s generally better to use an inductor larger
than the minimum value. The minimum inductor has large
ripple currents which increase core losses and require
large output capacitors to keep output voltage ripple low.
This analysis is valid for continuous mode operation (I
OUT
>
∆I
L
/2). For details of maximum output current in discontinu-
ous mode operation, see Linear Technology’s Application
Note AN44. Finally, for duty cycles greater than 50% (V
OUT
/
V
IN
> 0.5), a minimum inductance is required to avoid
subharmonic oscillations. This minimum inductance is:
L
MIN
=
V
OUT
V
F
1.25A • f
with L
MIN
in μH and f in MHz.
For robust operation under fault conditions at input volt-
ages of 40V or greater, use an inductor value of 47µH or
larger and a clock rate of 1MHz or lower.
Output Capacitor Selection
The output capacitor filters the inductor current to generate
an output with low voltage ripple. It also stores energy in
order to satisfy transient loads and stabilize the LT3988’s
control loop. Because the LT3988 operates at a high
frequency, minimal output capacitance is necessary. In
addition, the control loop operates well with or without
the presence of output capacitor series resistance (ESR).
Ceramic capacitors, which achieve very low output ripple
and small circuit size, are therefore an option. You can
estimate output ripple with the following equations:
V
RIPPLE
=
∆I
L
8 • f • C
OUT
for ceramic capacitors
and
V
RIPPLE
= ∆I
L
• ESR
for electrolytic capacitors
(tantalum and aluminum)
where ∆I
L
is the peak-to-peak ripple current in the inductor.
The RMS content of this ripple is very low so the RMS
current rating of the output capacitor is usually not of
concern. It can be estimated with the formula:
I
C(RMS)
=
∆I
L
12
Another constraint on the output capacitor is that it must
have greater energy storage than the inductor; if the stored
energy in the inductor transfers to the output, the resulting
voltage step should be small compared to the regulation
voltage. For a 5% overshoot, this requirement indicates:
C
OUT
> 10 • L •
I
LIM
V
OUT
2
applicaTions inForMaTion
