LTC1871-7
14
18717fd
applicaTions inForMaTion
Boost Converter: Ripple Current ∆I
L
and the ‘
χ
’ Factor
The constant ‘
χ
’ in the equation above represents the
percentage peak-to-peak ripple current in the inductor,
relative to its maximum value. For example, if 30% ripple
current is chosen, then
χ
= 0.30, and the peak current is
15% greater than the average.
For a current mode boost regulator operating in CCM,
slope compensation must be added for duty cycles above
50% in order to avoid subharmonic oscillation. For the
LTC1871-7, this ramp compensation is internal. Having an
internally fixed ramp compensation waveform, however,
does place some constraints on the value of the inductor
and the operating frequency. If too large an inductor is
used, the resulting current ramp (∆I
L
) will be small relative
to the internal ramp compensation (at duty cycles above
50%), and the converter operation will approach voltage
mode (ramp compensation reduces the gain of the current
loop). If too small an inductor is used, but the converter
is still operating in CCM (near critical conduction mode),
the internal ramp compensation may be inadequate to
prevent subharmonic oscillation. To ensure good current
mode gain and avoid subharmonic oscillation, it is recom-
mended that the ripple current in the inductor fall in the
range of 20% to 40% of the maximum average current.
For example, if the maximum average input current is
1A, choose a ∆I
L
between 0.2A and 0.4A, and a value ‘
χ
’
between 0.2 and 0.4.
Boost Converter: Inductor Selection
Given an operating input voltage range, and having chosen
the operating frequency and ripple current in the inductor,
the inductor value can be determined using the following
equation:
L =
IN(MIN)
∆I
L
• f
•D
MAX
where :
∆I
L
= χ •
I
O(MAX)
1– D
MAX
Remember that boost converters are not short-circuit
protected. Under a shorted output condition, the inductor
current is limited only by the input supply capability. For
applications requiring a step-up converter that is short-
circuit protected, please refer to the applications section
covering SEPIC converters.
The minimum required saturation current of the inductor
can be expressed as a function of the duty cycle and the
load current, as follows:
I
L(SAT)
≥ 1+
χ
2
•
I
O(MAX)
1– D
MAX
The saturation current rating for the inductor should be
checked at the minimum input voltage (which results in
the highest inductor current) and maximum output current.
Boost Converter: Operating in Discontinuous Mode
Discontinuous mode operation occurs when the load cur-
rent is low enough to allow the inductor current to run out
during the off-time of the switch, as shown in Figure 10.
Once the inductor current is near zero, the switch and
diode capacitances resonate with the inductance to form
damped ringing at 1MHz to 10MHz. If the off-time is long
enough, the drain voltage will settle to the input voltage.
Depending on the input voltage and the residual energy
in the inductor, this ringing can cause the drain of the
power MOSFET to go below ground where it is clamped
by the body diode. This ringing is not harmful to the IC
and it has not been shown to contribute significantly to
EMI. Any attempt to damp it with a snubber will degrade
the efficiency.
Figure 10. Discontinuous Mode Waveforms
for the Converter Shown in Figure 9
OUTPUT
VOLTAGE
200mV/DIV
INDUCTOR
CURRENT
1A/DIV
1µs/DIV
18717 F10
MOSFET
DRAIN
VOLTAGE
20V/DIV
