LTC3704 Datasheet, PDF (14/28 Pages) Linear Technology – Wide Input Range, No RSENSE Positive-to-Negative DC/DC Controller

LTC3704
APPLICATIO S I FOR ATIO
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 switch
current. For example, if the maximum average switch
current is 1A, choose a ∆I_L between 0.2A and 0.4A, and a
value ‘^χ’ between 0.2 and 0.4.
Inductor Selection
Selecting inductors for a positive-to-negative converter is
slightly more complicated than for a single-inductor topol-
ogy like a buck or boost. The use of separate, uncoupled
inductors can reduce the size of the solution, at the
expense of input and output ripple. Using a coupled
inductor complicates the design procedure, but can result
in significantly lower input and/or output ripple. It will also
reduce the number of components that the purchasing
department has to keep track of.
Regardless of the design goals, however, the inductor
selection process is an iterative one. The best recommen-
dation is to use the equations as a guideline, and then to
build a solution and measure the circuit’s performance. If
the measured performance deviates from the design guide-
lines, substitute a bigger (or smaller) inductor, as appro-
priate, and repeat the measurements. In addition, do your
best to minimize layout parasitics, which can have a
significant effect on circuit performance.
The inductor currents for a positive-to-negative converter
are calculated at full load current and minimum input
voltage. The peak inductor currents can be significantly
higher than the output current, especially with smaller
inductors and lighter loads. The following formulae as-
sume uncoupled inductors and CCM operation.
I_L1(PEAK)
=

− _1+
χ
2 
• I_O(MAX)
•
D_MAX
1– D_MAX
I_L2(PEAK)
=

− _1+
χ
2 
• I_O(MAX)
where “χ” represents the percentage of ripple current. In
a positive-to-negative converter, however, the switch cur-
rent is the sum of the two inductor currents. Therefore,
I_SW(PEAK)
=

–_1+
χ
2 
• I_O(MAX)
•
1–
1
D_MAX
Since the control loop is looking at the switch current, and
since the internal slope compensation is acting on this
switch current, the ripple current percentage should be
between 20% and 40% of the maximum average current
at V_IN(MIN) and I_O(MAX). This corresponds to a value of “χ”
in the equations above between 0.20 and 0.40. Expressing
this ripple current as a function of the output current
results in the following equation for calculating the induc-
tor value:
L1 =
L2
=
V_IN(MIN)
∆I_SW • f
• D_MAX
where:
∆I_SW
=
–χ
• I_O(MAX)
•
1–
1
D_MAX
By using a coupled inductor with a 1:1 turns ratio, the value
of inductance in the equation above can be replaced by 2L
due to mutual inductance. Doing this maintains the same
total ripple current and energy storage in the inductor.
Substituting 2L yields the following equation for 1:1
coupled inductors:
L1 =
L2
=
V_IN(MIN)
2 • ∆I_L • f
• D_MAX
For the case of uncoupled inductors, choose minimum
saturation currents based on the peak currents outlined in
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sn3704 3704fs