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LTC3704

sn3704 3704fs

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

∆IL 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.

L PEAK

O MAX

MAX

L PEAK

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,

SW PEAK

O MAX

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 VIN(MIN) and IO(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:

IN MIN

MAX

()

•

∆

where:

∆II

O MAX

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:

IN MIN

MAX

()

••

•

∆

For the case of uncoupled inductors, choose minimum

saturation currents based on the peak currents outlined in

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