As described, you intend this 'small' device to dissipate almost 4W with a linear solution. You should assume a surface temperature rise of one degree for every milliwatt dissipated by a square centimeter of surface area for the package. You might want to recalculate permissible losses on this basis and reappraise some basic design/cost considerations that include your power source.
In any system with a self-regulated supply voltage, the first question is 'Who's on first?'. Don't turn this into an Abott and Costello routine.
An SOT23 is not, in itself, the package that claims the Rthja rating; it counts on conduction through the leadframe to larger external surface areas (standard coupon patterns) and produces junction/surface limits greatly exceeding those permissible to commercial external surface touch or hold limits.
This simple rule of thumb for average surface temperature rise works at room temperature for packages between matchbook and breadbox sizes, without forced convection, to an accuracy of 20%.
This is not manufacturer's published bumph; it is not optimism or pessimism; it is the result of many physical demonstrations over the years, repeated usually for the benefit of midding-to-highly educated and highly over-paid doubting Thomases.
It is also demonstrated in the free magnetics and capacitor application software provided by mfrs such as Siemens, Magnetics Inc and Cornell Dubilier - with pedigrees that reach back into the ancient past of (gasp) print literature. Crunch the numbers back yourself on whatever packages you currently are familiar with. Any software package (no matter how expensive) has been mis-programmed or mis-applied, if it predicts otherwise. Ball park compliance is a good two-second paper and pencil check of the integrity of a convective simulation.
You mean some sort of pre-regulator before the linear? That might work, expecially if you make the the backlight is off until the pre-regulated voltage is withing range.
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Failure does not prove something is impossible, failure simply
indicates you are not using the right tools...
that is pretty good IC .Only the 150 uH spoils the picture . That needs 8x 8 mm minimum board size . The capacitors are fine. i think i will stick to that
Unfortunately your design requirements create a conundrum - "cost/size/efficiency - choose any two" works but wanting all three makes it well nigh impossible.
If cost is ignored, then a TO-220-ish integrated switcher like
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