Part 1 - Choosing The IC

The LT3420 is not the stereotypical boost converter IC, it is designed to work in a flyback topology (and hence uses a small transformer instead of a standard inductor). It is also not designed to be used in power supply applications since it is designed and marketed specifically as an IC for managing the charging of photoflash capacitors (big, high-voltage capacitors that enable the high pulse of current required for driving camera-flash bulbs at sufficient intensity).

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Despite all this, it does also offer a solution that is specifically designed to step up a low voltage (in this case from a USB port or even a li-ion cell) to a much higher voltage. It also does this in a manner that requires very few external components: 3 capacitors, 2 resistors, a diode and the transformer. Having a small number of external components has many advantages: lower cost of the overall design and a smaller BoM (and possibly lower production costs as a result); but more importantly, it results in reduced complexity and a simpler PCB layout. 

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Taking a more in-depth look at the device, it appears to have a current-driven control scheme that involves a maximum primary current and a minimum secondary current. It also states that the device effectively has two modes: charging mode or refresh mode. During charging mode, the converter is active and supplying current to the load. The refresh mode is used to provide a capacitor with a top-up charge (since the charge on a capacitor will gradually be lost through various circuit leakages). This can be shown in Figure 1 below, which is taken from the LT3420 datasheet.