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I've built an LM3405 LED Driver, which works (seem) well. The LED have a 3.2V of Vf and works at 700mA. The regulator uses an external boost voltage of 3V (from an LDO). Reading the datasheet of the LM3405 I can't find any information on the buck converter dropout voltage, but I see a full load regulation only at Vin > 5V. (11/03/2016 EDIT: 4V)

There is a general rule or something to know that?

Moreover, the regulator have an internal Rsense on the drain of the MOS (which is used to correct the feedback and it is NOT the external shunt resistor), which can cause the drop, but I can't find its value.

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The dropout voltage is dependent on the converter maximum duty cycle among other things. This is the first thing I check when choosing a buck regulator; some regulators have more complex issues (such as minimum switch on and off times)

This device lists a minimum of 85% and a typical of 94% on page 3 of the datasheet.

LM3405 Duty cycle from datasheet

The minimum is the value across the full temperature range (-40C to +125C Tj) and is what we would use in a design.

As the duty cycle in a buck converter is simply Vout / Vin to a very close approximation, then Vin(min) is simply Vout / duty cycle. The datasheet does has guidance for this specific device on page 13 to calculate a more accurate duty cycle for given conditions.

For your 3.2V output (assuming you have measured the output voltage of the converter to ground) that equates to a minimum Vin of ~3.8V (for guaranteed operation) ignoring other parts of the conveter that may need a higher voltage.

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