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TPS61169: Using separate bias to allow lower input voltage operation?

Part Number: TPS61169
Other Parts Discussed in Thread: TPS61060, TPS61158, , TPS92360, TPS61166, TPS61165

Hello,

See attached picture for a summary of what I am looking for.  LED driver application (5x LEDs in parallel).  I am looking to separate the LED driver bias and LX supply rails, to accommodate a supply rail (VSUP as drawn) that can droop considerably below the input voltage range of TI's LED drivers.

Here is the info in text form:

Vin (labeled VSUP in picture): 0.5V to 3.2V.  The 0.5V would be absolute worst case.

Vbias: 3.3V

LED Vf: 6.4V maximum

LED forward current: 100mA maximum total @ 100% duty cycle

Method of dimming will be PWM, ideally >20kHz to avoid any audible cap issues.

Is the drawing attached possible with TI's DC/DC solutions?  I can't seem to find a boost or LED driver solution that can handle such a low input voltage, while also supporting an output voltage > 6V using the standard supply rail topology.  I am hoping to avoid chaining 2x DC/DC converters together due to the inefficiency hit.