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LMR10515: Inrush current - how to fulfill USB 2.0 specs

Part Number: LMR10515

We have successfully implemented the LMR10515 with the following specifications: 4.8V-5.5V to 3.30V @ 1.5A.
In it's application it will be supplied from USB 2.0 ports. Therefore, the design has to fullfill the USB 2.0 specifications regarding inrush current.

In short, these specifications require the inrush-spikes to be either lower than 100mA or shorter than 100uS over a total time span of 100mS.

The measurement shows, that there is a series of short spikes followed by one that last for a about 1.5mS. And it's this one that makes the design fail the USB 2.0 specifications.
It's important to understand, that this start-up behaviour is pretty much unaffected by the load. The curves look almost identical whether the LMR10515 supplies our plug-in module or not.

That's the actual design with some remarks referring to the measurement

This shows the measurement-setup

The question is - how can I proceed with this design to make it pass the USB 2.0 specs?