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UCC28019A: Bias supply question

Part Number: UCC28019A
Other Parts Discussed in Thread: UCC28880

A customer is devising a bias power supply for the UCC28019A.

They are planning to use a capacitive voltage dropper to supply the required 10mA bias current at 12V. This arrangement is not directly tied to GND because of the rectifier voltage drop as per schematic below.

They have sent me some simulations showing roughly what they plan to use and the waveforms.

The current concern is the diode voltage drop from ground, since the current sense uses a negative voltage drop on the sense resistor, so we dont know how the variations in the ground voltage would affect the UCC28019A. The EVM only specs for a regulated voltage no lower than 10.5V. Customer would like to avoid expense of going with a flyback or buck solution for cost and space reasons.

Would this pose an issue and, if yes, what alternative options may I suggest?