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BQ51003: Small coil thermal issues

Part Number: BQ51003

Tool/software:

This is a follow up to my previous post about tuning the BQ51003 for a small coil.

We completed the tuning and shielding recommended by the last post and are now noticing significant thermal issues with the coil and battery. I assembled a test unit with longer leads to measure the temperature of each component as well as to get them out of the magnetic field.

When charging a 40mAh battery at 10mAh with the coil not perfectly centered, after 10 minutes I measured the temperature of the battery, the PCB, and the coil with a laser thermometer.

The battery stays around 80°F, the pcb is around 95°F, and the coil is 115°F around the edges, and 110°F in the center.
When the battery is also sandwiched between the coil (with shielding) and the PCB, it also gets hot, close to 110-115°F which is dangerously close to the rated maximum for the battery (45°C or 113°F). I also measured the PCB temperature at 122°F.

Does this suggest poor tuning of the coil, or insufficient shielding? Any ideas on how to fix this? How far beyond the edge of the battery and PCB must the shielding extend?