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TMP464: How to address error on smaller geometries

Part Number: TMP464

When using TMP464 with a small geometry process like with 5nm, I understand that the device onyl supports the n-factor correction but not the beta compensation. Therefore when used with 5nm sense devices will give quit some error.  I got the feedback from a third party that they meassured up to +/- 6 deg. C.   

Do we have any experience or advice how this error could be redused?  Is there any kind of algorithem to do some manual correction? With the 4 sense devices users usually have also indication of the board/ambient temperature.  Is this soem information which could be used to reduce the error?

Note:  TMP44x and TMP42x which support n-factor & beta compensation are no option as this would request for a layout change.

Thanks, Bertram