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why the curve of bandgap is not concave,but protruding

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incol

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why concave is wrong
 

2nd order tempco derivitive should be negative.
 

Well, the bandgap tempco voltage consists of two parts, Voltage due to the PTAT current over a resistor and -ve coefficient voltage, VBE. The PTAT Current is due to the ΔVBE/R of the input loop. Hence the final voltage will be responding positively at lower temperatures and to the VBE at higher temperatures. Hence you get a convex shape.
 

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