Thank you Andrew Beckett for the reply. I think I have figured out what was the problem. In practice, the derivation was made recursively to the capacitance and not just to the voltage. I had assumed that once the bias point was found the value of c was kept fixed according to the table. However, seems like it still considers c as variable and try to compute the derivative of it, thus adding that error i was experiencing. I have solved the problem by just doing the ddt before the multiplication with the looked up capacitance c. with best regards, Julian.
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