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The inaccuracy of the analyses commonly used for predicting the temperature behavior of the I/SUB C/-V/SUB BE/ characteristics of transistors and the output of bandgap reference sources is pointed out. The problem is traced to a basic assumption implicit in such analyses, namely that the variation of the bandgap voltage of silicon with temperature is linear; this assumption is shown to be of poor accuracy. By taking into account the nonlinearity in this variation, new accurate formulas are derived. Both the previous analyses and the proposed analysis are compared to experiment; a valuable improvement is demonstrated. Equations which should prove to value in the design of bandgap reference sources and bipolar transistor temperatures transducers are given. Higher order effects are discussed.