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This paper shows a systematic approach to calculate and to minimize mechanical-stress-related problems in bandgap voltage references. Mechanical stress is the main cause of long-term drift and packaging-induced inaccuracy in bandgap voltage references. Especially, low-cost epoxy packaging can cause a large mechanical stress, being in the range from -200 to +200 MPa. This stress shows local variations over the chip area and changes over time or during thermal cycling. Due to the piezojunction effect, this stress causes changes and drift in the base-emitter voltages of bipolar transistors and consequently in the output voltage of bandgap references. In this paper, it is shown that, even when using low-cost IC and packaging technology, a bandgap reference with a high immunity for the effects of mechanical stress can be realized.