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Reanalyzing the basic bandgap reference voltage circuit considering thermal dependence of bandgap energy

Abstract

The basic bandgap reference voltage generator, BGR, is thoroughly analyzed and relations are reconstructed considering dependency of bandgap energy, Eg, to absolute temperature. The previous works all consider Eg as a constant, independent of temperature variations. However, Eg varies around 25 meV when the temperature is increased from 2 to 92 °C. In this paper the dependence of Eg to absolute temperature, based on HSPICE mosfet models in HSPICE MOSFET Models Manual (Version X-2005.09, 2005), is approximated by a third-order polynomial using Lagrangian interpolating method within the temperature range of 2–92 °C. Accurate analysis on the simplified polynomial reveals that the TC of VBE must be corrected to −1.72 mV/°K at 27 °C which has been formerly reported about −1.5 mV/°K in Razavi (Design of analog CMOS integrated circuits, 2001) and Colombo et al. (Impact of noise on trim circuits for bandgap voltage references, 2007), −2 mV/°K in Gray et al. (Analysis and design of analog integrated circuits, 2001), Leung and Mok (A sub-1-V 15-ppm/°C CMOS bandgap voltage reference without requiring low threshold voltage device, 2002), Banba et al. (A CMOS bandgap reference circuit with sub-1-V operation, 1999), and −2.2 mV/°K in Jones and Martin (Analog integrated circuit design, 1997), Tham and Nagaraj (A low supply voltage high PSRR voltage reference in CMOS process, 1995). Another important conclusion is that the typical weighting coefficient of TC+ and TC− terms is modified to about 19.84 at 27 °C temperature from otherwise 16.76, when Eg is considered constant, and also 17.2, in widely read literatures, (Razavi in Design of analog CMOS integrated circuits, 2001). Neglecting the temperature dependence of Eg might introduce a relative error of about 20.5 % in TC of VBE. Also, resistance and transistor size ratios, which denote the weighting coefficient of TC+ term, might be encountered to utmost 20.3 % error when the temperature dependence of Eg is ignored.

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Correspondence to Sarang Kazeminia.

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Kazeminia, S., Hadidi, K. & Khoei, A. Reanalyzing the basic bandgap reference voltage circuit considering thermal dependence of bandgap energy. Analog Integr Circ Sig Process 79, 141–147 (2014). https://doi.org/10.1007/s10470-013-0248-y

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  • DOI: https://doi.org/10.1007/s10470-013-0248-y

Keywords

  • Thermal coefficient of reference voltage
  • Bandgap energy
  • Temperature-compensated BGR