Analysis and Design of Analog Integrated Circuits
Analysis and Design of Analog Integrated Circuits
A high-precision compensated CMOS bandgap voltage reference without resistors
IEEE Transactions on Circuits and Systems II: Express Briefs
A 1.2-V Piecewise Curvature-Corrected Bandgap Reference in 0.5 $mu$m CMOS Process
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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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 驴1.72 mV/°K at 27 °C which has been formerly reported about 驴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), 驴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 驴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驴 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.