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A high precision high-order curvature-compensated bandgap reference (BGR) compatible with standard BiCMOS process is presented in this paper that is capable of working down to input voltages of 1.6 V with 1.285 V output voltage. High-order curvature correction for this reference is accomplished by a novel piecewise technique, which realizes exponential curvature compensation in temperature range, and a logarithmic compensation term proportional to VT In T in higher temperature range through simple structures. Experimental results of the proposed BGR implemented in 0.5-μm BiCMOS process demonstrate that a temperature coefficient (TC) of 5 ppm/°C is realized at 3.6 V power supply, a power-supply noise attenuation (PSNA) of 70 dB is achieved without filtering capacitors, and the line regulation is better than 0.47 mV/V from 1.6 V to 5 V supply voltage while dissipating a maximum supply current of 25 μA. The active area of the presented BGR is 180 μm × 220 μm. [ABSTRACT FROM PUBLISHER]

This paper deals with the global convergence and stability of the Hopfield-type neural networks under the critical condition that M1(F) = L-1DF - (FW+WTF)/(2) is nonnegative for any diagonal matrix F, where W is the weight matrix of the network, L = diag(L1, L2,.. . , LN) with 4 being the Lipschitz constant of gi and G(u) = (g1(u1),g2(u2),. . ,gN(uN))T is the activation mapping of the network. Many stability results have been obtained for the Hopfield-type neural networks in the noncritical case that M1 (F) is positive definite for some positive definite diagonal matrix F. However, very few results are available on the global convergence and stability of the networks in the critical case. In this paper, by exploring two intrinsic features of the activation mapping, two generic global convergence results are established in the critical case for the Hopfield-type neural networks, which extend most of the previously known globally asymptotic stability criteria to the critical case. The results obtained discriminate the critical dynamics of the networks, and can be applied directly to a group of Hopfield-type neural network models. An example has also been presented to demonstrate both theoretical importance and practical significance of the critical results obtained. [ABSTRACT FROM AUTHOR]