In this paper, we propose an optimized method for nonlinear function approximation based on multiplierless piecewise linear approximation computation (ML-PLAC), which we call OML-PLAC. OML-PLAC finds the minimum number of segments with the predefined fractional bit width of input/output, maximum number of shift-and-add operations, user-defined widths of intermediate data, and maximum absolute error (MAE). In addition, OML-PLAC minimizes the actual MAE as much as possible by iterating. As a result, under the condition of satisfying the maximum number of segments, the MAE can be minimized. Tree-cascaded 2-input and 3-input multiplexers are used to replace multi-input multiplexers in hardware architecture as well, reducing the depth of the critical path. The optimized method is applied to logarithmic, antilogarithmic, hyperbolic tangent, sigmoid and softsign functions. The results of the implementation prove that OML-PLAC has better performance than the current state-of-the-art method.

In order to meet the requirements of modern portable electronics for high accuracy and low power consumption of bandgap reference circuits, a new low-voltage bandgap reference with a second-order compensated circuit at 1.8 V is proposed. It features a new self-biased fully symmetric differential operational amplifier circuit with the help of split transistors for achieving low power consumption and high accuracy; by adding a new sub-threshold compensated circuit. The results of simulation show that the temperature coefficient of the second-order circuit is 3.95 ppm/°C in the temperature range of −40 to 125 °C, and the power consumption is only 7.5 μW; this meets both the requirements of high precision and low power consumption. At the same time, the output noise voltage of the design is less than 30 μV/sqrt (Hz) at a frequency of 100 Hz, and the low-frequency supply voltage rejection ratio is −103 dB@100 Hz; these are acceptable for bandgap reference circuits.