This paper presents a multipath wide-bandwidth magnetic current sensor based on Hall effect. To simultaneously achieve wide bandwidth, minimal ripple and small area, the system incorporates a non-spun filter-free main path with offset elimination through a continuous-time compact auxiliary path. The auxiliary path cancels the main path offset via feedforward, alleviating the need for area-consuming blocking capacitor or DC servo loop. Therefore, the chip occupies only 1.52 mm2. To suppress ripple in the auxiliary path induced by spinning current, a ping-pong switch-capacitor (PPSC) filter is proposed which mitigates ripple by sampling and averaging in the forward path, with the system achieving a residual ripple of$4.1~{\mu }$T. Compared with the state-of-the-art Hall sensor, it achieves$5{\times }$bandwidth improvement,$2{\times }$ripple reduction while occupying$5{\times }$less area.

In this paper, an RC relaxation oscillator exhibiting robust performance over an extended temperature and supply range is proposed. By incorporating a digitally-assisted calibration loop, the design eliminates the errors from switch on-resistance, comparator offset and propagation delay. Fabricated using a 180 nm bipolar-CMOS-DMOS (BCD) process technology, the oscillator operates at a frequency of 7MHz with the supply sensitivity of 870 ppm/V across a voltage range of 1.7 to 4.2 V. The evaluation of 40 untrimmed samples achieved an average temperature coefficient (TC) of 52 ppm/$^{\circ}$C from$-$40$^{\circ}$C to 165$^{\circ}$C, with the worst observed TC being 81 ppm/$^{\circ}$C. The aging test results indicate small deviations of 0.3% and 11% in the oscillation frequency and its TC, respectively. Furthermore, the direct power injection test confirms its reliability and robustness with a maximum error of oscillation frequency of 6.4%.

This paper presents a RC relaxation oscillator with wide temperature range for automotive application. By using a digitally assisted calibration loop, the comparator offset and the loop delay are efficiently cancelled. With both reference voltage and current derived from the same ΔVBE-based bias circuit, the proposed design cancels leakage currents and makes the design insensitive to high-temperature. The oscillator was fabricated in a 180 nm BCD process, the oscillator operates at 7MHz and achieves a supply sensitivity of 870 ppm/V from 1.7 to 4.2 V at room temperature. Measurements on 40 samples without trimming show that it has an average temperature coefficient of 52 ppm/°C over a wide temperature range (-40°C to 165°C), with the worst case temperature coefficient of 65 ppm/°C.

We present a structured parallel geometry-based multifrontal sparse solver using hierarchically semiseparable (HSS) representations and exploiting the inherent low-rank structures. Parallel strategies for nested dissection ordering (taking low rankness into account), symbolic factorization, and structured numerical factorization are shown. In particular, we demonstrate how to manage two layers of tree parallelism to integrate parallel HSS operations within the parallel multifrontal sparse factorization. Such a structured multifrontal factorization algorithm can be shown to have asymptotically lower complexities in both operation counts and memory than the conventional factorization algorithms for certain partial differential equations. We present numerical results from the solution of the anisotropic Helmholtz equations for seismic imaging, and demonstrate that our new solver was able to solve 3D problems up to 600 3 mesh size, with 216M degrees of freedom in the linear system. For this specific model problem, our solver is both faster and more memory efficient than a geometry-based multifrontal solver (which is further faster than general-purpose algebraic solvers such as MUMPS and SuperLU_DIST). For the 600 3 mesh size, the structured factors from our solver need about 5.9 times less memory.