860 IEEE SENSORS JOURNAL, VOL. 7, NO. 5, MAY 2007 A Hall Sensor Analog Front End for Current Measurement With Continuous Gain Calibration Marc Pastre, Maher Kayal, Member, IEEE, and Hubert Blanchard Abstract—This paper presents a new technique for continuously calibrating the sensitivity of a current measurement microsystem based on a Hall magnetic field sensor. An integrated reference coil generates a magnetic field for calibration. Using a variant of the chopper modulation, the spinning current technique, combined with a second modulation of the reference signal, the sensitivity of the complete system is continuously measured without inter- rupting normal operation. Modulation and demodulation schemes allowing the joint processing of both external and reference mag- netic fields are proposed. Additional techniques for extracting the very low reference signal are presented. The implementation of the microsystem is then discussed. Finally, measurements validate the calibration principle. A thermal drift lower than 50 ppm/ C is achieved. This is 6–10 times less than in state-of-the-art implemen- tations. Furthermore, the calibration technique also compensates drifts due to mechanical stresses and ageing. Index Terms—Calibration, drift, Hall sensor, integrated coil, mi- crosystem, modulation, spinning current. I. INTRODUCTION T HIS PAPER presents a new sensitivity calibration tech- nique for Hall sensors [1]–[3]. Hall sensors are widely used to measure magnetic fields [4]. They can easily be integrated in conventional CMOS technologies without additional processing steps. However, they suffer from imperfections that limit their precision, and thus their use in high-performance measurement systems. In particular, the sensitivity drift due to temperature variations, mechanical stresses and ageing, is one of their cur- rent main limitations [5]. The technique presented in this paper allows the contin- uous calibration of the sensitivity of a Hall sensor-based microsystem. Using an extension of the spinning current technique, the sensitivity drift is continuously measured and cancelled. The temperature drift of the sensitivity is reduced by a factor of 6–10 compared with the previous state-of-the-art. Furthermore, the drift due to mechanical stresses and ageing is also compensated. Section II presents the Hall sensor, its limitations and com- monly used techniques to improve its performances. Section III presents the new calibration technique and the main issues in the design of the associated microsystem. Section IV discusses tran- sistor-level implementation. Finally, Section V presents mea- surement results and Section VI concludes this paper. Manuscript received June 9, 2006; revised July 28, 2006; accepted September 1, 2006. This work was supported in part by CTI. The associate editor coordi- nating the review of this paper and approving it for publication was Dr. Subhas Mukhopadhyay. M. Pastre and M. Kayal are with the Laboratoire d’Electronique Générale (LEG1), Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland (e-mail: marc.pastre@epfl.ch; maher.kayal@epfl.ch). H. Blanchard is with LEM S.A., chemin des Aulx 8, CH-1228 Plan-les- Ouates, Switzerland (e-mail: hbl@lem.com). Digital Object Identifier 10.1109/JSEN.2007.894902 II. HALL SENSORS Detailed explanations about the sensor design, optimization, functioning, and simulation can be found in [4] and [6]. Here, it is simply accepted that the Hall voltage can be calculated as (1) where is the sensor bias current, the perpendicular mag- netic field and the current-related sensitivity, which is equal to (2) In this equation, is the Hall factor, the elementary carrier charge, the carrier density, the thickness of the sensor, and a geometrical correction factor having a value in the [0, 1] interval, depending on the dimensions of the sensor. Integrated Hall sensors are subject to two main imperfections: the offset voltage and the drift of the sensitivity due to tem- perature variations, mechanical constraints and ageing. While the offset voltage can be eliminated using the spinning current technique, the gain drift can be compensated using the contin- uous digital calibration technique presented in this paper. A. Spinning Current The spinning current technique allows to strongly reduce the offset of Hall sensors [8], [9]. It is the sensor counterpart of the chopper modulation in amplifiers. The sign of the signal voltage is periodically reversed, whereas the sign of the offset of the sensor remains constant. Using an appropriate demodulation, the offset can be eliminated. It is noteworthy that an amplifier used in conjunction with the sensor has its offset and 1/f noise also cancelled, exactly as in a chopper amplifier. This is because the offset and noise of the amplifier are added to the sensor voltage with a constant sign. Both offsets of the sensor and of the amplifier are cancelled. Furthermore, if the noise voltage remains constant between both phases, it is also removed. In practice, only the noise at lower frequencies than the spinning (modulation) frequency are removed. Finally, it is noteworthy that while the offset is never totally eliminated in practice, it can be strongly reduced. The achieved performance depends on component imperfections. B. Sensitivity Drift The piezo-Hall effect [5] causes a modification of the cur- rent-related sensitivity when mechanical stresses are applied to the Hall sensor. The cause of these stresses are temperature vari- ations, packaging, and ageing [7]. 1530-437X/$25.00 © 2007 IEEE