280 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 47, NO. 1, FEBRUARY 1998 A Robust Capacitive Angular Speed Sensor Tibor Fabian and Georg Brasseur, Senior Member, IEEE Abstract—This paper presents a contactless capacitive angular speed sensor for automotive applications. The sensor is based on a passive rotating electrode placed between two mechanically static and electrically active electrodes. Differing characteristics of the charge transfer at various sensor positions is utilized as an input for the determination of the rotational speed. The mathe- matical model of the sensor further enables the optimization of the sensor characteristics for specific applications. Experimental results from a prototype designed for the speed measurement of a steering wheel show a relative speed error of 4% at a resolution better than 1 /s. Index Terms— Angular speed sensor, capacitive transducer, measurement, pulse amplitude modulation, ratiometric measure- ment principle. I. INTRODUCTION A NGULAR speed sensors are widely used in control and instrumentation applications. There exists a num- ber of established principles for angular speed measurement [1]. The classic method, mostly used with speed controlled electric motors, is the dc-tachometer generator where a speed- dependent dc voltage is produced. Robust applications need contactless sensors like ac-generators or incremental encoders. Both sensor types produce a pulse-train depending on shaft speed but do not generate a speed signal. Therefore this signal must be derived from the decoders output signal. Some well known methods to calculate the speed from the incoming pulse-train are described in [2]: for instance measurement of the time interval between successive pulses, counting the pulses during a prescribed time or measurement of the time duration for a variable number of pulses can be taken into account. It turns out that a high angular resolution of the incremental encoder is the key to an undisturbed speed signal at low shaft revolutions. This feature is very important for steering speed measurement in vehicles, where a minimum speed of less than 5 /s has to be detected. Absolute angular encoders have nearly infinite resolution and therefore they are ideal to produce an output signal for low speed measuring. The paper focuses on this topic. In the automotive applications the sensors must resist harsh environmental conditions such as: strong vibrations, excessive ambient temperature, dirt, and moisture. Additionally mass production requires low production costs and robustness. This implies a simple sensor design based on a working principle in- sensitive to mechanic tolerances. The robust capacitive angular Manuscript received June 1, 1997; revised May 1, 1998. The authors are with Institut f¨ ur Allgemeine Elektrotechnik und Elek- tronik University of Technology Vienna, A-1040 Vienna, Austria, (e-mail: sem-c@iaee.tuwien.ac.at). Publisher Item Identifier S 0018-9456(98)06312-8. Fig. 1. Sensor structure for 180 measurement range. Fig. 2. The sections of transmitter and rotor topology. position sensor described in [3] meets above requirements and was used for the presented speed sensor. For a proper analysis and sensor design a system model is required. This paper starts with the description of the sensors working principle, then a system model is described. Finally measurement data are presented. II. WORKING PRINCIPLE A. Sensor Topology The sensor electronics contains a charge amplifier, an A/D converter and a microcontroller. The sensor mechanics con- tains a rotor which is placed between two coaxial stator plates (see Fig. 1). One stator plate houses the receiving electrode for charge induced from the transmitting segments placed on the other stator plate. The total area of the transmitter is divided into equal conductive circle segments (see Fig. 2), where , we call it polenumber, is a nonzero positive integer. Periodically numbering all segments from one to four we obtain exactly sets of segments numbered from one to four: , and . The segments with the same number are electrically connected. Therefore we only distinguish between four electrically independent segments, times placed on the transmitter electrode. The rotor is made up of blades in the 0018–9456/98$10.00  1998 IEEE