978-1-4673-5943-6/13/$31.00 ©2013 IEEE Reactive Sub-nanometer Displacement Sensors: Advantages and Limitations Stoyan Nihtianov Electronic Instrumentation laboratory Delft University of technology Delft, the Netherlands E-mail: S.Nihtianov@TUDelft.nl Abstract— In this paper we present the results of an investigation on the performance of eddy-current and capacitive sensors for measuring very small displacements in the sub-nanometer range. The term “reactive sensor” is used as a generic name for inductive sensors (L) using the magnetic field, and capacitive sensors (C) using the electric field, to convert displacement into electrical signals. The need for an accurate displacement/position measurement in such extremely small scales as nanometers and picometers has increased significantly over the last few years. Application examples can be found in the high-tech industry, metrology, and space equipment. This study is based on our recent development results, as well as on the latest reports found in the literature. The goal of the paper is to analyze the commonalities between these two types of sensors, as well as the main performance differences and limitations which define the preferred choice for a specific application. The comparative assessment is done based on both theoretical analysis and experimental results. The main performance criteria used are: sensitivity, resolution, compactness, long-term stability, thermal drift, power efficiency. To the best of our knowledge, such a systematic comparison has not been done yet. Keywords: Capacitive sensors, eddy current sensor, reactance, displacement, performance I. INTRODUCTION Eddy current sensors and capacitive sensors have similar conversion principles and performance characteristics. The representation of both sensors in electric circuits operating with harmonic signals is reactance (X L =jωL and X C =1/jωC). A common application of eddy current sensors and capacitive sensors is for measuring the absolute position/displacement of a target with very high resolution and stability in the nanometer and even sub-nanometer range. In this way, pressure sensors, accelerometers, accurate positioning systems, vibro-meters, vibration dumping systems, etc., are built [1][2][3][4]. Despite the similarities in the conversion principle and the performance characteristics, capacitive and eddy current sensors possess important specific features which play a role when selecting them for each particular application. However, until now, to the best of our knowledge, no study has been presented which shows the latest advances in both types of sensors, based on: sensitivity, resolution, compactness, long- term stability, thermal drift, power efficiency. It is the ambition of the paper to fill in this information gap. In Section II we present the basic operating principle of the capacitive and the eddy current sensors. Section III discusses the interface principles. The conclusions are in Section IV. II. BASIC OPERATING PRINCIPLES OF CAPACITIVE AND EDDY CURRENT SENSORS A. Capacitive sensors The most sensitive way to measure small displacements with capacitive sensors is to use two parallel plates as shown in Figure 1 [1][2]. One of the plates is the target, and the other plate senses the distance to this target. The capacitance C between the two plates is inversely proportional to the distance d, while the surface of the electrodes A, the dielectric constant of vacuum İ o and the relative permittivity of the environment İ r are parameters (see expression (1)). Figure 1. Operating principle of capacitive displacement sensor. Based on expression (2), which is derived from (1), three important observations can be made: (i) the relation between C and d is hyperbolic, i.e. non-linear; (ii) the sensitivity ΔC/Δd is inversely proportional to the square of the distance d; (iii) changes of the relative permittivity İ r due to, for example, contamination, pressure variations, and humidity variations of the media between the two electrodes, will result in a change in C leading to an error. It is well known that a hyperbolic function can be linearized easily both in the analog and digital domain of the interface electronics. However, it is important to state that the d A C r o ε ε = d d A C d d C C r o Δ - = Δ ⇒ Δ - = Δ 2 ε ε (2) (1)