2450 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 59, NO. 9, SEPTEMBER 2010 Wireless Readout of Passive LC Sensors Reinhard Nopper, Remigius Niekrawietz, and Leonhard Reindl, Member, IEEE Abstract—This paper reports simple yet precise equations for automated wireless measurement of the resonance frequency, Q-factor, and coupling coefficient of inductively coupled passive resonant LC circuits. This allows remote sensing of all physical and chemical quantities that can be measured with capacitance trans- ducers. Formerly reported front-end circuit concepts for wireless sensor readout, i.e., phase dip measurement and the dip meter, are subsequently discussed. It is shown that, due to fundamental system limitations, the formerly reported circuit concepts are not applicable if the distance between the sensor and the readout electronic circuit becomes too small, resulting in large coupling coefficients. Therefore, we present an improved concept for an analog front-end circuit of the readout system that overcomes these limitations and hence allows wireless sensor readout under a wider range of operating distances. Index Terms—Capacitance transducers, inductive coupling, LC circuits, remote sensing, resonance detection, telemetry. I. I NTRODUCTION M ANY industrial, automotive, and medical applications require sensing of physical or chemical quantities at locations where a wired connection between the sensor and its evaluation circuit cannot be established. Examples of these applications are sensors on moving or rotating parts such as tire pressure measurement systems [1], medical sensing inside the human body such as intraocular eye pressure measurement [2], [3], or sensing under harsh environmental conditions, such as corrosive media or high temperature [4]. In particular, in the latter case, no damageable wire connections and electronic circuitry are desired at the point of measurement. Therefore, a completely passive and wireless sensor element is required. Passive wireless sensors for a variety of quantities to be measured such as temperature [1], pressure [2]–[5], humidity [6], strain [7], and chemical sensors [8] have been proposed in former publications. All these concepts are based on LC resonant circuits where the quantity to be measured affects the capacitance, which, in turn, affects the sensor’s resonance frequency. Change in the resonance frequency can be detected by another inductively coupled coil that is connected to the signal-conditioning electronics. Most publications focus on the design of the sensor ele- ment itself, which is usually a capacitor whose electrodes Manuscript received June 2, 2009; revised August 5, 2009; accepted August 18, 2009. Date of publication October 30, 2009; date of current version August 11, 2010. The Associate Editor coordinating the review process for this paper was Dr. Juha Kostamovaara. R. Nopper and R. Niekrawietz are with the Microsystem Technologies De- partment, Corporate Sector Research and Advance Engineering, Robert Bosch GmbH, 70839 Gerlingen-Schillerhöhe, Germany (e-mail: reinhard.nopper@ de.bosch.com; remigius.niekrawietz@de.bosch.com). L. Reindl is with the Laboratory of Electrical Instrumentation, Institute for Microsystem Technology (IMTEK), Albert-Ludwigs-Universität, 79110 Freiburg, Germany. Digital Object Identifier 10.1109/TIM.2009.2032966 Fig. 1. Equivalent network of the inductively coupled sensor system. are deflected by mechanical forces, or the dielectric’s relative permittivity is dependent on the quantity to be measured. Less research effort has been made to develop a robust and accurate readout system for these kinds of wireless sensors. In this paper, techniques for wireless measurement of the resonance frequency, Q-factor, and coupling coefficient of an inductively coupled LC sensor based on the air-core transformer-based system model are derived. Formerly published readout concepts for measuring the sensor’s resonance frequency are examined for their suitability for automatic resonance detection in a sensor system, and their fundamental limitations will be shown. Finally, an improved readout circuit avoiding these limitations will be presented to be suitable for automatic resonance detec- tion under a wide range of operation conditions. II. SYSTEM MODEL A. Analytical Model An analytical model of the inductively coupled sensor can be derived using the well-known transformer equations for harmonic oscillations with the frequency f using complex notation, i.e., V 1 = R 1 I 1 + j 2πfL 1 I 1 + j 2πfMI 2 (1) V 2 = R 2 I 2 + j 2πfL 2 I 2 + j 2πfMI 1 (2) where V 1 , V 2 , I 1 , and I 2 are defined as shown in Fig. 1. The mutual inductance M of the coupled coils can be written as M = k  L 1 L 2 (3) where k is the geometry-dependent coupling coefficient with a value between 0 (no coupling) and ±1 (maximum coupling). The sensor coil is terminated with the capacitance transducer C 2 , i.e., I 2 = −j 2πfC 2 V 2 . (4) The equivalent input impedance Z 1 at the terminals of the readout coil is derived using (1), (2), and (4), i.e., Z 1 = V 1 I 1 = R 1 + j 2πfL 1 + (2πf ) 2 M 2 R 2 + j  2πfL 2 − 1 2πfC 2  . (5) 0018-9456/$26.00 © 2009 IEEE