Available online at ScienceDirect. Procedia Engineering 120 (2015 ) EUROSENSORS 2015

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1 Available online at ScienceDirect Procedia Engineering 120 (2015 ) EUROSENSORS 2015 Multi-resonator system for contactless measurement of relative distances Tobias Volk*, Sebastian Stöcklin, Adnan Yousaf, and Leonhard M. Reindl University of Freiburg, Department of Microsystems Engineering, Freiburg, Germany Abstract A precise measurement of two relative distances requires more sophisticated measurement schemes, which often demand two channels and consequently additional technical effort. Based on our current research on multi-resonator systems, we can demonstrate a novel method using two passive structures and a single transceiver. This presented method does not require an optical connection and is therefore robust against dust or other iron-free surroundings Published The Authors. by Elsevier Published Ltd. This by is Elsevier an open access Ltd. article under the CC BY-NC-ND license ( Peer-review under responsibility of the organizing committee of EUROSENSORS Peer-review under responsibility of the organizing committee of EUROSENSORS 2015 Keywords: contactless distance measurment; multi-resonator system; relative distance measurement 1. Introduction In polluted environments, contactless magnetic distance measurement methods are an alternative to conventional optical approaches. Displacements can be therefore measured by using linear variable differential transformers (LVDT) [1], cross-armature transducers [2], or even simple passive structures [3,4]. For example, metal affects the characteristics of a nearby coil [3] or the frequency response exhibits a so-called double tip in case of a second resonator [4,5]. However, all of the aforementioned principles except of some methods (e.g., differential cross-armature transducers) focusing on a specific distance between two points. Alternatively, we are now able to provide a unique method exhibiting the relative relation between two lengths or respectively three reference points. * Corresponding author. Tel.: ; fax: address: tobias.volk@imtek.uni-freiburg.de Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of the organizing committee of EUROSENSORS 2015 doi: /j.proeng

2 Tobias Volk et al. / Procedia Engineering 120 ( 2015 ) Nomenclature Z 1 N ω L L M R 2 R 3 c x Reflected impedance Number of turns; 1: first, 2: second, and 3: third resonator Angular frequency at resonance Total inductance; 1: first and 2: second resonator Magnetizing reactance (equal to the mutual inductance M in case of equal coils); 1: first and 2: second resonator Losses of the intermediate resonator Losses and connected load of/to the third resonator Ratio between mutual and total flux of a transmitter coil Coils separation distances The proposed method therefore applies special electrical characteristics of electro-magnetic resonator systems, which are commonly used to transfer power or improve the communication bandwidth [6-9]. More specific, the reflected impedance of a three-resonator system will be observed. The following section 2 describes the operational principle and electrical model. Section 3 provides two reference measurements and a final discussion reveals key findings and drawbacks. 2. Concept The measurement principle applies three electro-magnetic resonators in a configuration as depicted in figure 1. All resonators are arranged in coaxial alignment and tuned to a common resonance frequency. The resonator on the right side is connected to a constant load, whereas another resonator interfaces the driver circuit and is used to measure the reflected impedance across the entire resonator configuration. Fig. 1. Schematic drawing of the presented measurement method, which uses three resonators to measure their reflected impedance. To model the electrical behavior, equation (1) and (2) from [10] are used, which ignore side effects due to the cross coupling between the outer resonators and also mismatches of the resonance frequency. (1) (2) The equations show that the value of the reflected impedance mainly depends on the mutual inductance, L M1 and L M2, between left and right coil pair. Equation (1) can be simplified to equation (2) when the inner resonator features a high Q-factor. In addition, implementation of three equal resonators allows a further reduction of the parameters as shown in equation (3).

3 182 Tobias Volk et al. / Procedia Engineering 120 ( 2015 ) (3) The input impedance is consequently only related to the load and the quotient between the coupling factors, which are corresponding to the typically used k-factors under this condition. The particular value of the factors depends on the geometry. More specific, it is related to the radii of the required coils and to the distance between each particular resonator pair. As depicted in figure 2 [11], the electro-magnetic coupling decreases with the cube of the radius of the biggest coil of the pair and slight inside a range of one radius using an unequal pair. Expected sensitivities can be therefore set via the geometry of the configuration. Moreover, the distances can be determined by applying the characteristic curves or preferably a single curve when a symmetrical configuration is used. Fig. 2. Ratio between total and mutual flux of a transmitter coil as function of the distance. The distance of both curves is normalized to the radius of the biggest coil. The left graph is furthermore normalized to the value at zero distance. 3. Evaluation Besides the theoretical analysis, the proposed principle is evaluated by performing measurements on two resonator configurations using a network analyzer. The first measurement demonstrated the principle in case of a fix distance and used resonators with various resonators sizes. More specific, the developed measurement setup consists of outer resonators with coil radii of 2 cm and an intermediate resonator with a radius of 4 cm. The corresponding Q-factors were 99 for each outer and 53 for the intermediate resonator. The resonator, which was connected to the network analyzer, was placed in a fix distance of x 1 = 2 cm to the intermediate resonator whereas the loaded resonator coil was moved along the axis to generate different measurement distances x 2. The result of the measurement for a load of 30 Ω is depicted in figure 3. The graph shows only the real part of the impedances, because depending on implementation and reference distances, cross coupling and mismatches generate an additional parasitic imaginary part, which is ignored within the presented work. Fig. 3. Reflected impedance as function of the distance

Tobias Volk et al. / Procedia Engineering 120 ( 2015 ) 180 184 183 For a fix distance in between the first pair, the real part of impedance forms an s-curve with a lower sensitivity on the corners.

4 Tobias Volk et al. / Procedia Engineering 120 ( 2015 ) For a fix distance in between the first pair, the real part of impedance forms an s-curve with a lower sensitivity on the corners. It is assumed that the changes are related to the coupling factor (figure 2) in case of smaller ranges and to the Q-factors for larger ranges. The graph can be approximated by a fourth order polynomial or by a linear function when a coefficient of determination of 98.9 % is acceptable. For the second measurements the distance x 1 between the first pair is varied. The intermediate resonator was therefore replaced by a resonator equal to the outer resonators. The result of these measurement is depicted in figure 4. Fig. 4. Left: reflected impedance as function of the distance; Right: reflected impedances in relation to the reference The graph on the left side shows similar curves as depicted in figure 3. The values on the ordinate are drawn on a logarithmic scale to better identify the influence of the changed reference distances. Smaller reference distances x 1 lead to higher resistance values and consequently validate equation (1)-(3). Moreover, the graph on the right side clearly shows the expected behavior. Further investigations show that remaining deviations between the points are due to the Q-factor of the intermediate resonator. 4. Discussion The measurements show that the method is operational in principle. Within the presented work, an initial prototype of contactless distance measurement system is developed, which is able to measure distance with a high sensitivity and can be flexibly adapted to different specifications by changing the geometric parameters. In case of relative measurements, the system shows the expected behavior, but several shortcomings, which should be considered for of future investigations are briefly discussed as follows: 1. The approximation, assumed in equation (2), induces a common mode error due to the limited quality of the resonators in real-world implementations. The measured impedance is always affected by absolute distances. It is therefore necessary to limit the usable range of the distance with respect to the tolerance. 2. The tolerances of the reference distance have to be taken into account. 3. Mismatches of the resonators and crosstalk generate an additional imaginary part, which could influence the measurement precision. Overcoming the abovementioned limitations, it would be possible to integrate the configuration into a voltage divider and significantly reducing the requirements of the future circuit. 5. Conclusion This work shows principle, theory, and setup of a new approach to measure distances by using three-electromagnetic resonators. It is shown that the quotient between the mutual inductances significantly influence the reflected impedance. More specific, the change depends on the relation of two distances. The principle allows either to measure a single length with high accuracy or the matching of two lengths in a predefined range.

5 184 Tobias Volk et al. / Procedia Engineering 120 ( 2015 ) Acknowledgements This work was supported within the project SEAM-WiT by the Brain Links Brain Tools Cluster of Excellence funded by the German Research Foundation (DFG grant number EXC1086). References [1] H. Tariq et al.: The linear variable differential transformer (LVDT) position sensor for gravitational wave interferometer low-frequency controls, Nuclear Instruments and Methods in Physics Research A 489 (2002), [2] W. Belke et al., Floating thickness monitor, US patent A, [3] Sorin Fericean and Reinhard Droxler, New noncontacting inductive analog proximity and inductive linear displacement sensors for industrial automation, IEEE Sensors Journal 7.11 (2007), [4] M. Dionigi et al., A simple ranging system based on mutually coupled resonating circuits, IEEE I2TMC, Montevideo, Uruguay, [5] A. Yousaf et al., Near-field wireless sensing of single and multiple open-ended micro coils, Journal of Sensors and Systems JSSS 2 (2013), [6] A. RamRakhyani and G. Lazzi, Multicoil telemetry system for compensation of coil misalignment effects in implantable systems, IEEE Antennas and Wireless Propagation Letters 11 (2012), [7] X. Wei et al., A critical review of wireless power transfer via strongly coupled magnetic resonances, Energies 7 (2014), [8] A. Kurs et al., Wireless power transfer via strongly coupled magnetic resonators, Science 317 (2007), [9] C. Lee et al., Effects of magnetic coupling of nonadjacent resonators on wireless power domino-resonator systems, IEEE Transactions on Power Electronics 27.4 (2012), [10] T. Volk et al., Wireless power distribution system for brain implants, IEEE I2MTC, Pisa, Italy, [11] T. Volk et al.: Theoretical approach to setup a multi-antenna system for brain implants, 2ND IDAACS Symposium Wireless Systems, Offenburg, Germany, 2014.

Available online at ScienceDirect. Procedia Engineering 120 (2015 ) EUROSENSORS 2015

Available online at ScienceDirect. Procedia Engineering 120 (2015 ) EUROSENSORS 2015 Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 120 (2015 ) 511 515 EUROSENSORS 2015 Inductive micro-tunnel for an efficient power transfer T. Volk*, S. Stöcklin, C. Bentler,