IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 64, NO. 4, APRIL 2015 865 Contactless Detection of State Parameter Fluctuations of Gaseous Media Based on an mm-Wave FMCW Radar Christoph Baer, Student Member, IEEE, Timo Jaeschke, Student Member, IEEE, Nils Pohl, Member, IEEE, and Thomas Musch, Member, IEEE Abstract—In this contribution, we present an approach on the fluctuation detection of gaseous media concerning their state parameter, i.e., concentration, pressure, and temperature. Dielectric mixing equations that link the gas permittivity with the gas concentration and pressure are introduced and discussed. Furthermore, we prove the small temperature influence on the gas permittivity, because of the obvious temperature–pressure dependence of gaseous media. To verify the suggested gas permit- tivity theory, a pressure-resistant test container was constructed and built up. By means of a highly precise millimeter-wave radar system, we performed numerous test series on different gases for various investigations. Index Terms— Frequency Modulated Continuous Wave (FMCW) radar, gas permittivity, millimeter wave (mm-wave), mixing equation. I. I NTRODUCTION N ATURAL and synthetic gases are valuable goods in terms of energy generation and chemical engineering. Therefore, the gas flow determination is an important and widely spread measurement task. Common gas flow meters rely on ultrasonic methods [1]–[2], hot-wire anemometry [3], or coriolis mass flow meters [4], to name but a few. However, when the gas under test is toxic, corrosive, or the gas velocity is high, common techniques are often not applicable due to physical effects or safety regulations. Furthermore, when the gas pipe leads to a safety device, the flow meter may not lead into the pipe. Baer et al. [5] presented an millimeter wave (mm-wave) radar-based technique for the mass flow determination of pneumatic conveyed bulk materials. In this case, the flow velocity determination relied on the correlation of bulk material content fluctuations, which were measured by two mm-wave radar systems that were arranged along the pipe. This technique is advantageous because it is contact free and does not affect the flow itself. To adapt this tech- nique to gas flow metering, fluctuations of at least one gas Manuscript received June 1, 2014; revised October 15, 2014; accepted October 16, 2014. Date of publication December 8, 2014; date of current version March 6, 2015. The Associate Editor coordinating the review process was Dr. Salvatore Baglio. C. Baer, T. Jaeschke, and T. Musch are with the Institute of Electronic Circuits, Ruhr University Bochum, Bochum 44801, Germany (e-mail: christoph.baer@rub.de). N. Pohl is with the Fraunhofer-Institut für Hochfrequenzphysik und Radartechnik, Wachtberg 53343, Germany. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2014.2374696 parameter that affects the mm-wave propagation, such as pressure, concentration, or temperature, must be detectable. Moreover, the measurement repetition rate must be sufficiently high in order to fulfill correlation theory. Therefore, the mod- ern mm-wave technologies provide fast and highly accurate measurement systems, which are promising with regard to the mentioned detection tasks as we already have shown in [6]. In this contribution, we investigate mm-wave related properties of gaseous media in order to lay the foundation for a fast and contact free gas flow fluctuation detection. Because only the detection of fluctuations is of interest for the proposed correlation techniques, we do not have to determine absolute values with high precision. Nevertheless, we will investigate the determination accuracy for some parameters in order to figure out detection limits. Therefore, we combine a highly precise FMCW radar system with a time domain relied postprocessing. It is based on a permittivity mixing theory that allows a fast and efficient, real-time data processing. II. FUNDAMENTALS A. State Parameters To investigate the elementary gas properties and depen- dences, we make use of the ideal gas law. It is the equation of state of a hypothetical ideal gas and approximates the behavior of many gases under many conditions. Its most prominent form is given by p · V = n · R · T . (1) In (1), the factors n, R, and T describe the amount of substance, the universal gas constant, and the temperature, respectively, while p and V represent the gas pressure and its volume. The ideal gas law shows that the fluctuation of a single parameter can have multiple reasons. Hence, a pressure increase can be caused by shrinking volume, an increased amount of molecules, or a raised temperature. This, however, can lead to additional and useful information concerning the general gas properties, if we can exclude effects caused by the measurement method. Among others, this means that for constant temperature and constant volume the increase of pressure is the result of the increasing amount of substance. Furthermore, we can describe the concentration of gas A within a gas mixture by its partial pressure p A . Hence, if we sum up all partial pressures p k of a gas mixture we will gain 0018-9456 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.