EuMC_ Determination of Soil Moisture Based on an Improved Sensor Design Using Time Domain Transmission Measurements.pdf

  Determination of Soil Moisture Based on anImproved Sensor Design Using Time DomainTransmission Measurements Bianca Will  #1 , Michael Gerding  ∗ 2 , Thomas Musch  ∗ 3 , Ilona Rolfes  #4 # Chair of Radio Frequency System Engineering, Ruhr-Universit ¨ at BochumUniversit ¨ atsstr. 150, 44801 Bochum, Germany 1 bianca.will@rub.de 4 ilona.rolfes@rub.de ∗  Institute for Electronic Circuits, Ruhr-Universit ¨ at BochumUniversit ¨ atsstr. 150, 44801 Bochum, Germany 2 michael.gerding@rub.de 3 thomas.musch@rub.de  Abstract —Delay time measurements, e.g. time domain reflec-tometry (TDR), are a well-established method for the mea-surement of permittivity in various materials, especially soils[1]. However, common measurement systems only provide anaverage value of the dielectric constant along the length of theTDR sensor. Furthermore the accuracy offered by common TDRmeasurements is limited due to multiple reflections caused by thematerial under test.This contribution deals with a new sensor design for the charac-terization of soil moisture using time domain transmission (TDT)measurements. The basis of the advanced TDT technique is a newwaveguide concept, which offers the possibility to perform trans-mission measurements in soils. Thus multiple reflections along thewaveguide do not influence the measurement accuracy. By usinga so-called ”concentric reversion coupler” TDT measurementscan be performed without a measuring port at the end of thesensor. I. I NTRODUCTION There are several well established techniques available forthe determination of the permittivity in homogeneous andinhomogeneous materials [2]. They all have in common, thattheir measurement results are limited to the mean value of thepermittivity of the respective material of interest.Due to the existing relation between the permittivity and themoisture of a material probe [3], permittivity measurementsbecome a common method for the determination of the watercontent of soils [4], [5], [6]. By the use of capacitive sensorsor delay time measurements it is possible to determine themean value of the water content along a sensor, which ispenetrating the medium. Furthermore it is already known thata dielectric profile can be determined by using a time-domaininverse scattering technique [7].In fact, the accuracy of common TDR-sensors used for thedetermination of soil moisture is limited. Even if TDR-systemsoffer highly accurate delay time measurements, multiple re-flections caused by the material under test can decrease themeasurement accuracy. In contrast to common TDR measure-ments, TDT measurements offer the possibility to eliminatemultiple reflections by the use of time gating methods [8]. Thisresults from the fact that the first transmitted impulse is uniqueand presents the useful delay time signal. In fact a measuringport at the end of the sensor is needed to enable commonTDT measurements. Related to permittivity measurements insoils, e.g. in boreholes, a measuring port at the end of thesensor is difficult to realize. This contribution deals with animproved sensor design, which enables TDT-measurementsin soils without the necessity of a second measuring portat the end of the sensor. Therefore a “concentric reversioncoupler” consisting of concentric coaxial lines is developed.Furthermore a compact sensor design is realized with regardto the application in boreholes with a diameter of a couple of centimeters.According to the increasing interest in spatially resolved soilmoisture measurements this compact sensor design enables thepossibility to perform spatially resolved TDT-measurementsas well. Due to its compact design, the TDT-sensor can bedisplaced inside the material of interest, enabling arbitrarymeasurement positions. Thus measurements inside layeredmaterials can be performed as well as measurements of smoothpermittivity variations.II. M ATHEMATICAL  F UNDAMENTALS One commonly used method for the determination of thewater content of soils is given by delay time measurements.Those are particularly suitable for permittivity measurementsdue to the dependence of the propagation velocity of elec-tromagnetic waves on the dielectric permittivity. Delay timemeasurements used for the detection of water in soils areusually performed in a frequency range up to 3 GHz. Thisfrequency range results from the extraordinary dielectric prop-erties of water at lower frequencies. Measuring delay timesby using such baseband signals requires waveguides whichare inserted in the material under test. In many cases open-ended two-wire lines or one-wire lines are used to lead the 978-2-87487-022-4 ©  2011 EuMA 10 - 13 October 2011, Manchester, UK Proceedings of the 41st European Microwave Conference 218  measurement signal in the tested material. By measuring thedelay time or the propagation velocity along the waveguide,the dielectric properties of the surrounding of the waveguidecan be determined.Concerning porous materials e.g. soils, a complex relativepermittivity  ε r  =  ε  r  −  j ε  r  yields the following relation forthe propagation velocity in the tested material [9]: c  = 1   µ 0 · ε 0 · ε  r 2  1 +   (tan δ  ) 2 + 1  (1)Thus the measured delay time depends on the real part of therelative permittivity and on its loss tangent  tan δ   =  ε  r /ε  r ,respectively. To obtain a more compact relation, the so-calledapparent permittivity [10] ε a  =  ε  r 2  1 +   (tan δ  ) 2 + 1   (2)can be used. Hence, the measured delay time  t meas  dependson the square root of the apparent relative permittivity of thematerial under test, the speed of light  c 0  and the mechanicallength of the sensor  l mech  as follows: t meas  =  l mech c 0 ·√  ε a  (3)Measuring the delay time along a sensor with a known me-chanical length  l mech  in a material with a known permittivity ε ref   yields a reference delay time  t ref  . Subsequently one canuse the difference between this reference delay time and thedelay in the material of interest to determine the apparentpermittivity  ε meas  of the material under test as follows: ε meas  =  ( t meas − t ref  ) · c 0 l mech + √  ε ref   2 (4)Furthermore this measured permittivity offers the possibilityto determine the water content  θ  due to Topp’s equation [3]: θ  =5 . 3 · 10 − 2 + 2 . 92 · 10 − 2 · ε meas − 5 . 5 · 10 − 4 · ε 2meas  + 4 . 3 · 10 − 6 · ε 3meas  (5)Additionally, the improved sensor design described in thiscontribution enables the possibility to determine spatiallyresolved dielectric profiles by moving the sensor along thematerial of interest without changing the mechanical length of the sensor. Hence one can determine the apparent permittivityand the corresponding water content in each sensor position i : ε meas ( i ) =  ( t meas ( i ) − t ref  ) · c 0 l mech + √  ε ref   2 (6)As shown by this relation the measured apparent permittivitysolely depends on the permittivity of the surrounding of the sensor. Neither the measuring position nor permittivitiesin other regions along the measured profile influence themeasured permittivity. Z  0 Z  0 12 d Fig. 1. Schematic design of a concentric reversion coupler with the baseimpedance  Z  0  and the coaxial ports 1 and 2   0 0.5 1 1.5 2 2.5 3-30-20-100-26     |         S   1       1     |          2  ,        |         S   2       1     |          2       /        d      B Frequency / GHz Fig. 2. Frequency domain transfer function  | S  21 | 2 (dashed) and insertionloss  | S  11 | 2 (solid) of the numerically optimized concentric reversion coupler III. S ENSOR  D ESIGN Concerning multiple reflections along the sensor, time do-main transmission measurements are advantageous comparedwith commonly performed time domain reflectometry mea-surements. According to this, a movable discontinuity ona one-wire line can be used to achieve a higher accuracycompared with common reflection measurements [11]. Al-though this setup offers advantages in comparison with usualtime domain reflectometry measurements, there are still somecharacteristics which can be improved.Even if results of reflection measurements achieved by us-ing a movable discontinuity are less influenced by multiplereflections, a separated measurement port to perform realtransmission measurements is advantageous. Thus a couplingstructure to lead the transmitted signal back to the feedingport of the sensor is necessary. Due to this, a so-calledconcentric reversion coupler which leads the transmitted signalback into the interior of a one-wire line was developed.This coupling structure consists of concentric coaxial linesas schematically shown in Fig. 1. A numerical optimizationbased on electromagnetic simulations yields a matching betterthan 26 dB for baseband signals up to 3 GHz as shown by thetransfer function in Fig.2.Furthermore a time domain filter structure for the separationof the pulse signals on these concentric coaxial lines isnecessary. A schematic design of the numerically optimizedfilter structure is shown in Fig. 3. The frequency domaintransfer function and the time domain impulse response of the numerically optimized time domain filter structure areshown in Fig. 4 and Fig. 5. Additionally a discontinuity isplaced on the one-wire line to obtain a higher influence of thesurrounding. Combined with the described coupling and filterstructures a compact sensor can be achieved as shown in Fig. 6. 219  21 ∆ l Fig. 3. Schematic design of a time domain filter structure to separate pulsesignals on concentric coaxial lines 0 0.5 1 1.5 2 2.5 3-30-20-100     |         S   1       1     |          2  ,       |         S   2       1     |          2       /        d      B Frequency / GHz Fig. 4. Frequency domain transfer function  | S  21 | 2 (dashed) and insertionloss  | S  11 | 2 (solid) of the numerically optimized filter structure 0 0.5 1 1.5 2 2.5 3-0.5010.67      A   m   p       l     i    t    u      d    e      /     a  .    u  .  Time / ns Fig. 5. Input impulse (solid) and corresponding time domain impulseresponse (dashed) of the numerically optimized filter structure TDT Fig. 6. Schematic design and realization of the improved sensor design fortime domain transmission measurements The key benefits of this new senor design are given by the shortunshielded signal path and its fixed mechanical length whichdoes not depend on the measuring position. Moreover, the useof the described coupling structures enables the possibilityto perform real transmission measurements in soils, e.g. inboreholes without the necessity of a second measuring port atthe end of the sensor.Thus, one can achieve highly accurate measurement resultsdue to the fact that transmission measurements are less influ-enced by multiple reflections caused by the material under testor the sensor itself. Additionally, this sensor is suitable for themeasurement of smooth permittivity variations as well as forthe measurement inside layered materials. Due to its compactdesign the new sensor design can be used for spatially resolved                  sensor plastic tubeTDTsystemsteppermotor Fig. 7. Measurement setup: TDT system, stepper motor and the sensorinserted into material of interest soil moisture measurement by moving it stepwise, e.g. in aborehole.IV. M EASUREMENT  S ETUP For the characterization of a soil moisture profile the sensoris implemented into a measurement setup which is describedin the following. The described sensor yields the permittivityfor one measurement position. To get a moisture profile itis necessary to perform measurements in several measuringpositions. Therefore the probe is inserted into a plastic tubein which it can be moved by a stepper motor. The step sizeof the probe movement yields the spatial resolution of themoisture profile. Naturally, this spatial resolution is limited bythe performance of the used TDT-system.Concerning this contribution the measurement system is basedon an industrial TDR system. This TDR system operates in thebaseband and offers a bandwidth up to 3 GHz. The jitter of thisTDR system, which defines the maximum spatial resolution of the TDR-system, is about 400 fs yielding a spatial resolutionin the sub-centimeter range. To perform TDT measurementsa further detector for the transmitted pulse is needed. Inthis case the detector is implemented by an extension of an existing system. Thus the resulting measurement systemremains as compact as usual TDR systems. Additionally theuse of an extended TDR system offers the possibility toperform reflection measurements as well. This allows to obtainfurther information about the permittivity.Fig. 7 shows the entire measurement setup inserted into amixture of soils with different permittivities.V. M EASUREMENT  R ESULTS The following part illustrates some exemplary measurementresults achieved with the presented sensor. For comparison,Fig. 8 shows a permittivity profile achieved with a displaceablediscontinuity which was moved along a one-wire line aspresented in [11]. In this case four sections of the surroundingof a borehole were filled with sand of different water contents.Between these sand sections there was one empty section (air).The step size of the displacement of the single measuringpositions is 1 cm in this case. The solid line is the 5-pointmoving average curve of all single data points measured witha common TDR-system. As the graph shows, the differentsections are clearly distinguishable, but nevertheless thereare some uncertainties regarding the effective permittivity.Concerning the sections without filling (air as surrounding) aspread of data is observed, which may be explained by externaldisturbances. Furthermore the positioning of the one-wire lineis not exactly centered for each measurement position. 220  0255575105145012345678       ε    m   e   a   s        /     a  .     u  . airairair sand 1 sand 2 Measuring Position / cmFig. 8. Reflection measurement results performed with movable discontinuity 0305070901101302000510152.512.57.51  Sensor Position / cm       ε    m   e   a   s        /     a  .     u  . airairair sandsandsandgraveldrydry wet Fig. 9. Measurement results for dielectric profile consisting of air, gravel,wet and dry sand performed with the newly developed compact sensor 02468101214161 2 3 4 5 6 7 40 %Vol   38.93 (real: 40 %)21.93 (real: 20 %)36.5833.1629.4325.36 real water content / % Vol.determined water content / % Vol. Time / h       ε     m   e    a    s         /      a   .      u   .  ε meas Fig. 10. Static measurement of the apparent permittivity  ε meas  and thewater content with one fixed measurement position and water dripping downon sand The following results are achieved with the improved sensordesign described in this contribution. Fig. 9 shows the apparentpermittivity for the case that the surrounding is filled withgravel, dry and wet sand. As expected, the results show avery smooth behavior. In comparison with the results achievedby performing reflection measurements, these results showa smaller spread of data concerning sections with air assurrounding. These improvements can be explained by theuse of a short unshielded signal path and the fact that realtransmission measurements are performed. Additionally reflec-tion measurements show a higher variation between the singledata points and the moving average if measurements withhigher permittivities are performed. This effect is caused bythe fact that these higher permittivities cause higher multiplereflections. Thus high permittivities in the surrounding resultin a higher spread of data. The results shown in Fig. 10 areachieved by a static measurement. In this case, the sensor wasfixed in one position and the surrounding was filled with drysand. Then a continuous measurement was started, e.g. the de-lay time was measured every 10 seconds. Furthermore, waterwas slowly dripped down on the sand for almost six hours.The graph shows the measured apparent permittivity  ε meas  andthe water content determined by using (5). A comparison withknown water contents shows that transmission measurementsperformed with the improved sensor design yield reproducibleand accurate measurement results. This measurement showsonce more, that there are nearly no fluctuations caused by ex-ternal disturbing signals or measurement uncertainties causedby the system itself.VI. C ONCLUSIONS The sensor design presented in this contribution enablestransmission measurements without the necessity of a measur-ing port at the end of the sensor. Additionally, performing timedomain transmission measurements offers the possibility toreduce the influence of multiple reflections by the use of timegating methods. Thus, the designed TDT-sensor is applicableinside layered materials as well as for the measurement of smooth permittivity variations. Furthermore, spatially resolvedpermittivity measurements can be performed by moving thesensor along the material of interest. Thus, the compact sensordesign presented in this contribution offers a very powerfulsolution for the measurement of permittivity in soils and e.g.in boreholes. The TDT electronic part can be attached to thesensor and be moved together with it, thus avoiding long RFcables. This solution allows very long measurement trackswithout a deterioration of the measurement accuracy.R EFERENCES[1] E. 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