A Wireless Inductive-Capacitive Resonant Circuit Sensor Array for Force Monitoring

A wireless passive sensor array based on inductive-capacitive (LC) resonant circuits capable of simultaneously tracking two points of force loading is described. The sensor consisted of a planar spiral inductor connected to two capacitors forming a resonant circuit with two resonant frequencies. When a load was applied to one or both of the parallel plate capacitors, the distance between the plates of the capacitor was altered, thus shifting the observed resonant peaks. Testing illustrated that applied loading to a particular capacitor caused a significant shift in one of the resonant peaks and also a smaller shift in another resonant peak. This interdependence resulted from each capacitive element being connected to the same inductive spiral and was accounted for with a developed analysis algorithm. To validate the experimental observation, a circuit simulation was also generated to model the sensor behavior with changing force/displacement. The novelty of this system lies not only in its wireless passive nature, but also in the fact that a single LC sensor was fashioned to detect more than one point simultaneously.


Introduction
Generally, wireless sensors consist of sensor components for taking local measurements placed at the areas of interest and a remotely located system to receive information wirelessly for processing and presentation [1][2][3].Since these systems lack physical connections between the sensing components and the processing apparatus, they are highly versatile in terms of sensor deployment, and are thus ideal for wide area monitoring.Additionally, wireless sensors have the capacity to operate, depending on the particular method of data acquisition and transmission, in an active or passive mode.Active sensors are powered with an internal source whereas passive devices receive power remotely.While active wireless sensors can monitor a wide range of parameters encompassing a large region, they can also suffer from significant installation and maintenance costs and battery lifetime limitations [4].Passive wireless sensors, on the other hand, have limited functionality compared to their active counterparts but are generally cheaper, easier to implement and last longer.There are many types of wireless passive sensors, and most of them are powered magnetically or electromagnetically.Examples of these sensors include magnetoelastic, inductive-capacitive, and surface acous-tic sensors [5][6][7][8][9].
A wireless passive sensor, known as the inductivecapacitive (LC) sensor, was developed to monitor changing environmental conditions such as temperature, humidity and pressure [10].This type of sensor altered its capacitance depending on the experienced environmental parameter, resulting in a shift in its resonant frequency.The change in resonant frequency was remotely captured with a coil antenna by monitoring its impedance change [10].Unfortunately, the limitation of the existing LC sensors is their inability to monitor multiple parameters.For applications that require simultaneous detection of multiple targets, more than one LC sensor is necessary, significantly increasing the overall sensor size with no improvement to sensor detection range.Therefore, a two element sensor was developed comprised of a planar square spiral inductor and two parallel plate capacitors.
While the operating principle of the presented sensor is the same as current LC sensor technologies [10], it features multiple sensing elements (capacitors) sharing the same inductor.As a result, there are interferences among the capacitive elements and further investigations were performed to realize the new, two-element sensor design.
The electrical representation of the two element LC sensor is shown in Figure 1, where the inductor is responsible for coupling to a nearby antenna, receiving power and transmitting information about changes in resonant frequencies, and the capacitors are responsible for sensing parameters of interest in terms of changing capacitance values.The inductor is separated into different segments, for convenience, named L 1 , L 2 , etc., that are connected to capacitors C 1 , C 2 , etc., respectively.To remotely detect the sensor's response, a network analyzer generates a frequency-varying electromagnetic field through the antenna to the sensor's inductor and then monitors the change in the antenna's impedance.This work focused on a sensor with two inductor-capacitor pairs for two-parameter monitoring.However, more inductor-capacitor pairs can be added to the circuit to form a more complex sensor capable of simultaneously measuring more than two parameters.
Prior to actual data collection, the background impedance (measurement with no sensor present) was collected so that all measurements could be subtracted from the background coil impedance to obtain the pure sensor response.Figure 2 shows the measured resonance spectrum of the fabricated sensor.Two resonant frequencies  are shown on the plot, where Resonance 1 and Resonance 2 resulted primarily from C 1 and C 2 , respectively.During testing, loading C 1 caused a decrease in Resonance 1 due to an increase in the capacitance value of C 1 .However, there was also a slight decrease in Resonance 2 even though loading on C 2 remained constant.This interference is expected and explained as a result of the interdependence between capacitors physically connected to one inductive spiral (see discussion for additional details).To account for this, an algorithm was developed to determine the actual force based on the changes in both resonant frequencies.

Analytical Model
An analytical model was developed to simulate the sensor response.The model was based on the equivalent circuit in Figure 1, assuming for simplicity that the coupling magnitudes of each inductor loop were equal at all frequencies (see Figure 3).Note the addition of R 1 and R 2 to more accurately predict the losses in the inductors and capacitors.The inductance, capacitance, and resistance values of the sensor were measured using an impedance analyzer (Agilent 4192) and were used for all simulations.The analytical circuital equations were plotted with MATLAB.
To determine the change in capacitance due to force loading, the compressive strain of the sensor's parallelplate capacitors during force loading was determined experimentally using a TestResources Inc. 100 Series mechanical testing device.The device exerted a compressive load (0 -100 N) onto the sensor's capacitors while measuring the compression of the capacitors.This allowed calculation of the change in the distance between the two plates of the capacitor for determination of the capacitance by the equation [11]: where ε is the permittivity of the medium between the capacitive plates, A is the overlapping surface area of the conducting plates, and d is the distance between them.The permittivity of the sensor medium was determined using the capacitance value, plate areas, and distance initially measured prior to loading.The capacitance calculated from change in displacement was then used as an input for the circuit model of the sensor impedance to find its resonant frequencies.
The simulation model was developed by determining the impedance of the resonant sensor, Z, when looking into the spiral inductor terminals (top of L 1 , bottom of L 2 ) as illustrated in Figure 4.The branches containing R 2 and L 2 in parallel with C 2 can be lumped as: where j is the imaginary number and ω is the radian frequency.Then, the series combination of Z 2 and L 1 can be e parallel C , resulting in: Equation ( 3) was then evaluated in MATLAB for frequ  3) that because the poles of the resonant circuit are dependent on both capacitors, C 1 and C 2 each affect both resonant frequencies.The same analysis can be extended for additional capacitiveinductive pairs, allowing design of sensors with higher numbers of sensing parameters.
Figure 4 illustrates the sens ricated from a printed circuit board using a milling machine.The line width of the pattern was 0.3 mm and the spacing between lines was 1.8 mm.The inductor part of the sensor was a square spiral measuring 90 mm × 90 mm encompassing 10 turns.Additionally, at the center of the sensor was a rectangular conductor measuring 48 mm × 48 mm.A parallel plate capacitor was then formed by adhering silicone foam between the conductor pad and two pieces of copper clad FR-4 fiberglass PCB, measuring 56 mm × 27 mm each.A multiple pole LC resonant circuit was then fabricated from this setup by connecting the top PCBs to the spiral inductor.The developed sensor was monitored using a 105-mm-diameter single loop detection coil connected to an Agilent Network/Spectrum Analyzer (4396B).
To evaluate the pe terms of signal strength, two single-element LC sensors with resonant frequencies at 10 MHz and 38 MHz, were fabricated.The single element sensor was similar in design with the previous work [10].The lengths of the inner and outer loops of the spiral inductor of both single-element sensors were 34.4 mm and 64 mm, respectively.Additionally, the center capacitors of the single-element sensors were 32 mm × 32 mm and the combined footprint of these two single-element sensors was equivalent to the footprint of a single two-element LC sensor.Moreover, to ensure the desired resonance was achieved (10 MHz and 38 MHz) the inductors of the sensors were adjusted to have 10 and 7 turns, respectively.w ized automated pneumatic mechanical loader system.The loader was controlled with a computer through standard RS232 communication using a customized Visual Basic program, and the detection antenna was situated around the loading platform.During experiments, the loader applied force to C 1 from 0 N to 89 N at 22.25 N intervals while a constant force was held on C 2 .This constant load at C 2 was then changed, from 0 N to 89 N at 22.25 N intervals, and full loading was reapplied to C 1 .The resulting sensor output was collected via an antenna with the network/spectrum analyzer.This process was then repeated with C 1 acting as the constant loading element.
To e ement sensors, the antenna was kept stationary and connected to the network/spectrum analyzer during distance testing.The two-element sensor was adhered to a beam with double sided adhesive tape and suspended above the antenna, with the opposing end of the beam adhered to an adjustable scaffold.During characterization, the distance between the antenna and the sensor was increased at 5.0 mm intervals until the resonant peak could no longer be measured.The sensor was then returned back to its original position at 5.0 mm intervals with data being collected at each interval.This procedure was then repeated with an antenna measuring 161 mm in diameter to further characterize and compare the sensors in relation to changes in sensor response as a result of altering the antenna size.The same experiment was repeated for both single-element sensors to determine their responses against separation distance from the antenna.
As indicated in Figure 1, the was in series with inductor L 1 and capacitor C 1 (instead of a parallel LC pair of L 1 and C 1 ).As a result, the impedance of the sensor was not a simple superposition of the two LC pairs but rather a complex relationship (as indicated in Equation ( 3)) that allowed the value of C 2 to interfere with the resonance of the first LC pair, and vice versa.Experimentally, the loading effect on each capacitor was also found to be interdependent on the load experienced by the other capacitor.As a result, an iterative algorithm was developed to determine the force loadings on C 1 (F 1 ) and C 2 (F 2 ) based on the resonant frequency shift of the associated resonant peaks (f 1 and f 2 respectively).Since the sensor is a forth-order circuit, the resonant frequency is expected to change with the capacitance following an inverse of quartic root curve.However, for simplicity and also due to the narrow force range, a 2nd order polynomial equation was applied to represent the resonant frequency change with loading.The 2nd order equation was found to provide a good fit with the experimental results (see Figure 6).Therefore, f 1 could be expressed in terms of F 1 as: However, to accommodate the depe 1 2 th ndency of f on F , e coefficients in Equation ( 4) were expressed as: where a i1 , a i2 , and a i3 were determined empirically.Similarly, f 2 was primarily dependent on F 2 with a slight dependence on F 1 and could thus be described by: where b i1 , b i2 , and b i3 were determined e te i and on ults of loading C 1 from 0 N to co mpirically.The i rat ve process began by setting F 2 to 0 N determining A using Equation ( 5), followed by so i lving for F 1 using Equation ( 4).The calculated F 1 was then substituted into Equation (7) to solve for B i , which was then used to solve for F 2 with Equation ( 6).The value of F 2 was then substituted back into Equation ( 5) and the process was repeated until both F 1 and F 2 converged within an acceptable error.depicts the results of loading C 2 from 0 to 89 N while C 1 was held constant at different loading conditions.As can be seen, changing the constant load on the other capacitor decreased the amplitude of the force loading curve.Analyzing the changes in the curves revealed that their behavior followed a 2nd order polynomial equation.By curve fitting this data, a set of 2nd order polynomial coefficients was obtained.These coefficients were used in Equation ( 4) and Equation ( 6) to solve for F 1 and F 2 .

Force Monitoring
Figure 7 plots the calculated F 1 and F 2 when the values of f and f corresponding to F 1 = F = 66.75 N w Figure 9 shows the signal amplitudes for the two-elent single-element sen- The result of the MATLAB simulation for the sensor hown in Figure 10.As (resonant frequency 1) and f 2 (resonant frequency 2).The values for F 1 and F 2 until converging to the correct solutions.For this particular input condition, the convergence occurred at about 25 iteration steps, which was typical for all loading conditions.Figure 8 plots the percentage errors of the calculated forces when F 1 = F 2 .These errors were largely due to errors in the collected f 1 and f 2 data when compared to the 2 nd order polynomial curve fit.Another observation in Figure 8 is that the errors in F 2 are larger than those of F 1 .This is due to a poorer curve fitting of the dependence of f 2 on the force loading at C 1 (as indicated in

Sensor Characterization
ment sensor and the two equivale sors with increasing separation distance from the antenna.As expected, the resonant amplitudes of the sensors decreased with increasing distance between the antenna and sensor.Additionally, it can be seen that the two-element sensor had larger signal amplitude and, as a result, a larger detection range than the two single-element sensors of equivalent footprint.Moreover, the differences between the two-element and single-element sensors were also larger with the larger antenna since the coupling between the antenna and the smaller single-element sensors changed more with increasing antenna size than the coupling between the antenna and the two-element sensor.

Theoretical Validation
impedance at zero loading is s depicted, the resonant peaks are at relatively similar frequencies when compared to the experimentally measured curve from resonant frequency is due to stray inductances and parasitic capacitances not accounted for in the circuital model.
Another notable point is the larger second resonance peak in the measurement (but not in the simulation).This is largely due to the self-resonance of the coil antenna (at about 60 MHz), causing signals closer to 60 MHz to be amplified.As a result, the amplification near the selfresonance of the coil antenna reflects on the measured sensor im nce.peda Figure 11 depicts the simulated circuit results in correspondence to the experimentally collected data.The error between the simulated and experimental curves is likely an effect created by parasitic capacitances and inductances within the sensor circuit.In addition, the change in permittivity of the silicone foam between the capacitor plates due to compression was assumed to be negligible, but may have been significant enough to cause the observed error.

Conclusions
f loading these capacitors was tested -to-reach civil engineering A wireless passive LC multi-element sensing array was presented.The fabricated system functioned by incorporating two parallel plate capacitors into a signal LC circuit, thus producing two resonant peaks from a single ircuit.The effect o c with a changing load of 0 N to 89 N at 22.25 N intervals applied to one capacitor while a constant load was applied to the other capacitor.The response of each capacitor was found to be interdependent on the constant load applied to the other capacitor.This interdependence was handled through the use of an iterative algorithm.A circuit model was also developed to validate the experimental results.Additionally, when compared to an equivalent setup of two single-element LC sensors, the two-element LC sensor not only had a stronger signal, and thus a larger detection range, but also exhibited less change when coupled with different sized antennas.Due to the limited detection distance (about 8 cm), the current version of sensor would be useful in places such as monitoring force loading in hard structures, for example, concrete and wooden beams in buildings.This device, with further development, represents an innovative method of multi-parameter/target sensing with a single LC circuit.One potential application that can highlight the advantage of this sensor compared t previous LC sensor is as an embedded sensor for pas monitoring of stresses in a large area, such as under a roadbed.If the single-element LC sensor is employed, the user needs to monitor the response at each individual sensor location, which could be time consuming for road condition monitoring.However, for the multi-element sensor design, a number of stress-sensitive capacito pacitors can be placed at different locations and connected to the inductor via wires as illustrated in With further development, the number of elements could be expanded thus providing for an even more robust force mapping sys terdigital capacitors functionalized toward certain chemicals and environmental parameters, a sensor could theoretically be developed and deployed for monitoring multiple parameters such as humidity and volatile compounds.The future works of this system include increasing the number of elements, investigating methods to decrease overall sensor size, increasing the detection range, and adapting the system to monitor other parameters such as heat, chemical concentrations, moisture, etc.

Figure 1 .
Figure 1. Circuit representation of the two-element LC sensor and the detection antenna.

Figure 2 .
Figure 2. Resonant spectrum of the two-element LC sensor measured with the network analyzer showing two resonant peaks corresponding to C 1 (Capacitor 1) and Resonance 1, and C 2 (Capacitance 2) and Resonance 2. The values of C 1 and C 2 were both measured as 12.5 pF, and L 1 and L 2 were measured as 3.3 µH and 4.4 µH, respectively.

Figure 3 .
Figure 3. Circuital model used in the MATLAB simulation.

Figure 4 .
Figure 4. (a) Isometric illustration of the two-element force sensor and (b) the top view of the sensor, as well as (c) a photograph of the fabricated sensor.The wire connections between the top capacitor plates and the spiral inductor are

2. 2 .
Sensor Fabrication or design.Sensors were fabrformance of the two-element sensor in 2.3.Experimental Setup and Procedure to evalu-encies from 10 MHz to 50 MHz at intervals of 1 kHz to determine its resonant frequencies at capacitance values corresponding to those acquired from the force-displacement curve.The values of the electrical components used in the simulation were measured as R 1 = R 2 = 5 , C 1 = C 2 = 12.5 pF, L 1 = 3.3 µH, and L 2 = 4.4 µH.It should be noted from Equation (

Figure 5
Figure 5 illustrates the experimental setup used ate the force response of the fabricated sensor.The sensor

Figure 5 .
Figure 5. Experimental setup for testing the force sensit y

Figure 6 (
Figure 6(a) depicts the res 89 N at 22.25 N intervals while C 2 was held nstant at 0 N, 22.25 N, 44.5 N, 66.75 N, and 89 N. The sensor was 1 cm from the center of the coil.Similarly, Figure 6(b)depicts the results of loading C 2 from 0 to 89 N while C 1 was held constant at different loading conditions.As can be seen, changing the constant load on the other capacitor decreased the amplitude of the force loading curve.Analyzing the changes in the curves revealed that their behavior followed a 2nd order polynomial equation.By curve fitting this data, a set of 2nd order polynomial coefficients was obtained.These coefficients were used in Equation (4) and Equation (6) to solve for F 1 and F 2 .Figure7plots the calculated F 1 and F 2 when the values of f and f corresponding to F 1 = F = 66.75 N w

Figure 7 .
Figure 7. Calculated F 1 (force loading on Capacitor 1) nd F (force loading on Capacitor 2) based on the values of f expected values for F 1 and F 2 were 66.75 N.

Fig- ure 6
(b) where the curves are not as well spread as the curves in Figure6(a)).

Figure 2 .Figure 8 .Figure 9 . 2 .
Figure 8.The percentage errors of the calculated forces compared to the actual force loadings when F 1 = F 2 .

Figure 12 .
Figure 12.Illustration of the difference between single and multi element LC sensors when applying for wide area monitoring.The shaded squares represent the sensing element and the white squares the inductor.The detection points are represented by arrows.

Figure 12 .
As a result, a number of sensors can be m d tem.Additionally, by utilizing in-o the sive r caonitore simultaneously, which can significantly shorten the monitoring time.