Micromachined Ceramic-based Chipless LC Resonator for High-Temperature Wireless Sensing Application in Harsh Environments

: The primary objective of this work was the fabrication and testing of a wireless LC resonator based on micro-patterned electroceramic materials for the monitoring of high-temperature systems. The two-dimensional planar LC resonator sensors were designed and simulated using ANSYS Maxwell software, and these sensors were then fabricated from electrically conductive La 2 NiO 4 /Al 2 O 3 particulate inks. The patterning and deposition of the ink were completed using a novel micro-casting process onto Al 2 O 3 ceramic substrates, and the final pattern was bonded onto the substrate at 1200 o C for 2 h. The final patterned materials were characterized using X-ray diffraction (XRD), scanning electron microscope (SEM), and four-point conductivity to characterize the phase and microstructure development, and the resultant electrical conductivity (at 500-1200 o C), respectively. The frequency shift with respect to temperature was measured, which is directly related to changes in the sensor’s dielectric permittivity and pattern dimensions. The sensors were characterized at 500 – 1000 o C in an ambient atmosphere with an RF signal ranging from 10 – 80 MHz at 175 kHz·s -1 sweep rate. A new robust and adaptive signal processing approach was introduced to increase the degree of freedom for analyzing the wireless sensors.


Introduction
Wireless communication is very desirable in high temperature applications as it allows sensors to be placed at critical sensing locations where making electrical connections to the sensor is difficult and degradation of these electrical lines may cause altered sensor response due to connection and interconnect changes. The major limitation with the conventional temperature measurements using solid-state sensors such as thermocouples, resistance temperature devices (RTD), and thermistors is that one end of the sensor filament should reside in a relatively cold zone. These devices cannot be applied in a sophisticated high-temperature system due to several design incapacities and the interconnect issues as discussed above. The passive feature of the sensors is critically important as the extremely harsh environment renders the use of batteries for power to be impractical or infeasible. To mitigate the issue of high temperature sensing in harsh environments for sophisticated systems, a passive wireless temperature measurement strategy has been implemented by exploiting various wireless communication technologies. Among various reports, recent studies show that the surface acoustic wave (SAW) and RF-based wireless resonator mechanisms can be applied to high temperature sensor application since these two mechanisms do not require an external power source for the operation [1][2][3][4][5][6][7]. R. Behanan utilized the SAW mechanism coupled with an RF antenna for various mechatronic application in ambient environmental condition [3]. Unfortunately, many of the high-performance piezoelectric materials properties (with temperature) can be utilized, and the sensor may be further protected by a barrier coating. In addition, these sensors can be fabricated with no lead wires that extends through the high temperature system, which means that the lead wire influence on the sensor measurements is not present.
RF powered inductor/capacitor (LC) technology shows great promise to be embedded within (or on) active components. In most cases, these LC resonators are printed or deposited on the surface of a component to form a planar structure composed of an inductor (L) and an interdigitated capacitor (IDC) connected in series. The fundamental mechanism of the sensor is based on change in capacitance with respect to the temperature [12,13]. The change in capacitance will alter the resonant frequency which is unique to every temperature. The shifts in the resonant frequency can be wireless detected and temperature data can be inferred. The inductor which is connected in series to complete the LC resonator circuit is used to absorb and re-radiate the electromagnetic radiation which enables wireless interrogation capability of the sensor. where, f r is the resonant frequency, L is the inductance, and C is the capacitance of the sensor.
The capacitance is inversely proportional to the resonant frequency which shows, as the capacitance increases, the resonant frequency will decrease. In general, the dielectric permittivity of most dielectric ceramic materials, such as alumina and zirconia, increase with temperature [8][9][10][11][12]. As the temperature of these electroceramic material increases, the resonant frequency of the LC resonator will decrease or in other words, the peak will shift towards the left side of the spectrum.
The IDC and capacitor may be deposited onto stable dielectric substrates such as alumina (Al 2 O 3 ) or yttria stabilized zirconia (YSZ). The "fingers" of the IDC and the spiral inductor are usually fabricated using a conductive material. As discussed above, the change in capacitance as a function of temperature can be attributed to: 1) a change in dielectric permittivity of substrate, 2) the thermal elastic strain causing a change in dimension of the IDC/inductor pattern, and 3) a change in the conductivity of the IDC/inductor pattern. Among these factors, the former of the two has a well-established relation to the change in resonant frequency as a function of temperature.
Although, electrical conductivity plays a role in the overall sensor response, there are no reports showing its effect on the sensor response. In general, higher conductivity is preferred for an effective change in the resonant frequency. Theoretically, a minimal change in electrical conductivity will not affect the sensor response because the other two mechanisms dominates over the electrical conductivity. When the electrical conductivity is lower, there will be a significant shift in the resonant frequency because lower conductive material leads to lower capacitance as well as mutual inductance.
LC sensors were shown previously in lterature to be used as passive wireless sensors at high temperatures, but stability issues with the conductive material still needs to be addressed. The sensors reported in the literature are predominantly fabricated by depositing precious metals such as silver or platinum on ceramic substrate by thick film technology [8][9][10][11][12][13][14]. For example, the sensor presented by E. Birdsell was fabricated from platinum (Pt) onto a ceramic substrate [6].
Unfortunately, the LC components were quite large (>3 inch in minimum dimension) and were not able to fit onto a singular ceramic substrate. The IDC was also found to be unstable and was not operated for many cycles, since Pt (and other precious metals) are known to de-wet and form hill-lock structures during high-temperature operation when deposited onto oxide substrates. Also, there is a large difference in coefficient of thermal expansion between Pt and the oxide substrates, which will cause thermomechanical issues. Although, metals may provide better signal response in the low to moderate temperature regime, they cannot be applicable in a high temperature regime; therefore, the use of a highly conductive ceramic may be a feasible alternative. As with the E.
Birdsell work, the dimensions of the reported sensors are large (again, >3 inch in minimum dimension) to integrate with sophisticated systems, such a fuel cell, gasifier, turbine blades, and other micro high temperature systems [6]. An alternate fabrication approach is needed in order to miniaturize the dimension of the sensors to overcome the geometric constraints of the current fabrication approach [8][9][10][11][12][13][14].
In this work, a pure ceramic and electroceramic-based LC resonator (sensor) was fabricated, which is capable of measuring temperatures to 1000 o C and above. The sensor was fabricated with an electrically conductive electroceramic composite patterned on a polycrystalline alumina (Al 2 O 3 ) substrate. We introduced a novel fabrication process for the miniaturization of the sensor without compromising the expected wireless signal response. The miniaturization technology discussed in this work allows for the integration of a passive wireless sensor to numerous applications to monitor the temperature and health of the high-temperature system.
In this paper, we also introduce a novel approach for processing the received wireless response from the temperature sensor. The conventional approach is to track changes in the resonant frequency with the expectation that the inductance and/or capacitance of the sensor will change with temperature in a predictable way [8][9][10][11][12][13][14] This requires that the electrical characteristics of the substrate and electrode materials and their interactions can be well modeled as temperatures vary, and that the material properties are stable over many heating and cooling cycles. In practical scenarios, material properties are not known accurately, and they may change (particularly for the wired interconnects) during heating and cooling cycles. To mitigate these issues, we have chosen to measure the response of the sensor over a wide band of frequency around the expected resonant frequency (which may not be precisely correct). In order to achieve this goal, we created a database of known signature wideband frequency responses at each temperature of interest. This permits the measurement of unknown temperatures by comparing the measured wideband frequency response with the database of known responses. Thus, the temperature measurement problem is transformed into a signal matching problem, which is a well-studied fundamental issue in statistical digital signal processing. Applications in biometrics, RADAR ranging, digital communications, and other areas use a similar method to analyze and correlate measured signals to databases of known signals. This approach has the advantage of not requiring the tracking of any particular resonant frequency. All that is required to measure temperature accurately is that the wideband frequency response changes in some measurable way as the temperature changes. Our approach can even be made adaptive, i.e., it works when material properties change over time simply by creating new signatures at desired time intervals.

Modeling and simulation of the LC resonator
ANSYS Maxwell (Ansys Inc., Canonsburg, PA) software was used to perform initial modeling and simulation of the LC resonator. ANSYS Maxwell is a low frequency electromagnetic (EM) field simulator. The software utilizes finite element analysis to simulate the inductance, mutual inductance, capacitance, EM fields, and other key features of the 2D or 3D models of the sensors. The software allows one to select the materials used in the 2D and 3D models. The electrical properties of the materials (electroceramic composites and the dielectric substrate) were entered into the software for the computational analysis. ANSYS Maxwell is also able to build nonlinear equivalent circuits from the 2D and 3D models and perform frequency analysis on these circuits. Fig. 2 shows the schematic of the 2D representation of the modelled passive wireless sensor for high temperature application. For the square planar inductor, we used a fifteen-turn (n) inductor coil. The coil was 0.15 mm wide with 0.15 mm spacing between turns. The outer diameter was 19 mm with an inner diameter of 10.3 mm, as shown in table 1. An interdigitated capacitor (IDC) was chosen for this work, since this type of capacitor could be easily patterned or deposited onto planar surfaces and substrates. An IDC is specified by the following physical characteristics: number of fingers (n), the width of the fingers (w), the spacing between the fingers (G), and the distance between the fingers (λ). A target resonant frequency of 13.56 MHz was chosen, and this was the basis for choosing a suitable capacitance which resulted in the target frequency whose specifications are listed in table 1. Using these physical characteristics, a 3D model of the square planar inductor and IDC were built in ANSYS Maxwell and its inductance and capacitance were simulated. The inductance and capacitance values are estimated as 5.25 µH and 25.5 pF for the physical specifications shown earlier.

Digital signal processing methods for temperature measurement
As discussed above, our signal processing approach differs from the state-of-the-art in that we do not track a single resonant frequency. Instead, we measure the wideband frequency response of the sensor around the expected resonant frequency to capture frequency changes that cannot be modeled or expected. This includes resonant frequency changes, but our approach will work even if the resonant frequency does not change as expected, as long as the wideband frequency response changes in any measurable way as temperature varies. Once we have the wideband frequency response signal (a vector), we compare it to a database of frequency response vectors at known temperatures, which we call signatures. This is similar to matched filtering, which is used in RADAR systems and digital communications [15,16]. We use two signal processing approaches to complete the matching: crosscorrelation and maximum absolute error. For our application, cross-correlation is extremely simple.
Assume that the columns of the matrix C (the signature database) contain the frequency response vectors (taken across a wide band of frequencies around the expected resonant frequency) at each of the m temperatures of interest, i.e., = [ , , … … , ]. Suppose that the measured frequency response at an unknown temperature is contained in the column vector r. We create the 1 × decision statistic Our temperature estimate (index) is simply given as the index of the maximum component in d, call it ̂ for the cross-correlation algorithm. We look up the temperature that corresponds to this index and we have our temperature estimate. Importantly, our method does not rely on any particular physical material model. It only requires that the wideband frequency response change in some way across frequencies. When material properties change due, for example, to heating and cooling cycles, we need only update our database matrix C with new signatures at known temperatures. Thus, our approach is robust and adaptive.
Our minimum absolute error method simply finds the signature which has the minimum absolute error difference relative to r. Let = | − |, i =1, 2, …, m be the absolute difference vector between r and the i th signature. Let ̅ be the sum of the elements of . The minimum absolute error temperature (index) estimate can be simply written as ̂= ̅ .
Both temperature index estimates ̂ and ̂ can be computed easily using Matlab or any computing language. To improve performance, we used a sliding window optimization technique to determine the best band of frequencies to use (within the wideband response) for temperature estimation. We can determine this a priori by experimentation before the algorithm is used for temperature estimation. Instead of analyzing the entire spectrum of data, we use overlapping windows of various sizes and center frequencies and choose the window width and center frequency that maximizes performance. The window size and the position of the window are both variable and can be optimized based on its performance. This example shows a window size of 5 and changing the window position from 10.1 MHz in the first case to 10.2 MHz in the second case and so on. After running the methods through all these cases, the new algorithm will output all cases which give the correctly predicted temperature. In this work, the algorithm with window sizes of 5, 10, 50, 100, 500, 1000, 2000 and 2400 were used to predict the temperature from the wireless signal response irrespective of its resonant frequency.

Fabrication of the all-ceramic wireless LC resonator sensors
As previous stated, the active sensor circuit was composed of a conductive ceramic composite  photolithography process to create the micro-molds, (b) micro-casting of the LNO -Al2O3 ink within the micro-molds using a squeegee blade (shore hardness -70 durometer).

Wireless characterization setup
The pure passive functionality of the sensors was not evaluated in this work but were reserved for the follow-up publications. In this paper, the sensor concept was tested by hardwiring the sensor with Pt interconnects as explained in the previous section. A pair of identical resonators (as shown in fig. 4a) were used to characterize the wireless signal response where one resonator was connected to the signal generator (actual working sensor) and the other to the spectrum analyzer (interrogator antenna).
Identical resonators were used to maximize the mutual inductance between the sensor and the interrogator, which leads to better coupling and increased signal efficiency. The interrogator can also be replaced with a commercial PCB antenna with a frequency range between 10 -100 MHz. However, the RF signal from the interrogator needs to be amplified to have a higher signal-to-noise ratio. The The initial characterization of the sensor was performed by measuring the frequency response from 500 to 1000ºC with an increment of 100ºC. The frequency response is logged multiple times for a given temperature and the average of the data points were used in further analysis. The data from this initial run will be referred to as a signature database since the temperature readings were known by measuring with an external thermocouple. In order to characterize the sensor, the temperature was cycled between 500 and 1000 o C with in situ wireless signal acquisition as explained above. The sensor response from the unknown temperature is compared to that of the signature database to estimate the unknown temperature by the signal processing algorithms.

Phase development in the electroceramic composite
The LNO and its composites with Al 2 O 3 were used as the conductive material to fabricate the wireless resonators. Any change in the microstructure and/or chemical composition during the sintering process (or continuous thermal cycle) may alter the electrical property of the conductive composite. This change in electrical property may reflect in the wireless response as additional noise or frequency shift. Therefore, it is important to understand the chemical/phase stability of the LNO-Al 2 O 3 electroceramic composites at high temperature printed onto the given substrate.
The phase analysis study was performed by XRD on the pure LNO and LNO-Al 2 O 3 composites to understand the phase development and secondary phase formation in the ceramic composite. The XRD phase analysis of the LNO particles calcined at 1400 o C was performed to confirm there are no secondary phase formation during the calcination process. Fig. 5 shows the XRD pattern of single phase LNO which has a tetragonal crystal structure with a space group of I4/mmm [17].
The single phase tetragonal LNO with a pure K 2 NiF 4 structure was reported to be a good electronic semi-conductor for high temperature electroceramic applications [17][18][19][20].   fig. 6(a & b), the XRD pattern over this time scale shows that after the initial thermal processing step, there is no further phase transformation/degradation.

Electrical characterization of the ceramic composites
The electrical property of the LC resonator such as capacitance and inductance depend on the electrical conductivity of the electroceramic composite, and these conductive lines forming the LC sensor must remain consistently conductive during operation. Therefore, the conductive properties of these materials must remain stable over the duration of high-temperature operation; otherwise, the intrinsic electrical signature may alter which would lead to a misinterpretation of a temperature or mechanical event. So, the electrical conductivity of the 50-50 and 60-40 LNO-Al 2 O 3 composites was tested from 500 to 1200 o C. Fig. 8(a & b) shows the electrical conductivity of the

. Previous reports on
LaAlO 3 stating that it is a high-κ (but weak dielectric) material [22]. Suzuki et al. [23] report showing the band gap of LaAlO 3 is 6.5 eV which clearly proves it is an electronic insulator.
Materials with such a large band gap will stay as a stable insulator even at high temperature [23].
Kou et al. [24] study shows NiAl 2 O 4 spinel phase is a p-type semiconductor under similar operating conditions. The report also shows that the conductivity mechanism of the NiAl 2 O 4 spinel phase which is due to the formation of nickel vacancies as a function of temperature. The temperature dependent conductivity response is also similar to the one presented in this work.
Based on the evidences reported by Kou et al. [24], it can be confirmed that the electrical conductivity of the 50-50 LNO-Al 2 O 3 composite is due to the presence of NiAl 2 O 4 spinel phase.
However, the conductivity of the composite is lower than the conductivity of the pure NiAl 2 O 4 phase since the composite is a combination of an insulating and a semi-conducting phase [24].  reported on temperature dependent electrical conductivity of NiO, where NiO is also a p-type semiconductor and the mechanism of electrical conductivity is due to the formation of nickel vacancies as a function of temperature. Feinleib et al. [26] performed first principle calculations on the band structure of pure NiO to showcase temperature electrical conductivity of the NiO. The results also corroborate the experimental values reported by Mitoff et al. [25]. The temperature dependent electrical conductivity behavior presented in fig. 8

(b) is similar to the work reported by
Mitoff et al. [25]. It is desirable to have higher conductive electroceramic composite for the sensor fabrication in order to improve the signal response as well as reduce signal-to-noise ratio. Owing to the microstructural stability and increased electrical conductivity, the 60-40 LNO-Al 2 O 3 composite was chosen to fabricate and characterize the wireless sensor.

Microstructure of the ceramic LC resonator
If there is a microstructural change such as densification or grain growth as a function of thermal cycles, then the electrical conductivity (and wireless response) of the sensor composite will be altered. The microstructure of the LC resonator was analyzed by using SEM in order to understand the effect of grain growth or coarsening during the thermal operation cycles up to 1200ºC.
Microstructural stability is very important for repeatable and long-term sensor operation. Similar sensors (LC circuits) were fabricated and cut into 10 ×10 mm squares to perform SEM analysis which underwent the same thermal cycle as per the wireless sensor. One of the samples were imaged after sintering for 2 h at 1200 o C and a similar sample was imaged after undergoing several thermal cycles during the wireless characterization. Fig. 9 (a, c) shows the SEM microstructure of the LC circuit which underwent only the sintering cycle at 1200 o C for 2 h. The micrograph reveals the necking and percolation of the grains was well pronounced. Fig. 9 (b, d) shows the SEM micrograph of the LC circuit which underwent several thermal cycles during the wireless characterization. The micrograph is similar to the sensor before the wireless characterization. The micrograph was analyzed by computation image analysis, and the average grain size ranges from 0.5 -3 µm, which corroborates that there is relatively low coarsening or other microstructural changes during the operation cycle. Also, from image analysis, the porosity within the printed LC circuit ranges from 50 -60%, which also indicates that there is relatively no densification occurring during the repeated thermal cycles. It is evident from the microstructural analysis that the microstructure is stable after several cycles of thermal loading.  fig. 10 (a-d) which shows that there is no short circuit or macroscopic defects such as a discontinuity in the IDC and inductor pattern. It also shows that there is no residue from the micro-casting process after sintering and cleaning of the patterned substrate in an ultra-sonication bath. Fig. 10 (e-h) shows the SEM micrograph of one of the IDC/inductor patterns. Fig. 10 (h) shows the magnified image of the sensor material which has a porous structure as discussed above. Fig. 10 (g) shows the magnified image of the dense Al 2 O 3 substrate.
A thorough optical inspection was completed in order to make sure there are no defects in the IDC/inductor. If there is a defect such as delamination of the electroceramic composite, it would lead to an open circuit where the entire sensor becomes inoperable. If there is a short-circuit between two lines by means of a residue or improper cleaning during the pre-or post-processing of the micro-casting process, it will lead to electrical fluctuation and reduced capacitance or inductance.

Wireless characterization
In literature [8][9][10][11][12][13][14][15]    Since there are noticeable shifts recognized at different locations of the spectrum, the entire bandwidth of the spectrum (10 -80 MHz) was considered for further analysis. Wireless signal processing was performed in two steps for the entire bandwidth of the spectrum: 1) a temperature signature was created by averaging the frequency response from the wireless sensor over ten cycles while simultaneously measuring the temperature with an external thermocouple, 2) a similar approach was completed to the collect the signal response from the sensor at each characterization temperature but without using an external thermocouple and labeled as unknown temperature readings. There are three measurements taken for each sensor, where the first measurement was collected with the direct relationship to the temperature with an external thermocouple. The sensor was cycled two more time and the response was recorded. In this work three different sensor/antenna pairs (hereafter, named as Sensor 1, 2, and 3) were tested to complete the wireless characterization, where the sensors pairs were fabricated using in the same fashion with the same materials. Fig. 13 (a & b) shows the broadband wireless response of the first sensor/antenna pair (Sensor 1) during the second and third thermal cycles, respectively. The first cycle was completed with an external thermocouple to measure the response with respect to temperature. In the second and third cycles shown in this Fig. 13, an external thermocouple was not used, and these measurements were termed as "unknown" measurements (labelled as Unk 1 and Unk 2 measurement). The first thermal cycle is represented in the fig. 13 and labelled as Sig (i.e the temperature signature). Both the Unk 1 and Unk 2 macroscopically looked the same with peak shifts observed at various location of the spectrum. For Sensor 1, we used Pt wire to connect the sensor shown in fig. 13 to the signal generator. The Pt wire was bonded on to the contact pads of the sensor with an ink synthesized by Pt particles with ~1-3 µm in diameter. The pure metallic Pt ink connection began to delaminate after undergoing two thermal cycles from 500 to 1000 o C. The delamination arises from the coarsening of the Pt particles at high temperature. This may also be a contributing factor to the change in the shape of the RSS. As inferred from fig. 13 (a & b), there is a change in peak shape around 25 MHz. This may have been caused by the slight delamination of Pt interconnect at the contact pads because all the other parameters were kept the same during the wireless characterization. As discussed previously, two additional sensor pairs (Sensor 2 and Sensor 3) were fabricated and characterized in the same fashion as that of the first sensor pair showed in fig. 13. In order to see the effect of sensor electrical contact to the Pt wire on the wireless response of the sensor, we replaced the Pt ink with the same composition as the sensor design (with LNO-Al 2 O 3 ink). The LNO-Al 2 O 3 showed better adhesion to the contact pads as the contacts were made with the same material system. The wireless response from the second and third sensor pairs (Sensor 2 and Sensor 3) are shown in fig. 14 (a, b) & (c, d), respectively. It can be inferred from fig. 13 and 14 that there is a difference in the wireless response of the sensor tested with Pt and LNO-Al 2 O 3 interconnects at the contact pads, respectively. It is evident from above analysis that the sensor connection plays an important role in that the wireless response of the wireless response (in this case, where both sensor and integrator antennae are physically wired and in the hot-zone).
Additionally, the wireless response of the sensors shown in fig. 14 (a, b) & (c, d) is similar with a minimal change in the shape of the RSS, which may be due to the previous discussed materials, electrical and/or external parameters. For instance, small changes in microstructure and chemistry may have occurred during processing, and/or changes in the potential interconnection, which could have resulted in the intensity changes seen in the response. To identify these effects, it may take materials scientists extensive time to better understand and provide a solution. Therefore, a signal processing method should be applied that permits an adaptive analysis of the sensor signal, regardless of initial or in situ changes in the sensor response.
To further analyze the large dataset, we used a sliding window optimization technique to determine the best band of frequencies to use (within the wideband response) for temperature estimation using the Matlab software as discussed in section 2.2. The sliding window technique utilizes a modular and piecewise approach to compare a set of frequencies instead of the entire spectrum. The sliding window technique used in this work had a window size ranging from 5 to 2400. The window size determines the set of frequencies that are taken into account for the analysis. For instance, a window size 5 represents the first five data points considered for analysis and the algorithms find the correlation for that particular data set before moving to the consecutive (next 5) data points. A similar approach was performed for the other window sizes to determine the best matching window size for each data sensor pair. The optimal window size was chosen to yield the best match between the signature database and the unknown. After defining the window size, the two signal processing algorithms were used to match a Sig with Unk 1 and Unk 2 for each sensor pair. In particular, the cross-correlation algorithm looks for the signature (Sig) that has maximum similarity with the unknowns (Unk 1, Unk 2). On the other hand, the minimum absolute error algorithm looks for the minimum absolute difference between the temperature signature (Sig) and the unknowns. In order to compute the cross-correlations and absolute differences easily, a database of signature waveforms (Sig) at each temperature of interest are initially created offline, before real-time data collection. These waveforms are placed as column vectors in the matrix as discussed in Section 2.2. The first column of C represents the signature for 500 o C. The second column represents the signature for 600 o C, and so on to 1000 o C.
We denote each column separately using a subscript, i.e., The column vectors for the unknowns from 500 to 1000 o C can be written as, The matrix is multiplied with the transpose matrix of the temperature signatures ( T ) in order to derive the decision statistics ( ) which is represented as, The elements of the decision statistics matrix ( ) is represented as 500 −500 , 500 −600 ….., 1000 −900 , 1000 −1000 which is obtained by processing the elements in T and with the cross-correlation and minimum absolute error algorithms. The elements in the matrix represents a numerical value which is considered as a "score" to evaluate the goodness of the match. The first column of the matrix represents the data obtained by evaluating the Sig measured at 500 o C with all the unknown temperatures (500 to 1000 o C). A similar evaluation was performed on the rest of the temperatures (600 -1000 o C) in the columns two to six. As inferred from the Eq. (9), the diagonal elements in the matrix represents data evaluated for the temperature signatures and the unknowns at same temperature, i.e., 500 −500 represents the evaluation of the wireless response of Sig and Unk 1 at 500 o C, 600 −600 represents the data for Sig and Unk 1 at 600 o C and so on. For a good match, the diagonal elements in the matrix must be the larger than the non-diagonal elements. If any of the non-diagonal elements is greater than the diagonal elements, then the sensor response at that particular frequency range (or window size) is rendered incorrect.
Additionally, this method of processing wireless signals does not require a user defined threshold because the score provided to each element in matrix is relative and eliminates a hard threshold limit. The non-diagonal elements simply represent how distinguishable the unknown waveforms with respect to the temperature signatures. The higher difference between the diagonal and the non-diagonal elements represents the temperature signatures and the unknowns are more distinguishable from the other temperatures. for at least one algorithm, then there will be a minimum of 6 matches. In the case of windows with 5 or fewer matches, both the cross-correlation and minimum absolute algorithms failed to match at least one temperature. Therefore, the window sizes with less than 6 matches can be ignored for further discussion.   fig. 14 to estimate the window(s) which showed at least one match for each temperature. Table 5. Summary of the results of the signal processing methods using the split window technique for the two best matches for Sensor 1 using the spectrum shown in fig. 13.   Table 6. Frequency bandwidth of the two best matching windows with respect to each sensor pair.

Conclusion
In this work, a robust passive wireless sensor was modelled, fabricated, and characterized for high temperature applications, where the active sensor/antenna design was composed solely of a conductive ceramic material. The initial composition consisted of a operation. At the same time, the micro-casting method showed the capability of printing the complex LC circuit at a micron-level resolution. The micro-casting process is an improvement over any physical vapor deposition method and direct ink method, where a composite ceramic thin film would be nearly impossible to deposit, and the films would generally display nanometer grain sizes that would be unstable over extended high temperature operations.
The wireless characterization of the sensors was performed between 500-1000 o C with a frequency sweep between 10-80 MHz in an open-air muffle furnace without electrical insulation/shielding to mimic realistic working environment of the sensor. The sensors did not show the predicted peak shift at 500-1000 o C near the 13.56 MHz frequency. The initial measurements indicated that many intrinsic and extrinsic variables may affect the sensor signature.
This was unexpected since the sensors were fabricated in the exact same manner (using the same materials batches) and tested in the same exact manner. The seemingly scattered sensor response may have been exacerbated by the operation at the high temperatures used in this work, where this temperature range was not tested by previous researchers using a similar sensor design.
Most sensor developers would consider the sensor to be deemed unusable or a failure, since the expected signal shift was not identified for the given design at the various test temperatures. But after further review of the data, it was identified that the signal shifted from the centered frequency to other locations within the frequency bandwidth of the spectrum (depending upon the influences of the unidentified mechanisms and variables). It is believed that this phenomenon will be further seen in the future as the sensors are inserted in further "non-ideal" environments and at higher temperatures (which will translate into various influences on the electromagnetic, mechanical and chemical properties/behavior of the sensor). Therefore, an approach of analyzing the wider bandwidth of the spectrum was applied to characterize and monitor multiple peak shifts across the 10-80 MHz range. The work analyzed the received signal strength (RSS) instead of the S 11 parameter, or the phase angle ( o ) shift, to characterize the wireless response of the sensor. The use of the RSS translates a temperature sensing problem to a signal processing problem, which allows for more than one degree of freedom for data analysis. Thus, the sensors reported in this work can respond to the temperature variation irrespective of its resonant frequency. A temperature signature database was collected by simultaneously measuring the wireless signal from the sensor and the temperature of the furnace with an external thermocouple. In consecutive measurements, the wireless response from the sensor was also collected without the external thermocouple and compared against the temperature signatures. Both the cross-correlation and minimum absolute error methods, when used in conjunction with the sliding window technique, achieved the best results with the sensors in matching the unknown temperature readings to that of temperature signatures. Although the shape of the RSS may vary between various sensor/antennae pairs, the sensors showed similar frequency bandwidth (40 -65 MHz), where matches between the unknown reading with the temperature signatures were achieved effectively.
The signal processing methods proposed in this work were proven to be effective irrespective of the variation in the intensity and shape of the RSS. The robustness and adaptivity of the splitwindow technique proved to be very effective over conventional signal processing methods when the sensors operated in the harsh and varied conditions used in this work. The methods used were not only robust, but also adaptive to the change in the shape of the signal. As stated above, these signal processing strategies may be important in the further development of harsh-environment sensor systems where more complex sensor materials and operational environments are encountered in such extreme conditions.