Design and Fabrication of a Wireless Strain Gage for Gas Turbine Engine Applications

This thesis describes the design and fabrication of a wireless strain gage (WSG) prototype that utilizes a radio-frequency (RF) transponder for the compressor section of a gas turbine engine. The passive transponder will be printed, welded or deposited directly onto the compressor blades, and thus several key issues have to be addressed in the design of the distributed-element microwave circuit. Some of these issues are the temperature inside the engine, which may vary from 300 °F to 1,600 °F; the large "g" forces experienced by the blades rotating at 12,000 RPM; the RF transponder thickness, which should be below that of the boundary layer thickness (800 microns) so the gas flow path through the engine is not affected. The footprint of the RF transponder circuit should not be larger than a few millimeters in any direction to accurately measure strain The proposed WSG concept employs a capacitive/inductive RF transponder design with a specific resonant frequency, which responds to a short band pulse of energy from a transceiver module, such that the return signal has been modulated by the strain transmitted by the component. The goal is to correlate the frequency shift of the modulated signal to the strain in the substrate. The specifics of the transceiver module are beyond the scope of this research. However, a literature review was conducted to determine some possible technologies and approaches to solve this problem. Specifically, this research explored four different approaches for the design and fabrication of RF transponders; including one based on thin film planar structures; one based on thick film technology; one based on a "free standing" structure with a buckled-beam capacitor and one with an antenna being the actual sensing element. Results from this investigation have shown that the "free standing" structures yielded the largest gage factor, i.e. 1000, compared to the thin-film and thick-film transponders which had gage factors between 11 and 14.

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CHAPTER 1 Introduction
The current technology for measuring strain on compressor blades of a jet engine uses wire strain gages bonded onto the rotating components. The wire leads are then routed from the strain gages to the data acquisition system through a slip-ring assembly. Slip-ring systems are used extensively in the industry to collect data from rotating parts and have been the mainstay for many years. But assembling the equipment can be expensive and time consuming: from six to nine months and several million dollars (DeAnna 2000). Furthermore, several specific problems in contact slip-ring systems have been identified (Bates 1999), among which are inadequate capacity, size and reliability as well as the wear of the brush/ring contacts which makes the signal noisy and changes the electrical characteristic of the gages over time.
Such performance degradation leads to high maintenance costs beyond the normal installation costs. In addition, the end of the rotating shaft has to be accessible to install the slip-rings; otherwise the slip-rings have to be installed in series between shafts (DeAnna 2000). All these disadvantages have motivated the development of non-contact systems to measure strain on compressor blades of gas-turbine engines, including telemetry systems.

Gas-turbine engine environment
The gas-turbine environment is a very challenging one for RF transponders in that it is characterized by high temperatures, large "g" forces on the compressor blades, high ambient radio-frequency (RF) noise and highly-conductive metallic materials.
The challenges of the gas-turbine environment can be appreciated from As shown in Figure 1.1 , the turbine engine has several intricate gas flow paths which result in high gas velocities. The individual components that have to be instrumented include the fan blades, the inlet case, the low pressure compressor section, the high pressure compressor section, the burner section, the high and low pressure turbine sections, the exhaust duct and the exhaust duct nozzle (Pratt and Whitney 1982). Each section performs a specific function from compressing the air, mixing it with fuel, and burning the fuel-air mixture to accelerate the hot exhaust gas through the duct nozzle and generate thrust.
The low pressure compressor region typically operates at temperatures below 400 °F but the temperature increases in the engine as one move back until reaching the high pressure turbine section as shown in Figure 1.2 where the inlet temperatures can reach 1,600 °F for some large gas-turbine engines.  Figure 1.2 Temperature profile for gas-turbine engine (Pratt and Whitney 1982) In addition to the high temperatures inside the engine, the blades can experience large "g" forces between 75 ,000 -100,000 g (DeAnna 2000) for rotating components that operate at speeds approaching 12,000 rpm. Another important challenge inside the turbine engine is the propagation path of RF signals. Metallic objects in the propagation path may reflect RF signals. Depending on the frequency of operation and the thickness of the material of the turbine housing, RF propagation can be attenuated. The depth of penetration of an RF field is defined by where f is the frequency of the field, a is the conductivity of the material and, Jl is the permeability of the conductor. It can be deducted from equation (1) that the skin depth at practical RF frequencies is much smaller than the thickness of the turbine engine casing. Therefore, it is not possible to transmit RF signals from inside the turbine 3 engine to an external signal processing system without line of sight access to the transponder circuit.
Furthermore, another constraint for the development of a wireless strain gage concept is the resolution and sensitivity of the sensor, since the strain experienced by the blades can vary from a few microstrain to 1400 microstrain. Finally, the dimensions of the transponder are important for stability of the turbine engine. The blade can only accommodate a few micro grams of additional mass of the transponder and its thickness should be well below the gas phase boundary layer thickness ( ~ 800 microns).

Research objective
This thesis describes the design and fabrication of a prototype passive radiofrequency transponder that works as a wireless strain gage for gas-turbine engine applications. The research is focused on the development of a wireless strain gage to be used in the low pressure compressor section. Some studies (Gregory and Luo 2000) have reduced the temperature dependence of thin film strain gages by combining acti ve strain elements with positive and negative temperature coefficients of resistance. The scope of this research is limited to the development of a few techniques that can be used in the wireless strain gage concept to self-compensate strain measurements to reduce temperature effects, i.e. apparent strain.
Additionally, the signal processing concept to be employed by the WSG system is beyond the scope of the research work The signal processing limitations were taken into account only for the design of the RF transponder.

Wireless strain gage concept
The ·wireless strain gage (WSG) concept consists of a passive RF transponder that is printed or welded onto the blade within the low pressure compressor section of the engine. The distributed-element microwave circuit consists of a strain gage, i.e.
resonator, capacitive/inductive/resistive element, and a small antenna. A transceiver unit is located outside the turbine engine housing (See Figure 1.3). The placement of the Tx/R,"X antenna of the transceiver unit is chosen to be close to the instrumented blade without requiring major modifications to the casing. For signal processing purposes, the passive transponder can be modeled as lumped parameter RLC resonant circuit and that the strain on the blade induces a change in the capacitance of the resonant circuit. The two key parameters for the design of the RF transponder are the gage factor G and the quality factor Q.
The gage factor is the product of the quotient of change in resistance, capacitance, or frequency and strain E. This is : (2) where K can be resistance, capacitance or resonant frequency. The gage factor is a measure of the sensitivity of the sensor or a quantity change per unit applied strain.
The quality factor is the ratio of energy stored per cycle vs. the energy dissipated in a cycle. For a resonant circuit, the quality factor measures how sharp a resonance is. The quality factor is very important since it determines how fast a system loses stored energy.

CHAPTER 2 Literature review
This chapter discusses the different technologies reviewed previous to the proposal for a feasible design of a wireless strain gage. The intention of this literature review was to determine if there was some information on strain sensors that could be utilized in the development of the wireless strain gage concept. Information collected during the literature review determined the direction of this research, by either ruling out some of the technologies and/or techniques, or contributing to a combination of different devices to achieve a feasible wireless strain gage for the compressor section of a gas turbine engine.

Surface Acoustic Wave (SAW) devices
One of the technologies considered during the early stages of this research was the use of SAW devices for the wireless strain gage. Research on this family of devices as potential sensors started in the early 1970s. Some of the earliest studies on sensors using SAW devices were performed by Das (1978) and Wohltjen (1979), on sensors used to measure pressure and chemical properties of thin films respectively. SAW devices are also used as high performance signal processing elements such as filters and delay lines (Campbell 1989;Morgan 1991).
It was our purpose to investigate the use of SAW devices as wireless and passive sensors. Some of these contactless sensors measure temperature (Schmidth et al. 1994;Buf et al. 1994;Buff 2002), pressure Pohl and Seifertl 997) and torque (Wolff et al. 1996;Beckley et al. 2002;Kalinin 2004). The latter type of sensors has significance for our purposes since torque can be seen as a rotational force that causes stress on the surface of a given material. Some of the torque sensors based on wireless SAW devices are reviewed in the following sections. 7

.1.1 Nature of surface acoustic waves
The term SAW is used to describe a non-dispersive surface wave that is bound to the surface of a solid medium. This wave, discovered in the nineteenth century by Lord Rayleigh, has two particle displacement components: a surface normal component and a surface parallel component. As mentioned by Auld (1990), the particle displacements occur "both in the direction of wave propagation and perpendicular to the direction of propagation while normal to the substrate surface". The particle displacements decay exponentially away from the surface. Most of the energy, i.e. more than 95%, is contained within a depth equal to one wavelength (Morgan 1973). The wave longitudinal velocity is determined by the substrate material and the cut of the crystal but it is typically in the range of 1500 to 4000 ms-1 .

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There are several types of acoustic waves (Hoummady et al. 1997) including shear horizontal surface acoustic wave (SH SAW), the shear horizontal acoustic plate mode (SH APM), the flexural plate wave (PFW) and the thickness shear mode (TSM) among others. However, these acoustic waves are beyond the scope of this research work and will not be considered further.

Principle of operation of SAW sensors
A SAW sensor consists of piezoelectric substrate with thin-film interdigital transducers (IDTs) and reflectors deposited on the surface (Morgan 1991). An IDT is a structure of overlapping metal fingers fabricated on the substrate usmg photo lithography.
The electrical signal in the IDT induces a SAW on surface of the substrate due to the piezoelectric effect. LikeYvise, a SAW generates an electric charge distribution at the IDT, creating an electric response. Therefore, the IDT converts electrical energy to mechanical energy in the form of a SAW, and conversely the process is partially reversible. Based on this effect, the principle of operation of a SAW sensor relies on the acoustic wave propagating time, amplitude and phase velocity between IDTs and reflectors change with the variation of physical variables such as temperature, stress and pressure.

Interdigital Transducer (IDT)
An IDT consist of several interleaved electrodes made from thin metal lines or fingers deposited on a piezoelectric substrate as shown in Figure 2.2. As mentioned in the previous section, piezoelectricity in the substrate material is necessary for the operation of IDTs. The line width of the interleaved electrodes is typically equal to the spacmg between electrodes. Then, the periodicity of the IDT, L , is four times the linewidth of the electrodes as shown in Figure 2.2. As mentioned by Morgan (1973), when a voltage is applied to the IDT, a strain pattern of periodicity L is created. If the frequency is such that L is similar to the surface wave wavelength, the electrical energy is coupled into surface wave energy.
The frequency of operation or synchronous frequency of the IDT is given by: ( where: lo is the synchronous or resonant frequency v is the speed of the acoustic wave propagating on the substrate L is the periodicity of the IDT The IDT has N sections, each section of length (periodicity) L, so the total number of interleaved fingers is 2N + 1. Another important value is the aperture of the IDT, W, which is related to the total capacity of the transducer as discussed later in this section.
IDTs can be modeled by an approximate simplified theory ). In this model, the IDT is considered an array of sources, each one being related to a piezoelectric plate transducer for launching bulk waves. Each bulk wave transducer is represented by an equivalent circuit in which a piezoelectric coupling constant has a value suitable for surface waves (Morgan 1973). Some of the necessary parameters to design an IDT for SAW sensors are obtained from this model. These parameters are : the static capacity per section (Cs), the piezoelectric coupling constant (k2), the resonant frequency (fa) and the number of sections (N).
It must be noted that the piezoelectric coupling constant is an indicator of the effectiveness with which a piezoelectric material converts electrical energy into mechanical energy. So, when choosing a substrate material, the piezoelectric coupling constant should be as large as possible. Additionally, the static capacity per section is proportional to the aperture Wand is independent of the periodicity L (Farnell et al. 1970).

Wireless SAW devices
Wireless interrogation of a SAW sensor is achieved by connecting an antenna to the IDT. The antenna receives a burst of energy, i.e. a high frequency electromagnetic wave, emitted from the interrogation unit. The IDT converts the electrical energy to mechanical energy as mentioned before, by the reverse piezoelectric effect. Figure 2.3 shows a schematic of a wireless SAW device.
' RF In t err og at ion lnt er dig it al T 1a n !;d u cer Re f l ect.or S i g n l al · . / / ~ . . · .. .. · . · --~~J~ ~ .. · . ·· ··· · · · · ···· · · · · /,,:;YJ . -- • .. · . . . . . . · ..• • · •... · . . : · · · ·=· . . · · ~'"""""' c ,, .. ., Figure 2.3 Schematic layout of a wireless SAW device (Reindl et al 1998) There are four basic designs of wireless SAW devices : delay line, reflective delay line, one-port resonator and t\vo-port resonator as shown in  A delay line consists of two IDTs. In this configuration, the acoustic wave launched by the electromagnetic signal propagates from the input IDT or port through the surface of the piezoelectric to the output port where the mechanical energy is converted back to an electrical signal. A slight variation of a delay line is a reflective 1 l ·ne which instead of two ports it consists of only one IDT and a set ofreflectors de ay 1 placed at a certain distance. The effect is that the SAW propagating from the input port is partially reflected back by the reflectors, generating echo pulses that arrive back to the IDT with a certain delay. When a strain E is applied in the x-direction along the length of the substrate of a SAW delay line, the change of geometry changes the propagation velocity (Grossman et al. 1996). The result is a change in the phase difference given by: where: l is the distance between reflectors v is the wave propagation velocity This type of saw devices has been used as ID-tags for remote sensing identification applications (Nysen et al. 1986;Bulst and Ruppel 1994) and more specific information on the design of reflective delay lines can be found in Reindl et al. (1998) and Pohl (2000).
As opposed to SAW delay lines, SAW resonators have the IDT(s) positioned in the middle of the cavity with reflectors on both sides as shown in Figure 2.4. A oneport resonator has only one IDT which is connected electrically whereas a two-port resonator has two IDTs. The induced SAW has a resonant frequency fa given in Eq. 2.
The response of a SAW resonator is a damped harmonic oscillation has shown in  (Pohl 1998) When the RF interrogation signal excites the resonator, the received burst of energy is stored in the cavities of the resonator. After the RF signal is switched off, the resonator uses part of the stored energy to generator a decaying pulse response.
When a strain E is induced in the x-direction of the substrate of a SAW resonator, the effect is a change in the resonant frequency given by: where: L is the periodicity of the IDT v is the wave propagation velocity This type of SAW devices have been used for remote railroad car identification and torque measurements on rotating transmission shafts (Grossmann et al. 1996;Beckley et al. 2002;Kalinin et al. 2004), as well as other applications (Reindl et al. 1998;Pohl et al. 1998Pohl et al. , 2000.
2 6 shows a visual comparison benveen the response of a SAW delay line and Figure · Ons e of a resonator when these devices are used for wireless measurements. the resp +---· +-  (Wolff et al. 1996) and SAW resonators (Grossmann et al. 1996;Beckley et al. 2002) have been used as remote sensors during the past 18 years to measure torque for stress analysis and process control.
Strain on the rotating shaft is proportional to the applied torque at +/-45° angles with respect to the ax is of rotation. Typically, two SAW resonators are applied to the surface of the rotating shaft for differential measurement. Each SAW resonator has its own antenna wound around the shaft. The resonant frequencies of each resonator change in opposite direction when torque is applied . So by measuring the difference between the two resonant frequencies, the torque applied can be measured.
Additionally, temperature compensation can be achieved with this setup since a temperature change will affect both SAW sensors but the absolute difference in resonant frequency will remain the same. Figure 2.7 shows a typical setup for wireless torque measurements using SAW resonators. one-port SAW resonators using quartz as a piezoelectric substrate. The contactless system operates in the 430 to 430 MHz range with a sensitivity of 2.8 kHz/µstrain or a GF of approximately 6.5.
The authors did not elaborate m the specifics of the design of this .sensor, however, to estimate the basic parameters, the frequency of operation has to be taken into account as well as the substrate material to determine longitudinal speed of the acoustic wave and the periodicity of the IDT. Using a SAW resonator operating in the 430 MHz range using a Y+34° rotated cut of quartz as the propagation surface and assuming a 6000 mis longitudinal speed for this type of cut of quartz (Kushibiki et al. 2002), the periodicity of the IDT is approximately 15 µm by equation (3). This implies that the spacing between the IDT electrodes and the line width of the electrodes themselves is around one fourth of the periodicity or about 3.8 µm.
Based on this literature review on SAW resonators as torque sensors, it was decided to explore this type of devices for the WSG concept. As it is shown in the ne>.'t section, a number of issues arose that were addressed in the design of a SAW resonator for gas-turbine applications.

Proposed SAW design for the WSG concept and shortcomings
To verify the feasibility of SAW devices as a wireless strain gage, an initial SAW   Because of the fabrication limitations, the idea of using SAW devices to develop a wireless strain gage was eliminated. Although, no additional research on this type of devices was pursued, this initial approach helped sort out to understand the fabrication constraints. Therefore, a different approach using thin film and thick film deposited sensors was explored to develop a wireless strain gage. Furthermore, two other approaches using "free standing" structures are explored and introduced in Chapter 4.

CHAPTER 3 Thin/thick film designs and simulations
This chapter discusses the different designs used for both the thin film and thick film approaches and it addresses the importance of the simulations for the next stage of the research: the fabrication process. The simulations were used to make some important decisions regarding the type of materials and design parameters such as : dielectric material, the thickness of the metal layer, the line width and spacing of electrodes of the transducer and its general dimensions. The software tool used for simulations is called Sonnet Lite, which is an electromagnetic high frequency software that allows the simulation of many of the planar structures used in this research. The simulations were of great importance since they allowed us to pick the best combination of parameters, not spending extra time fabricating prototypes that would not comply with the requirements and constraints of the project. First, the design parameters of thin-film approach is presented, including multiple simulations, followed by the thick-film designs.
3.1 Thin film approach: parallel capacitor vs interdigital capacitor The first approach explored was a thin film capacitor using a couple of interdigital electrodes, similar to the IDTs discussed in Chapter 2. The idea was to create a stacked capacitor by depositing a thin metal layer, followed by a dielectric material and then a second metal layer. The reason why these thin film metals have the shape of an IDT is because simulations showed a bigger change in capacitance when using interdigital shaped electrodes as compared to a typical capacitor made out of parallel plates. The simulations showed that the parallel capacitor had a base capacitance of about 17.6 pf and when the structure was strained by the value increased to 20.3 pF.
Therefore using equation (2) and a strain value of 20,000 µstrain, the gage factor is about 7.6. The reason why such a large amount of strain was induced was that the version of the software tool Sonnet Lite was a free, limited one and it would not allow us to input smaller values of strain. Still, it was sufficient for the decision-making process since the same strain was applied to the interdigital capacitor. The simulation results for the interdigital capacitor design showed a base capacitance of about 4.9 pF and when the planar structure was strained the capacitance value increased to 6.5 pF, ge factor of about 14. Therefore, the interdigital capacitor was chosen over the for a ga regular parallel plate capacitor design because of its lager gage factor.
During the design of the interdigital capacitor, several parameters were varied to determine the best gage factor achievable by this type of planar structure. The parameters varied were the line width and spacing of the interdigital electrodes. Table   3. l shows the two sets of parameters used in Sonnet to determine the best combination of line width and spacing. The results of the simulations showed a slightly better gage factor for design 1 and are shown in Table 3.2. Additional plots of the simulations can be found in Appendix B.  Table 3.2 it can be seen that the change in capacitance is the same and the n "'or this is that since the designs have different dimensions, when strain is reaso 1 ' applied the increase in the overlapping area of the interdigital fingers is the same, resulting in the same ~C. If the applied strain is the same in both designs, then the ~C \\~11 be different. In the end, the definition of the gage factor takes into account the change in capacitance with respect to the base capacitance and the strain. An additional interdigital capacitor design with a smaller line width and spacing ratio was simulated, yielding even a higher gage factor of about 15 . As a result, it can be determined that the smaller the line width/spacing ratio the layer the larger gage factor. The limitation is the minimum feature size. As the line width and spacing between electrodes decreases, the fabrication process becomes more complicated as described in Chapter 5. Therefore, it was decided to use the parameters of design I.

Thin film interdigital capacitor: design parameters and simulations
In order to save time and resources, it was important to run some simulations before fabricating a prototype with the design parameters to be described in Table 3.3.
During these simulations, not only the expected base capacitance value was estimated but also, the strained capacitance value (See Table 3.2 and Appendix B). Interestingly enough, the simulations showed in fact that the interdigital capacitor itself acted as a resonant structure. Unfortunately, its resonant frequency was outside the I -2 GHz frequency of operation range desired. Therefore, an antenna element was added to the structure to try to shift that resonant frequency.
First of all, the parameters used for both the simulation and fabrication of a thin film interdigital capacitor are show in Table 3.3 . For a visual representation of these design parameters, see Appendix B.

Dielectric material Polyimide
Dielectric constant 3.5

Number of fingers 4
Antenna length 6-7 mm

Antenna width 1 mm
Sonnet Lite calculates the capacitance by using the admittance and impedance formulas. The admittance formula can be use when the resistance of the capacitor is negligible. These formulas are given by : where Ye is the admittance of the circuit Z is the impedance of the circuit f is the frequency C is the capacitance of the interdigital transducer 24 (6) 'I I I Combining equations (5 ) and (6), the capacitance can be written in terms of the admittance. This is : Therefore, the capacitance plot given by Sonnet Lite is actually a plot of the admittance of the interdigital capacitor. This is shown in Figure 3.2. As it was expected, it can be seen in Figure 3.2 that the capacitance value increases as the frequency increases, and the only reason for this is because of how the EM simulator calculates the capacitance. For our purposes, the estimated capacitance value was taken whenf is equal to 1, and these values are shown in Table   3.2 for design 1. Additionally, it must be noted that the plot shows a spike when f is 25 close to zero. This is because the frequency is in the numerator in equation (8), which makes the estimated capacitor value go to infinite when/ is very small.
Furthermore, when the simulation was swept from DC to 3 GHz, it was found the interdigital capacitor behaved like a resonant circuit. This is that a resonance condition was observed at a frequency when the admittance was at a maximum point.
These can be seen by plotting either the real part of the admittance, called conductance (G), or the imaginary part, called susceptance (B). It can be seen in Figure 3.5 that the resonant frequency of the interdigital capacitor is 1.39 GHz and 1.31 GHz, for an antenna length of 6 mm and 7 mm respectively.
This frequency range is now within the 1 -2 GHz range of operation needed.
Finally, a couple more simulations were executed to determine the expected gage factor when using an antenna length of 6 mm and 7 mm. Previously, the gage factor in terms of frequency without an antenna element and at an operating frequency above 2 GHz was about 5.1. Figure 3.6 shows the shift in the resonant condition when the interdigital capacitor including a 6 mm antenna was under about 20,000 µstrain. The resonant frequency of the interdigital capacitor is 1-38 GHz and 1-24 GHz when the structure is at normal condition and when stress is applied respectively. This yields a gage factor of 4.56 which is very similar to the 5.1 gage factor obtained when the antenna element is not included. Therefore, the antenna is only shifting the resonant frequency to the desired range while keeping a similar gage factor in terms of frequency_ A similar gage factor was also obtained when the antenna length was increased to 7 mm The next step was to fabricate the thin-film interdigital capacitor using the design parameters previously mentioned following the fabrication steps described in Chapter 5_ Next section of this chapter explains a different approach using a thick-film capacitor design_ 29

Thick film interdigital capacitor: design parameters and simulations
One of the issues never addressed in the previous design using thin films was the skin effect and its relation to the thickness of the metal film or skin depth. First, the skin effect is a phenomenon where the current density decreases exponential with depth from the surface of a conductor. Furthermore, the skin depth (b) is defined as the depth below the surface of a conductor at which the current density reaches ; of the current on the surface (Js). The skin depth is a variable that measures how far electrical conduction occurs in a conductor and as it is shown in equation (1), it depends on the frequency of operation. At DC, the skin depth can be neglected since the entire cross-section of the conductor is used for propagation. However, when it comes to higher frequencies of operation, the skin depth plays an important role to reduce losses. The higher the frequency of operation the smaller the skin depth is. For our purposes, since our target frequency is between 1 and 2 GHz, the thickness of the conductors can considerable decreased, as it was done in the thin-film approach, using a 1-µm metal film.
It is important to note that the metal surface nearest to the dielectric material is the surface that carries the RF current. Therefore, RF currents are highest in the lower and upper surface of the top and bottom interdigitated electrode. Regardless of this, one of the issues of the thin-film approach was the thickness of the metal. For a frequency of operation between 1 and 2 GHz, the minimum skin depth is between 1 and 2 µm. Therefore, the thickness of the film deposited in the previous design, falls short from the minimum skin depth to avoid large RF losses.
Additionally, it is the rule of thumb to have at least 5 skin depths of conductor so most of the energy is contained and losses are minimized. As seen in Figure 3. 7, the 5-skin depth mark for the 1 to 2 GHz range shows a minimum of 10 µm of film thickness. Based on this analysis, modifications to the thin film approach were made and a thick film design was developed.
The thick film interdigital capacitor consisted of two 4-finger interdigitated copper electrodes with a dielectric in between, just like the previous thin film design.
Similarly, the line width and spaces between the electrode fingers remained the same since the main issue to be addressed with the new approach was to reduce the skin effect. Table 3.4 summarizes the design parameters of the thick film approach. Basically, two main changes were made to the thin film approach; first, the metal thickness was increased to 10 µm to stay within the 5-skin depth mark given for a 1 to 2 GHz operation. Additionally, the thickness of the dielectric layer had to be increased to more than 10 µm since this layer is not only deposited on the area where the fingers overlap to form the capacitor but also under the antenna (See Figure 3.8).
This is that, the dielectric layer has to come down from the bottom metal layer to the ceramic strain beam, creating a small step on the surface where the top metal layer is deposited. If the dielectric is not at least as thick as the metal film, the step created is too large, so the deposition of the top electrode becomes more difficult and the joint between the antenna and the interdigital electrodes are at risk. Note that Sonnet Lite was also used to simulate the response of the new design. First, the expected base capacitance and the change in capacitance when strain was applied were assessed. From basic theory of parallel capacitor plates, a decrease in the base capacitance was expected. Since the distance between the interdigital electrodes increases by almost a factor of 8 (from 10 µm in the thin film design to 60 µm in this approach), it was expected to see a decrease in the base capacitance of similar · magnitude. As mentioned before, the EM simulation tool calculates the capacitance base in the admittance, using equation (8).  the thick-film capacitor, the capacitance increased to 1.083 pF. Therefore, using equation 2 and a strain value of about 20,000 µstrain, a gage factor of 11.87 was estimated. Table 3.5 shows a comparison between the capacitance and gage factor values of the thin-film capacitor and the new thick-film approach. capacitor Based on the simulation results sho~rn in Table 3.5 , the gage factor is smaller in the thick-film approach than the thin-film one. One hypothesis for this behavior is that since the dielectric layer is thicker, the strain applied to the bottom electrode of the capacitor does not transfer efficiently to the top electrode, undermining the change in capacitance and therefore, the gage factor.   GHz, only about 0.1 GHz from the expected value. Figure 3.1 0 also shows the shift in the resonant frequency. When the thick-film capacitor is strained by about 20,000 µstrain, the resonant frequency moves to 6.575 GHz, for an estimated gage factor of 4.04, which is consistent with the gage factor obtained in the thin-film approach with no antenna element. Regardless of the gage factor, the resonant frequency was completely outside the 1 to 2 GHz range of operation targeted. Therefore, an antenna element was needed for the frequency range of interest. Naturally, the length of the antenna needed was expected to be longer than the 6-mrn long antenna used for the thin-film approach. Unfo rtunately, an antenna length of more than 10 mm was not possible because of the size limitations of the constant strain beam. If the antenna would be longer, the interdigital capacitor had to be placed too close to the wider part of the strain beam.
A simulation with an antenna length of 6 mm and 10 mm long was executed to see the effect in lengthen the antenna.
Frequency (GHz) led us to believe that either using a thin-film or thick-film approach, the gage factor that can be achieved with an interdigital capacitor is in the range of 4 -5, and in terms of capacitance, the expected gage factor is around 11 anc;l 14.
Therefore, two additional approaches were explored in order to increase the gage factor. This time, free standing structures were used to design a couple of transponders with the particularity that the sensing element is not completely attached to the surface of the substrate. Chapter 4 reviews the proposed designs, expected capacitance and projected gage factor.

CHAPTER 4 Free standing structure approach
This chapter presents a different approach to solve the problem of the wireless . gage As mentioned in the previous chapters, the simulation results of the thinstnun · film and thick-film capacitor designs yielded gage factors in the range of 11 -14 for capacitance and gage factors between 4 -5 when measuring the shift in frequency with respect to a unstrained resonant frequency. It was of considerable interest to boost the gage factor as much as possible in order to maximize the resolution of the sensor, i.e. maximum capacitance or frequency change for a given strain value. Therefore, an additional literature review \Vas performed at this stage of the research to consider other types of transponder designs with improved gage factors. One the technologies explored was the passive sensors used in automobiles, specifically the strain monitoring systems used to develop smart tires or tires with integrated sensors that measure their pressure or deformation during service (Todoroki et al. 2003 ;Todoroki 2005, 2006). In addition, the concept of mechanical amplification was explored by means of a buckled beam scheme incorporated to a capacitive strain sensor used for torque measurements among other applications Guo et al. 2004Guo et al. , 2005. At the end, a buckled beam capacitor design was proposed as well as several modifications to the initial design.
The part of this chapter explains the second free standing structure investigated. In this case, the transponder was not formed by a capacitor or based on a capacitance change. Rather, the design proposed includes the use of an antenna as the sensing element. So by looking at the change in the tuning frequency of the antenna, the induced strain can be calculated. When strain is applied, the distance to ground along the antenna increases which modifies the frequency of operation of the antenna.

Development of the buckled beam capacitor concept
The idea of the buckled beam capacitor came from the combination of two applications previously developed by other researchers; a wireless strain monitoring system for tires (Todoroki et al. 2003), using capacitance and tuning frequency changes; and second, a high-grain mechanically amplified MEMS capacitive strain sensor using a buckled beam scheme developed by Young and Ko (2004).
Todoroki (2003) proposed a wireless strain monitoring method that uses the tire itself as a sensor, attached to an oscillating circuit with a battery to activate it which made it a non-passive approach. Still, the steel wire belt of a tire is an electrically conductive material the rubber is a dielectric material, and all the structure together resembles a capacitor.  (Matsuzaki and Todoroki 2005) In this model, the capacitance is given by where: C is the total base capacitance s is the dielectric constant of rubber 40 (9) 5 is the permittivity of free space (8.85 x lOE-12) 0 I is the length where the steel wire overlap dis the distance between two steel wires (center-to-center) r is the radius of a steel wire Later, the authors improved their own design to produce a passive wireless sensor and enhanced the tire capacitance by building an interdigital electrode shown in  The principle of operation is based on the fact that when strain is applied, a small lateral displacement, Llx, is induced. If the buckling angle, o.., is small, i.e. less than 10°, then the center deflection of the sensing beam, Llw, is larger than the lateral displacement, Llx, which results in a mechanical amplification. For their application, the authors determined that the best angle a was 5.7° based in their nominal gain and . ors as a function of bucking angle. This was starting point for the present gain err .
At the end the limitation in the footprint of the buckled-beam capacitor and design. ' the overlapping area of the interdigital electrodes determined the angle for our design as it is discussed in the following section.
The authors fabricated a device using MEMS technology that had a sensitivity of 282 af/µ£ , with a base capacitance of 0.44 pf, for an estimated gage factor of 640.
Again, the large gage factor reported by the authors led us to explore the buckled beam approach to develop a capacitor, also using interdigitated electrodes.

Design parameters
For the design of the buckled-beam capacitor, several key factors were taken into account among which was the footprint of the sensor, the total base capacitance and the buckled-beam angle. As mentioned in the previous section, the buckled-beam angle with the largest amplification occurs when the buckled-beam is set at 6° from the horizontal axis. Such a small angle has several complications when designing the capacitor. Among the difficulties faced were the fact that the smaller the angle the longer the buckled beams. Longer buckled beams ·result in less space to place the interdigital electrodes, in this case made out of metal wires. The fewer interdigital wires, the smaller the capacitance is, which then leads to a smaller resonant frequency which may be outside the desired range of operation. Additionally, longer buckled beams mean that the ratio between center of deflection Llw and the distance w , i.e. the distance from the base of the interdigital wires to the horizontal of the buckled beams, is smaller. Thus, the capacitance change is smaller compared to shorter buckled beams. Therefore, as an initial design, it was decided to start with a buckled beam angle of 10° with respect to the horizontal axis as shown in Figure 4.4 . 43  in the overlapping length of the interdigital fingers , and therefore, yielding a larger change in capacitance. Furthermore, the joint points circled by 1 and 2 not only have to attach the top rail (non-grounded electrode) to the substrate, but also these joint points have to isolate the top rail from the substrate or ground plane. The reason for tha t the antenna is meant to be connected to the top rail and then the tip of the this was would be grounded, grounding the entire top rail. Similarly, the joint points antenna . 1 d by 3 and 4 are parts of the structure that not only had the purpose of pinning c1rc e the bottom rail (grounded electrode) of the capacitor but also for grounding purposes.
It is worth to mention at this point that the buckled beam capacitor was meant to be fabricated on titanium constant strain beams similar to the ceramic constant strain beams used to fabricate the thin-film and thick-film capacitors. More details on how the top and bottom rail of the buckled beam capacitor are pinned to the substrate are discussed in Chapter 5 The following table summanzes the parameters of the initial buckled beam capacitor design. Finally, the initial design was arranged in such way so the buckled beam amplification scheme would be implemented. Both the top and bottom rails that form the capacitor were setup parallel to the horizontal axis of strain, i. e. the wire electrodes are perpendicular to the axis of strain.

Expected base capacitance and gage factor
Based on the design parameters, the total capacitance of the buckled beam capacitor can be determined, as well as the change in capacitance that would be introduced due to strain in the long axis of the titanium beam.
Using equation (9) multiplied by the number of vv'ires in the interdigital capacitor, and the design parameters from / 25 x 10-6 According to Figure 4.4, the distance w, from the base of the interdigital wires to the horizontal section of the buckled beam is 300 µm. When 100 µstrain is applied to the buckled beam capacitor, a displacement L1x= 0.2 µmis introduced. This is comes from the following calculations : . 300 x 10-6 (Unstramed) x = = l.7013mm tan 10* 46 (Strained) x' = x(l + c) = x(l + lOO x l0 -6 ) = l.70l5mm The displacement Llx translates into a decrease in the distance w from 300 µm to 298 _8 µm , or a Llw= 1. 8 µm, which provides the mechanical amplification scheme of the buckled beam.
As LJw changes the length in the region where the interdigital wires overlap the capacitance decreases. The wires overlapped 400 µm when no strain was applied and when the titanium beam is strained, the overlapping length decreases to 398.8µm.
Similarly, using equation (9), the capacitance value when strained is given by: .

Antenna strain gage design
The antenna strain gage concept was based on the idea that the resonant frequency of an antenna can vary depending on the distance between the whole length of the antenna and the ground plane. This phenomenon was observed in a very thin antenna 47 developed by Argon ST (formerly SDRC). In the initial configuration, an 8prototype nun long copper tape antenna was placed over a 50-µm layer of kapton tape. The ncy of resonance of the antenna was 4.83 GHz.

Antenna gage configurations
As seen in the very thin antenna prototype, the length of the antenna was 8 mm, which yielded a frequency of resonance close to 5 GHz. For our study, we wanted to decrease the frequency of operation to at least below 3 GHz. Therefore, the first approach was double the length of the antenna to 16 mm One of the problems of using larger sensing elements is that the strain measurements are not a spot measurement of strain and rather and integration of the strain along the entire antenna element.
The antenna \Vas made of tungsten wire with 50 µmin diameter. The material and diameter wire were chosen because small diameter ~d stiff er wires are not affected by large "g" loading, as long as the entire structure is thinner than the boundary layer of the gas path flow in a rotating blade. Additionally, a titanium frame was built around the antenna wire and it was designed only for protection purposes. Titanium was the material of choice since the constant strain beam was also made of titanium, so the fabrication process would be simplified. Finally, the initial configuration also included a diode so the frequency of resonance could be measured wirelessly. The diode would generate a second harmonic, with a frequency twice the fundamental frequency of resonance of the antenna; this would allow distinguishing the Rx signal 49 frorn the Tx signal. As shown in the previous figure, the antenna wire had to be kept at least 5 wire diameters from the frame so the frequency of resonance is not affected by the titanium frame that surrounds the wire. In addition, the diode needed to be placed between the antenna wire and the ground plane and at distance between 1.5 to 3 mm from the base of the antenna connected to the frame. Once the prototype was fabricated (See Chapter 5, section 4), the initial prototype was tested to measure its resonance frequency and the second harmonic produced, as well as the effect of strain and how much change in frequency would be obtained.
Unfortunately, as discussed in Chapter 6, section 4, the expected frequency of resonance was about 3 GHz, which means that the backscattered signal would be twice as much that frequency. This required different filters, amplifiers and Tx/Rx antennas. Therefore, a slight change in the design was made by increasing the length of the antenna and increasing the starting height of the antenna from 25 µm to 75 µm to prevent the antenna from being too close to ground.
The antenna was lengthened enough to move the resonance near the 2.4 GHz band. In this band, much higher power and cheaper amplifiers were available for RF measurements. Therefore, the length of the antenna was increased to 27 mm for the modified design. One of the prototypes fabricated using the modified configuration did not included a diode; instead a solderable wire was placed. The purpose of this wire was to be able to attach an external diode. More details on the fabrication of these prototypes in Chapter 5.

CHAPTER 5 Fabrication process
This chapter discusses the different fabrication process used for all four different d ·gns The first ones to be discussed are the fabrication steps for the thin-film and es1 · thick-film capacitors which are quite similar. Later in this chapter, the fabrication process for the free-standing structures is discussed.

Fabrication steps of thin-film interdigital capacitor
The fabrication of the thin-film interdigital capacitor invol ved several steps.
Before the description of these steps, it is important to mention that the interdigital capacitors were deposited on ceramic constant strain beams. These substrates are fabricated with a material called YSZ (yttria-stabili zed zirconia). Figure 5 .1 shows one of the YSZ substrates used throughout the fabrication process. That is why there is a limitation in the length of the antenna to 6 to 7 mm; otherwise the sensor would be deposited too close to the narrower part of the beam or too close to the wider part.

Axis of strain
For the fabrication of these sensors, the YSZ substrate is cleaned by rinsing it with de-ionized water, acetone and methanol. Then, it is blown dry with nitrogen, followed by a bake for 10 to 15 minutes at 135° C.
Then, a photolithography process is used to deposit both the bottom and top layers of the interdigital capacitor. For these purposes, a photomask with the sensor pattern was designed using AutoCAD according to the design parameters discussed in Chapter 3. First, LOR lOB polyimide is spin-cast on the substrate at 500 rpm for 15 seconds followed by spinning at 2500 rpm for 45 seconds, resulting in a nominal thickness of lOµm. Then, the substrate is baked at 139° C for 15 seconds. Once the substrate cools down, SCI 827 photo-resist is spin-cast on the substrate, for 500 rpm for 15 seconds followed by spinning at 2500 rpm for 45 seconds. Then, the substrate needs to be baked for 2 minutes and 40 seconds at 110° C. Next, the photomask with the pattern is placed over the photo-resist layer and it is exposed to UV light for 6:45 minutes. Care needs to be taken when exposing the substrate to UV light, not to over or under expose it. Next, AZ developer is applied to the exposed resist layer to achieve a clear and well-defined pattern. The last step in the photolithography process is to hard bake the substrate for 10 minutes at 13 9° C. After this process, the ceramic strain beam has a clear pattern of the sensor so a thin-film layer of metal can be deposited.
The thin-film is deposited using a sputtering machine. The metal of choice is copper since it is a material that does not take long time to sputter, especially when h ·ckness of the metal is around 1 µm. For more details on the sputtering process, the t i see Appendix C. After the metal is deposited, a process called lift-off is required

Ve the additional metal deposited and have a clear metal interdigital electrode. remo
Lift-off is achieved by soaking the substrate in acetone for a few minutes. Acetone attacks the LOR/photo-resist layer that remains under the metal layer and that is not part of the pattern. Figure S.2 summarizes the photolithography and lift-off processes.
For more information on these procedures, see Gardner et al. (2001) -· -L~-· · . . ~J C ________ " 1 _ · _·· . . -----" (1) . ' (2) .  Several issues had to be addressed during the fabrication process of the thin film capacitor. One of the biggest difficulties was de deposition of the dielectric material in between the metal layers. As mentioned before, a material called LOR SOB was used as the dielectric layer. This material needed to be fire up to above 2SO °C for about 2S minutes in order to change its properties, evaporate some of the compounds that make it sensitive to acetone. It is important to point out that during the lift-off process of the second metal layer acetone comes in contact with the LOR SOB dielectric layer. If this material is not heat up such high temperature, the dielectric layer is dissolved by acetone and when the second layer of metal is deposited, the interdigital electrodes may come in contact, shorting the capacitor.
In the other hand, care was taken when firing up the LOR SOB. Some initial tests using this material showed that if the substrate is heated up too rapidly, bubbles develop on the surface of the ceramic substrate, specifically in the area where the LOR SOB was spin-casted. This is because the temperature of the LOR SOB is Increased so suddenly that the evaporated compounds get trapped in bubbles.

S7
I al ly these bubbles disappeared when the substrate temperature reached 200 °C Eventu , but left a very rough and irregular surface. Such surface is not suitable for depositing the metal film, since the thickness of the film is only 1 µm and some of these . ularities were more than 1 µm thick. This is the reason why the temperature has irreg to be increased slowly, at a rate of about 8 °C per minute, during 25 minutes. Still, some bubbles developed on the surface of the ceramic substrate, especially on the edge of the substrate as shovvn in Figure 5.3, in the lower edge of the sensor area.
Three different thin-film interdigital capacitors where fabricated during this stage.
For pictures and more details on the remaining two interdigital capacitors, refer to Appendix D.

Fab1;cation steps of thick-film capacitor
The thick-film capacitor was fabricated following a process similar to that of the thin-film capacitor. Using photolithography was used to create the electrode pattern and then deposit a thin film by sputtering copper on the surface of the ceramic substrate. The only difference is that, this time, the thin-film electrode thickness was increased by electroplating. As mentioned in Chapter 3, the electrodes of the capacitor should be thicker to avoid the skin effect between 1 to 2 GHz. Unfortunately, the surface area of the wire was much smaller than the surface of the capacitor electrodes to be plated. Therefore, the wire was substituted by a larger silicon wafer with a layer of platinum previously deposited. Additionally, the solution used for plating the thin films was cupric sulfate (CuS04) and water (5H20). Another observation for the electroplating process is that both the cathode and the anode need to be in parallel so copper is deposited evenly on the surface of the interdigital capacitor electrodes.
Several attempts were made to find the best deposition rate and conditions. The deposition rate depends on the current applied to the circuit and the time the current runs through the circuit Likewise, the electric current depends on the applied DC voltage as well as, on the distance between the cathode and anode. In our experiments, this distance was no more than 4 cm and a variable current supply of 9 V was used to control the current. Some of our initial tests showed that the higher the deposition rate, the worse the definition of the electroplated metal lines. Thus, the contour of the original thin film becomes more distorted and metal grows beyond the 59 . . al boundaries of the metal. This is especially critical in the case of the ongtn . di.aital fingers since the spacing between the interdigitated electrodes is only a inter 1::» few rnicrorneters. Thus, better results were achieved by extending the deposition time and lowering the deposition rate. The best deposition rate in our experiments in terms of definition was 3µm/minute and this was achieved by applying 200 mA of current and keeping the cathode and anode distance at approximately 3 cm, requiring just 3 minutes to achieve a total thickness of 10 µm.
Once the lower metal layer was electroplated, a layer of kapton tape applied to form the dielectric. Ideally, the kapton tape should only be applied underneath the interdigitated fingers, to keep the antenna on top of the ceramic substrate, and not on top of the dielectric. Unfortunately, for the reasons previously mentioned in the design chapter, the kapton tape had to be placed underneath the upper metal layer as seen in  After the kapton tape was applied, the upper thin-film layer was deposited using photolithography and sputtered copper deposited onto the surface of the ceramic 60 . b am Then the thin film was electroplated onto the copper using the same strain e · ' d re described above. The final steps in the fabrication of the thick-film proce u ·tor were the deposition of the ground plane by sputtered copper on the back of capac1 the ceramic substrate and make a physical connection from the top and bottom metal layers to the ground plane by applying silver paint on the edge of the ceramic beam.
Once again, DC measurements were performed before the electrodes of the capacitor were shorted to ground. An additional thick-film capacitor was fabricated but the quality of the interdigital electrodes was not good enough since some of the fingers were shorted due to a too rapid deposition rate. Details on this prototype can be found in Appendix D.

Fabrication steps of buckled beam capacitor
The fabrication steps used for the implementation of the buckled beam capacitor were completely different from those used to fabricate the thin-film and thick-film capacitors. No photolithography steps or sputtering processes were involved since no thin films were necessary. Instead, small wires were mounted on a metal wire rail and were welded together to create a buckled beam interdigital capacitor. Moreover, the constant strain beams up to this point were made of YSZ (yttria-stabilized zirconia) but in the case of the buckled beam capacitor, titanium constant strain beams were used.
The reason for this is that an electrical connection from one of the electrodes or rails of the capacitor to ground was required. Instead of sputtering copper onto the back of the ceramic strain beam, the titanium strain beam would act as ground plane itself. In order to attach the buckled beam rails to the titanium beam, a conductive and non-conductive connection were required for the bottom and top rails, since the first rail had to float and the other had to be grounded. Therefore, silver epoxy and nonconductive epoxy were used for these connections respectively.
The first step in the fabrication process was to roughen up the surface of the titanium beams using a piece of SiC paper to remove the oxide layer and make good electrical connections to ground. Then, a small piece of kapton tape applied to the surface approximately at 6 cm from the narrow end of the strain beam. Next, small cuts were made in the kapton tape so the top and bottom rails could be attached to the titanium substrate. Before attaching the electrodes to the rails the larger diameter wires had to be bent to form a 10 ° as specified by the design. The rails were too stiff b d t o the desired angle. Instead, as shown in Figure 5.8, both the top and bottom to en . 1 ere bow-shaped. As a consequence, the mechanical amplification scheme of nus w the buckled beam was diminished. Using a microscope, the top and bottom rails were align to the notches in the kapton tape, and small drops of epoxy were applied to the four joint points. As seen in the figure 5.8, large globs of silver and non conductive epoxy were used to pin the top and bottom rails which further decreased the amplification effect of the buckled beam Finally, the epoxy was let dried out for around 8 hours to make sure the buckled beams stayed attached to the titanium substrate when strain was applied.
Two additional buckled beam capacitor designs were developed as well. The uias that the original design did not yield the results and a number of parasitic reason .. capacitances were introduced during the fabrication process due to the large globs of Y These capacitances were of greater magnitude than the designed base epox.
capacitance allowed in the design. Thus, the ~C was smaller with respect to the total base capacitance (including the parasitic capacitances), which led to a smaller gage factor. The modifications to the original buckled beam capacitor are described in Appendix E.
The fabrication steps used in the modified designs were similar to those described above. However, the greatest difference was in the way the top and bottom rails were attached to the titanium substrate. For the last buckled beam design, laser welding was used instead of silver epO:\.'Y to attach the bottom rail to ground. Furthermore, the length of the buckled rails was shortened in one of the designs and the thickness of the kapton tape was increased to see the effect on the parasitic capacitances. Additional details are discussed also in Appendix E.

5.4
Fabrication steps of antenna strain gage The steps followed to fabricate the prototypes, for the most, used a similar laser welding technique than the latest buckled beam design. Basically, the prototype consisted of 5 components : the titanium strain beam, the titanium frame, the tungsten antenna wire, a layer of kapton tape and a silicon diode.
First, the surface of the titanium strain beam was roughed up with sand paper.
Then, the frame was built with four small titanium shims, all of them welded by a laser beam. The next step was to attach the tungsten \Vire to the metal frame, also by means of a laser-welding machine. One of the most difficult steps in this process was 64 I I , I to attach the diode to the tungsten wire. This was done also by aiming the laser beam to the join of the wire and the surface of the silicon diode. Some of the diode material was removed and melted by the laser, so the melted material would attach the two pieces together. After these three pieces were all connected, a layer of kapton tape was placed on the substrate. Finally, the last step was to weld the frame to the substrate by shooting the laser beam at an angle of 45 degrees at the joint of the two pieces. The laser parameters used in every step of the fabrication process are included in Appendix F, as well as some observations and comments.

CHAPTER 6 Testing and results
This chapter explains the testing procedures used to verify the estimated capacitance, resonant frequency and gage factor for the different approaches used in this study. Most of the testing performed at URI was DC measurements because of the limited measuring capability at higher frequencies. High frequency measurements were performed by San Diego Research Center (SDRC), now Argon ST, since they had the appropriate filters, amplifiers, Tx/Rx antennas and signal processing equipment to test all of the prototypes fabricated at URI Before presenting the test results of the different capacitor and antenna designs, an initial assessment of the ceramic substrate was performed. The purpose was to determine the dielectric loss of ceramic substrate at these frequencies. It is important to note that these measurements were performed by SDRC but provided important insight when designing and fabricating the sensors.
The loss tangent of the material was quite high, about -19 dBi peak gain. Such a low gain would impact the ability to measure the back-scatter signal. However, this was solved by using a Tx signal with a 20 to 30 dBm of power and placing the Tx antenna as close as possible to the strain beam under test. In addition, an antenna of similar dimensions was used for the thin-film and thick-film capacitors, i. e. 1 mm x 6 -10 mm was deposited on the ceramic substrate. Because the material was lossy, the antenna had a Q value of about 25. In order to track the back-scattered signal, a change in capacitance had to be as large as possible.

Thin-film capacitor: analysis and results
Capacitance measurements where performed on the three different thin-film capacitors by means of a capacitance meter with a resolution of 0.01 pF in the range of0.01to10 pF. The following procedure was used: the ceramic beams were clamped at the narrower end while applying stress to the wider end of the ceramic beam in bending mode. The ceramic constant strain beams used were designed to have the same strain along the longitudinal axis of the substrate. For this specific substrate, the strain introduced by deflecting the end 2 cm is about 800 µstrain. So the gage factor was estimated by relating the change in capacitance from the base capacitance when 800 µm strain was applied.
The capacitance measurements for the 3 thin-film capacitors fabricated are as follow: The thin-film capacitor was designed to have a base capacitance of about 4.9 pF.
From the measurements above, it can be seen that two of the fabricated capacitors had a capacitance value above the aimed base capacitance whereas, the other capacitor had a very small base capacitance. The reason for the small capacitance of the latter capacitor with an antenna length of 6 mm (broken when strained) is that the interdigital fingers where not aligned correctly during fabrication. Thus, the overlapping area was smaller than originally designed and a decrease in the total ca · pac1tance was observed. In the other designs, the reason for the larger total 67 I I II capacitance was that the dielectric layer would have to be thinner than the originally 10 µm design. Still, the gage factor of the two thin-film capacitors was about 14 which is what was anticipated from the simulations.
For the high frequency measurements, a test cable (micro-coax) was soldered to one of the fabricated sensors to verify the resonant frequency vs. strain behavior.
Unfortunately, some of the deposited metal layer vaporized when in contact with the soldering iron. Even though the micro-coax was attached, no resonant frequency was found in any of the three the thin-film transponders. At first, it was believed that the ground plane was too thin so additional copper tape was placed on the bottom surface of one of the ceramic beams. Still, no discernible resonance between 1 to 6 GHz was observed. It was suspected that either the capacitor became shorted or the capacitance was so small that the resonant frequency was outside the frequency sweep previously performed. Therefore, the connection between the capacitor and the antenna was broken to measure only the resonance of the antenna which resulted in no antenna resonance. At this point it was determined that the skin depth might be an issue. Base on these experiments and skin depth calculations, it was concluded that the metal film had to be thickened to 10 micrometers if possible. The hypothesis here was that, maybe plating the ground plane with copper tape introduces losses; we believed that the reason was that when the ground plane was covered with copper tape, the electric field must first penetrate the lossy layer and the tape might not be making good contact with the ground plane. This led us to the development of a new approach with thicker films using an electroplating technique, to increase the thickness of the interdigital capacitor, antenna and ground in order to bypass the copper tape.

Thick-film capacitor: analysis and results
Capacitance measurements were performed on one thick-film sensor smce interdigital electrodes of the second thick film sensor were shorted. This was corroborated by conductivity measurements. Once again, the measurements were performed by means of a capacitance meter with using a similar setup to the thin-film measurements. The ceramic beam was clamped at the narrower end while bending it at the wider end, introducing 800 µstrain for every 2 cm that the ceramic beam was bent.
The result of the capacitance measurement for the thick-film capacitor as a function of strain is as follows: The thick-film capacitor was designed to have a base capacitance of about 0.85 pF, and the fabricated thick film sensor had a capacitance of 0.90 pF. The resulting gage factor of the fabricated sensor was approximately 14, slightly higher than the gage factor of 12 obtained with the simulation. The fabrication of the thick-film capacitor was easier than the thin film because both the thickness of the dielectric (kapton tape) and the thickness of the film were well controlled. Thus, the fabricated sensor had very similar parameters to the ones used for simulation.
Once again, the only accurate way to measure the resonant frequency of the sensor is to connect a test cable (2 connections: antenna element and ground) or by using a 69 diode to differentiate the input signal from the output signal by a doubling effect when using an RF pulse of energy.
High frequency measurements showed at resonant frequency of 2.4 GHz under normal condition, i.e. unstrained condition. The targeted resonant frequency was 2.6 GHz when using a 10 mm-long antenna. The fabricated sensor had a smaller resonant frequency, possible due to its slightly higher capacitance. The higher the capacitance for a given antenna length, the smaller the resonant frequency. When a strain of 800 µstrain was applied, a shift of 7 MHz was observed. This change in the resonant frequency yielded a gage factor of 3.64, as opposed to a gage factor of 4.5 from the simulator. The hypothesis for this smaller gage factor was attributed to dielectric (kapton tape) not adequately transferring the strain to the sensor.
These small gage factors led us to develop a totally different approach in order to boost the sensitivity of the strain gage. The design of free standing structures such as the buckled beam capacitor or the antenna strain gage, were the result of the pursuit for better resolution and a larger shift in the resonant frequency.

Buckled beam capacitor: analysis and results
To obtain a better understanding of the original buckled beam capacitor concept, a buckled beam sensor was analyzed as a 6-component circuit. Figure 6.1 shows the physical layout of the buckled beam capacitor and associated components that form the complete structure. The resonance of the first buckled beam capacitor design was found approximately 880 MHz. When 800 µstrain was applied to the titanium beam, a very small shift was measured (6 MHz), for a gage factor of 8.5 as compared to the expected gage factor of 60. Also, the resonance of the buckled beam capacitor was very low because of the large parasitic capacitances Cl and C2, which also degrade the gage factor since the contribution to the shift in frequency is largely due to the variable interdigital capacitor C3 .
This provided motivation to modify the design to decrease the parasitic capacitances. As discussed in Appendix E, the thickness of the dielectric (kapton tape) was increased to 200 µm and the length of the top rail was decreased in the second design by increasing the number of fingers from 16 to 60 for the third buckled beam design.

Second buckled beam cap design: shorter top rail
The setup shown in Figure 6.3 was used to test the modified design of buckled beam capacitor. The nominal capacitance and ~C was measured by flexing the beam.
A strong resonance at 1.503 GHz and a shift in the resonance of 1.565 MHz with 2 cm of deflection were obtained for an applied strain of 800 µstrain. This yielded a gage factor of 51 , very close to the design value of 60. A shift in frequency of about 4.1 % was both repeatable and stable. The calculated parasitic capacitance from the short (top rail) and the non-conductive epoxy was about 0.29 pF in total (Cl + C2).
Adding the parasitic capacitance to the nominal capacitance from the interdigital capacitor (C3) gave a total capacitance of 0. 66 pF. This compared favorably to the expected base capacitance of 0.62 pF . The deflected beam lowered the buckled-beam capacitor to 0.57 pF. The change in the buckled-beam capacitor is about 15% so the total circuit response was affected to some degree by the parasitic capacitance.
Lowering the parasitic capacitance further was difficult since the third buckled beam design included more wires which increased the base capacitance C3.

Third buckled beam capacitor design
The best results to date were achieved with the third buckled beam capacitor design. This design included 60 interdigital wires to form the capacitor, a 200 µm dielectric, a bottom rail that was laser-welded to the titanium beam and a smaller volume of non-conductive epoxy to keep the parasitic capacitance low.
The buckled beam capacitor design appeared to have about 1.8 pF of capacitance.
This was the total capacitance between the wires and the capacitance to ground from the top rail and the non-conductive epoxy. The targeted capacitance was 1.42 pF, so the actual capacitance of the fabricated buckled beam capacitor was close to that of the original design. The contribution of the parasitic capacitances was approximately 40 pF. The resonant frequency was 953 MHz with a 10 nH inductor as shown in

Antenna strain gage: analysis and results
A test fixture was put together to generate the fundamental excitation for the antenna strain gage prototypes. As mentioned in the antenna gage design section, it was expected that the resonant frequency would be around 3 GHz. Adjustments to the filters, amplifiers and Tx/R,-..,;: antenna were necessary since the original setup was tuned for a lower frequency of operation.
The initial configuration using a 16-mm long antenna was illuminated from 1 to 3.6 GHz but the second harmonic produced by the diode could not be found. It was possible that the antenna resonance was higher than 3.6 GHZ, which was the highest frequency attainable by the test fixture and capable to generate enough RF power. The other hypothesis was that the diode might have not been working or that its response uldn ' t be good enough to generate a second harmonic. wo Further analysis using a test cable on the antenna showed that its efficiency was only about 4%. With the diode connected, the second harmonic was also not possible to see, even knowing where to look around 6 GHz. The low efficiency was caused by the low conductivity of the ground plane which was made of titanium.
One idea to get around this problem and still being able to use the titanium strain beams was to lengthen the antenna to move its resonance to the 2.4 GHz band. In this band, higher power amplifiers were available, so more power could be use to illuminate the antenna. Therefore, the design was changed as mentioned in Chapter 4, increasing the length of the antenna to 27 mm and putting a solderable wire instead of the fabricated (chip) diode to measure the frequency of resonance of the modified design. A second prototype included a chip diode on the antenna.
The frequency of resonance measured in the modified prototype was exactly where it should be, around 2.44 GHz, measured by attaching a test cable to the solderable wire. The resonance moved about 360 MHz ·to 2.8 GHz with just 3 mm of deflection of the beam, i.e. 120 µstrain. Therefore, the estimated gage factor for this prototype was 1229, the largest gage factor seen during this investigation by far.  ' I I

CHAPTER 7 Conclusions
Strain measurements on compressor blades of jet engines are currently performed through wire strain gages routed to the acquisition system through a slip-ring assembly. However, slip ring systems tend to wear off, especially the brush/ring contacts which make the signal noisy. This performance degradation leads to high maintenance costs in addition to the high cost of installing slip-ring systems.
Therefore, there is the need to develop non-contact systems to measure strain on compressor of jet engines. This thesis described the research work performed during the last year and a half to develop a prototype of a passive RF transponder that works as a wireless strain gage for gas turbine engines. The design, simulation, fabrication and testing of several prototypes have been described in the content of this thesis. The signal processing concept to be employed by the wireless strain gage system was beyond the scope of this research work. The passive transponder prototype needed to be printed, welded or deposited directly onto compressor blades; thus several key issues had to be addressed during the design of the transponder. Among these issues are the thickness of the transponder, the footprint and weight of the sensor and the large "g" loading experienced by the blades.
The proposed wireless strain gage concept uses a shift in the frequency of the resonance of a capacitive/inductive transponder or antenna wire over a ground plane, to measure strain. The principle of operation of all the approaches explored by this investigation is the same: a pulse of energy within a shot frequency band is transmitted to the transponder which, depending on the surface strain, returns a signal with a different resonant frequency. A change in the capacitance or in the distance between the antenna wire and ground introduced by strain, changes the frequency; thus a gage factor can be calculated.

81
Four different approaches were used to develop a prototype with the largest gage factor possible. Initially, thin-film and thick-film capacitors were designed, simulated, fabricated and tested to determine the maximum possible change in capacitance using such planar structures. Thin-film capacitors were developed by photolithography and sputtering processes. Simulations showed that the interdigital capacitor was a resonant circuit itself, but its resonance was above the frequency of operation required by the signal processing module. Therefore, an antenna element was added to move the frequency of resonance to the 1 to 2 GHz range.
Measurements \• vere performed at DC using a capacitance meter and a gage factor of 14 was observed in terms of capacitance. It was expected that the gage factor in terms of frequency would be lower since only the capacitance change would contribute to the change in resonant frequency ; thus, the gage factor expected for the thin-film capacitor was around 5. Unfortunately, the skin depth of the thin-film capacitors was too thin to so the transponder was not able to operate in the 1-2 GHz range. No resonance was detected when high frequency measurements were performed.
Therefore, a thick-film capacitor was developed to address the skin effect issue.
It was expected that the thick-film capacitors would yield very similar gage factors, and when tested at DC, a gage factor of 4 and 11 were obtained in terms of resonant frequency and capacitance respectively. Since the thick-film capacitors required a thicker dielectric, the capacitance decreased, increasing the frequency of resonance of the transponder; therefore, longer inductive elements were required to decrease the frequency of operation. High frequency tests showed only a 7-MHz frequency shift out of a base resonance of 2.4 GHz, for a gage factor of about 3.7.
This was probably due to the fact that a thicker dielectric was not correctly transferring strain from the surface of the substrate. 82 A third approach using a buckled beam amplification scheme combined with a capacitor made of interdigital wires yielded gage factors as large as 57. Parasitic capacitances introduced in the sensor during fabrication reduced the gage factor; the only contribution to a change in resonant frequency came from the variable interdigital capacitor and not from the parasitic capacitances. A laser-welding technique to attach the buckled beam capacitor to the titanium strain beam minimized the parasitic capacitances and boosted the gage factor close to 60.
The last approach explored was the antenna strain gage design. This prototype correlated the change in the distance from the antenna to the ground due to strain, to a change in the tuning frequency of them antenna. Very large gage factors of around 1000 were observed with this approach. Although, this approach had two main issues: first, the length of the antenna was about 27 mm which means that strain is measured over the entire length of the antenna; and second, the chip diode placed on the antenna did not work as expected. An external diode was needed to performed RF measurements.
In summary, this research examined four different prototypes for the wireless strain gage concept, two of the using thin-film and thick-films and two more using free standing structures. It has been shown that the free standing structures yielded larger gage factors compared to the thin-film and thick-film capacitors. This is due to the fact that the free standing structures are only in contact with the substrate at one or two places and not over the whole structure. Therefore, if a large gage factor is what is needed by the signal processing system, the free standing approach is the best. On the other hand, thin-film and thick-film structures can be more easily fabricated than free standing structures, besides the fact that they can probably withstand the large "g" loading better.   The input admittance of the IDT appears like a series resonant circuit in parallel with the transducer capacitance CT. The capacitance CT contributes to the major part of the reactance. The impedance Z(f) is then given by: where Ga(f) and Ba(f) are the conductance and susceptance, and Ra(f) and X a(f) are the resistance and the reactance respectively.

I
From the crossed-field model (Morgan 1976), Ga(f) and Ba(f) are given by: where e = 2ef / f o Jo is the resonant frequency c s is the static capacitance per section of the IDT in p F/m k 2 is the piezoelectric coupling factor of the substrate N is the number of sections of the IDT Ga(/) has a maximum atf = fo given by: where Cr = NC sW W is the aperture or length of the fingers of the IDT in meters (A4) According to Farnell et al. (1970), the capacitance per meter of a finger length is given by: where Cs is in (pF/m) , c 0 is the dielectric constant of the substrate and K as a empirical value given by K = 6.s(%)2 + 1.08(% )+2.37 where le is the effective cavity length (distance from cl?sest reflector on the left of IDT to closest reflector on the right ofIDT).
Based on equations A. l thru A.9, the design parameters proposed were as follows:  As mentioned in Chapter 3, although the change in capacitance for design 1 and 2 is the same, the base capacitance of the first design is smaller with a similar induced strain, which makes the gage factor larger compared to design 2.

Visual representation of design 1 parameters
The follo\~ring figures show a 3D dimensional view of the proposed interdigital capacitor design, as well as the top and bottom layers that form the electrodes of the capacitor. It must be noted that the dimensions shown in Figure B.3 are not to scale. That is why the dielectric layer looks more than the 8 µm specified by the design parameters.
Additionally, for simulation purposes, a larger lager of air was left on top and below 92 the planar structure. The reason for this is that the simulator sees every side of the virtual (transparent) box as a ground plane and it is important to keep the planar structure as far as possible from the walls.

APPENDIX C Sputtering procedure
The following steps were used to deposit the different metal thin films. Prior to sputtering a background pressure between 4.9x10-6 Torr and 6.5x10-6 Torr was desired.
Argon gas was introduced into the high pressure chamber after the throttle valve was closed and the Argon gas was introduced. The Argon introduced into the chamber was also monitored with the Pirani gage on the sputtering machine.
The RF power level was increased and he reflected power must be kept close to zero using load and target tuning features. The tuners should adjusted until a stable plasma was reached, keeping the reflected power close to zero. Once again, Argon gas was decreased to 5-7 mTorr and the RF power level increased to the desired value.

Additional thin film capacitors
Figures D. l and D.2 show two additional thin-film capacitors that were fabricated following the procedure described in Chapter 5. As shown in Figure D. l , the narrower part of the ceramic strain beam broke during testing due to excessive stress applied to the strain beam. The fabricated thin film-capacitor shown in the previous figure shows a lot more bubbles developed not only in the lower edge of the substrate but also close to the interdigitated fingers of the capacitor. It is believe that the reason for this was that temperature of the ceramic substrate reached 250 °C in less the 25 minutes previously specified.
Another important detail during the fabrication process was the fact that once the bottom metal layer was deposited, at least the edge of this layer had to be protected before spin-casting LOR SOB for the dielectric layer. The reason for this is that for capacitance measurements, access to the top and bottom metal layers is needed.
Therefore, if LOR SOB is deposited on the entire surface without protecting the bottom metal layer, this layer gets buried underneath the dielectric and measurements are not possible. A small strip of uncovered metal can be seen on the top edge of the ceramic beam in the sensor area in Figure   A final comment on the fabrication of this type of capacitors is that before sputtering the back of the ceramic strain beams for the ground plane, measurements and testing had to be performed on the capacitors. This is because once the back of 97 the strain beam was sputtered with copper, the bottom and top electrodes are connected to ground and it is technically impossible to measure the capacitance of the interdigital electrodes since they are shorted.

Additional thick film capacitors
Following the same procedure described in Chapter 5, a second thick-film capacitor was fabricated with a faster deposition rate. This time, the deposition rate was 5µm/minute, applying an electric current of 350 mA for 2 minutes. Figure D.3 shows the fabricated capacitor. It can be seen that the shape of the antenna was deformed as well as the shape of the interdigital fingers.
DC measurements were not possible on this capacitor because the top and bottom metal layer were shorted out after electroplating. Some issues arose after the initial buckled beam was fabricated and tested, as described in Chapter 5 and further analyzed in Chapter 6. The biggest concerns with the buckled beam capacitor were the parasitic capacitances created when attaching the non-grounded electrode (top buckled rail) to the titanium beam; and the fact that the large globs of silver epoxy were preventing the grounded electrode (bottom buckled rail) from achieving the maximum displacement; thus decreasing the mechanical amplification which leads to as smaller b.C/C. Therefore, several observations to the initial fabricated buckled beam capacitor were made and some modifications were scheduled for the next designs. Figure  The previous figure shows the large globs of non-conductive and silver epoxy developed after small drops were put in place to hold the buckled rails to the titanium beam. The non-conductive epoxy globs create some parasitic capacitances (Cl and C2 as shown in Figure E.2). The variable capacitance (C3) given by the interdigital electrodes was designed for 0.49 pF. As discussed in Chapter 6, it was estimated that the nominal capacitance of the fabricated capacitor was close to 0.5 pf which is what was expect. The problem was that the magnitude Cl = 0.75 pf and C2= 1.5 pf were much larger than the actual variable capacitance given by C3 . Therefore, Cl and C2 dominated the resonant circuit and prevented the small change in C3 from shifting the resonant frequency.
In order to address the problem of the parasitic capacitances created by the nonconductive or regular epoxy, it was suggested reducing the length of the top rail as well as increasing the thickness of the kapton tape to decrease these capacitances. By shortening the top rail and thickening the dielectric, the parasitic capacitances would shrink since, by a basic parallel capacitor theory, the distance between the top rail and the ground plane was increased and the area were the top rail and the titanium substrate decreases because of the shorter length. Figure  Unfortunately, the down side of these changes is that by shortening the top rail, the buckled beam amplification scheme modified. In this case, only the bottom rail 100 would contribute to change of capacitance. But the biggest concern of these modifications was that, if the buckled beam capacitor was arranged in a horizontal position with respect to the axis of strain, the non-conductive epoxy was not going to be able to hold the top electrode to the titanium beam. This is that, since there is no buckled beam, the top rail would tend to elongate as strain is apply to the substrate. So in order to corroborate that the changes in the design were going to decrease the base capacitances, the buckled beam capacitor was rotated 90°, so that now the capacitor is perpendicular to the axis of strain. The fabricated capacitor is shown in Figure E.3.

Figure E.3 Fabricated capacitor with non-buckled shorter rails
As seen in the figure above, the buckled beams of the bottom rail were also cut-off to make sure strain was transferred adequately. The fabrication steps were the same as for the original design with the exception that this time, instead of only 1 layer of kapton tape, 8 layers were placed to thickening the dielectric up to 200 µm. The overlapping length was also increased to 500µm to increase the variable base capacitance (C3) to 0.62 pF. The diameter and space between the interdigital wires was the same as in the original design. Results of these modifications are discussed in Chapter 6.
In addition to the previous modifications, a third design was proposed to address the issue of the large globs of silver epoxy used to hold the bottom rail to the titani urn substrate. Also, the number of interdigital fingers was increased from 16 to 60 to increase the variable base capacitance (C3) and the overlapping length was about 300 µm. Using equation (9), C3 is given by: CJ = ;r(l)(8.85 x l0 -12 )(300 x 10-6 )(60-1) = l. 4 Gp F in( (60 x l0-6 -25 x 10-6 ) / ) / 25 x 10-6 The greatest modification was the substitution of silver epoxy with a difference approach. This time, instead of using a drop of silver epoxy, a laser-welding machine was used to attach the bottom rail to the titanium substrate. The fabrication procedure was once again similar to the steps followed by the other two designs: the titanium substrate was cleaned up using sanding paper, and then 8 layers of kapton tape were placed. The buckled beam scheme was used again since the bottom rail was attached by laser-welding, while the top beam still used non-conductive epoxy. This time, the non-conductive epoxy deposited was a smaller drop so it would not spread out to form large capacitances. Figure E.4 shows the fabricated buckled beam capacitor with 60 interdigital fingers and using a laser-welding approach.
102 Figure E.4 Fabricated buckled beam capacitor with 60 interdigital fingers Several parameters can be modified in the laser-welding machine to achieve a better joint: the profile of the laser beam, the aperture, the frequency, the voltage, the time and the energy of the laser beam among others. All these parameters and some other observations are discussed in Appendix F.   The prototype shown in the figure above did not include a diode; instead a solderable wire used to attach an external diode was connected to the antenna wire.
The figure below includes a diode and a layer of copper tape between the diode and the substrate for better contact.

APPENDIX I Additional antenna gage measurement details
Tx amplifier output: +23.5 dBm (224 mW). This is the output power at the fundamental freq (about 2.45 GHz). Tx antenna gain at 2.45 GHz: +6.3 dBi. So, the total ERP (effective radiated power) is almost 1 watt (+29.8 dBm).
The antenna strain gage was located 6" from the Tx antenna The antenna gage prototype had a gain at 2.45 GHz: -11.5 dBi (only 7% efficiency losing a lot of performance here).
The Tx signal produced about 350 µWat the antenna gage terminal (about 2.6 mV in 50 ohrns).The 2nd harmonic generated by the 2.6 mV from the e:;...1emal diode is about -32 dBm This is the signal that is re-radiated by antenna gage.
The antenna gage prototype had a gain at 4.9 GHz: about -9 dBi (a little higher at 5 GHz than at 2.45 GHz). The -32 dBm second harmonic input to the -9 dBi antenna produced about -65 dBm at the output of the Rx horn antenna at a 6" range. (The R.-x antenna gain is +8 dBi).