L-C MEASUREMENT ACQUISITION METHOD FOR AEROSPACE SYSTEMS Stanley E. Woodard1 NASA Langley Research Center B. Douglas Taylor2 Swales Corporation Qamar A. Shams3 and Robert L. Fox4 NASA Langley Research Center This paper describes a measurement acquisition method for aerospace systems that eliminates the need for sensors to have physical connection to a power source (i.e., no lead wires) or to data acquisition equipment. Furthermore, the method does not require the sensors to be in proximity to any form of acquisition hardware. Multiple sensors can be interrogated using this method. The sensors consist of a capacitor, C(p), whose capacitance changes with changes to a physical property, p, electrically connected to an inductor, L. The method uses an antenna to broadcast electromagnetic energy that electrically excites one or more inductive-capacitive sensors via Faraday induction. This method facilitates measurements that were not previously possible because there was no practical means of providing power and data acquisition electrical connections to a sensor. Unlike traditional sensors, which measure only a single physical property, the manner in which the sensing element is interrogated simultaneously allows measurement of at least two unrelated physical properties (e.g., displacement rate and fluid level) by using each constituent of the L-C element. The key to using the method for aerospace applications is to increase the distance between the L-C elements and interrogating antenna; develop all key components to be non-obtrusive and to develop sensing elements that can easily be implemented. Techniques that have resulted in increased distance between antenna and sensor will be presented. Fluid-level measurements and pressure measurements using the acquisition method are demonstrated in the paper. 1 Senior Scientist, Structural Dynamics Branch, Structures and Materials Competency. Associate Fellow AIAA. [email protected] 2 Design Engineer, Systems Engineering Competency 3 Senior Electronics Engineer, Instrument Systems Development Branch, Aerodynamics, Aerothermodynamics and Acoustics Competency. [email protected] 4 Senior Electrical Technician, Technology Development and Integration Branch, Systems Engineering Competency [email protected] 1 American Institute of Aeronautics and Astronautics Introduction L-C circuits and the interrogation methods have limited applications to where the distance separating the L-C Wireless methods are being developed for vehicle circuits and their interrogation systems are less than 15 systems as a method for measurement acquisition1. To cm. date, many of these systems are existing sensors One example of a L-C sensor interrotation system is physically connected to a power source, microprocessor that presented by Konchin et al for interrogating a fluid- and transmitters. Another method of acquiring measurements is the use of radio frequency level sensor4. The fluid-level sensor consists of two identification (RFID) tags. RFID systems eliminate the capacitive plates coupled to an inductor. The sensor need for physical connection to a power source. A uses the dielectric variation that results from a fluid RFID system consists of an interrogator (reader), a filling the space between two capacitive plates. As the silicon chip electrically connected to an antenna coil fluid level increases, the capacitance increases and thus and host computer. The silicon chip includes the resonant frequency of the circuit decreases. The modulation circuitry and non-volatile memory. When fluid-level sensor interrogator is a receiver that consists the interrogator near the antenna coil transmits a time of an amplifier circuit with an inductor coil connected varying radio frequency wave, an alternating current to the amplifier input and another inductor coil (AC) voltage is created via Faraday induction2,3 The connected to the amplifier output. The coils are wound and are positioned with respect to each other to balance AC voltage is rectified to create a direct current (DC) mutual inductance such that feedback between the coils power source for the silicon chip. When the DC level is approximately zero. The balancing objective is to not reaches a critical threshold, then sufficient power exist create a positive input voltage to the amplifier. A to operate the chip. The chip can be electrically voltage is applied to the amplifier thus powering the coupled to a sensor and measurements thus stored in the output inductor. When the fluid-level sensor is placed nonvolatile memory. When the RFID is activated, the in proximity to the two coils, its inductor causes the contents of the nonvolatile memory can be transmitted amplifier output inductor to oscillate. The amplifier to the reader. The distance for which RFID devices can output inductor will cause the amplifier input inductor be used is limited to approximately 15 in within the to oscillate thus creating a feedback system. The imput frequency range of 1 – 25MHz that is available for to the amplifier is then correlated to a value of fluid- aerospace system1. Another measurement technique is level. The limitation of this interrogation method is that the use of L-C sensors embodied as inductive- the prefered separtion distance between the sensor and capacitive circuits. the interrogator is no more than 3.5 cm. A L-C sensor has a capacitor developed such that its Allen et al5, 6 discusses several methods of L-C sensor capacitance, C(p), varies with changing physical interrogation. In all cases, the sensors are within the properties, p, which it is designed to measure. The perimeter of the antenna used for interrogation. In one capacitor is electrically coupled to an inductor, L, method, an impedance analyzer applies a constant forming a L-C(p) circuit2,3. The electrical resonant voltage signal to a transmission antenna. The frequencies of the L-C(p) circuits change as their frequency of the antenna is scanned across a capacitance change. The capacitive changes are a result predetermined range. When the antenna frequency is of changes in dielectric properties or geometric that of the L-C sensor frequency, the current across the changes, which result from a physical property antenna peaks. The frequency at which the current changing. An example would be that as a fluid fills the peaks is correlated to a physical property measurement. void between two capacitive plates, the dielectric Another method presented by Allen et al is to use a properties between the plates and thus the capacitance transmission antenna and receiving antenna. White changes. Piezoelectric materials (e.g., piezo-ceramics noise within a predetermined range is transmitted. such as lead zirconate-titanate (PZT), or piezo- Current is produced in the L-C sensor via Faraday polymers such as polyvinlydinofloruride (PVDF)) have induction. The current induced in the L-C sensor draws electrical properties similar to capacitors. These power from the transmission antenna. The receiving materials develop electric polarization when force is antenna receives the transmission antenna signal less applied along certain directions in them. The the power absorbed by the L-C sensor which appears as magnitude of polarization is proportional to the force a dip in the received response. Hence, the frequency of (within certain limits). The capacitance varies as the the response dip is correlated to the physical property polarization varies which suffices for measuring measurement. Chirp interrogation is another technique resulting strain from material deformation. discussed by Allen et al. A transmission antenna Deformation can be due to either mechanical or thermal broadcast white noise and then is turned off after a loading (pyroelectric effect). To date, the design of the 2 American Institute of Aeronautics and Astronautics predetermined amount of time. The white noise • Key components can be developed as metallic foils induces a current in the L-C circuit. The receiving or thin films (inductors, antennae, some capacitor antenna then listens to the L-C response. A final types) method by Allen et al is to couple the transmission • No line-of-sight is required between antenna and L- antenna to a tank circuit. The oscillator of the tank C(p) sensing element. circuit varies the frequency of the transmission antenna. • The entire L-C(p) sensing element can be embedded The frequency of the transmission signal is altered by in non-conductive material. For conducting material, the L-C sensor. A frequency discriminator is used to the capacitive element can be embedded and the provide a signal from which the resonant frequency can inductive element can be placed away from the be identified. 6 surface of the conductive material. • No specific orientation of sensing element with The key to practical use in vehicles is increased respect the antenna used to excite the sensing element interrogation antenna-inductor separation distance and is required except that they cannot be 90 deg to each to facilitate multiple measurements having different other. dynamic characteristics. An L-C sensor serves as a • Easy to implement into existing vehicles/plants means of acquiring power via Faraday induction, a • Easy to add new measurements. No wiring is sensor and a means of transmitting the measurement via required. All that is required is a partition of a RF the harmonic magnetic field created by the inductor. bandwidth used in the measurement spectrum and The distance at which the magnetic inductor response frequency/measurement correlation table. can be received is proportional to the strength of the magnetic field created in the inductor. The magnetic Following the introduction, the paper contains an field strength is dependent upon the current in the overview of the measurement interrogation method. sensor. Therefore, interrogation distance is also Examples of L-C sensors and respective test results will dependent upon the energy efficiently of the L-C sensor follow. Results will then be presented on methods circuit. The higher the energy efficiency, the more being used to increase antenna Q and inductance Q. current is created for the same level of power used by Increasing inductor Q and antenna Q allows an L-C(p) the interrogating antenna(e). The quality factor, Q, is circuit to be interrogated at increased distance from the the gage for this efficiency. Q is the ratio of reactance antenna. Techniques presented in this paper have to DC resistance. A stronger magnetic field is created resulted in measurements acquisition when antennae with higher Q. separation is 11ft using 1.5 w of power applied to transmission antenna. Using a single antenna The L-C measurement acquisition method presented in electrically switched from a transmitting to receiving this paper can be used to acquire measurements even antenna, an interrogation distance of 2 ft has been when the sensing element (inductor and capacitor) is achieved using 0.1 w of power applied to the antenna. embedded in material that is transmissive to the radio frequency energy that interrogates the sensing element. An advantage of this method is that the components for Overview of Measurement Interrogation Method the method can be non-obtrusively added to the vehicle for which it is being used. An antenna can be produced Fig 1 shows a schematic of the L-C measurement as a metallic foil or as metal deposited on a thin acquisition method using a single radio frequency dielectric film. Either aforementioned version of the antenna and multiple L-C sensing elements. The antenna can be mounted to an existing bulkhead or components of the L-C measurement system are a radio other structural components. Furthermore, the antennae frequency antenna for transmitting and receiving RF and L-C(p) elements can be fabricated using thin film energy; a processor for regulating the RF transmission deposition methods such as photolithography. The and reception; and software for control of the antenna thin-film devices could be added to a vehicle during and for analyzing the RF signals received; and, L-C manufacturing. Other advantages of the method for sensing elements. The sensing elements are capacitors, vehicle applications are: C(p), and inductors, L, placed in parallel with their respective capacitors forming L-C(p) circuits. The • Physical connection to a power source (i.e., lead processor modulates the input signal to the antenna to wires) is not needed produce either a broadband time-varying magnetic field • Physical connection to data acquisition equipment is or a single harmonic magetic field. The variable not needed magnetic field creates an electrical current in the • Multiple sensing elements can be interrogated using passive inductor-capacitor, L-C(p), circuits as a result the single data acquisition channel (used for antenna). of Faraday induction. The circuits will electrically 3 American Institute of Aeronautics and Astronautics oscillate at resonant electrical frequencies that are dependent upon the capacitance and inductance of each circuit. The oscillation occurs as the energy is harmonically transferred between the inductor (as magnetic energy) and capacitor (as electrical energy). When the energy is in the inductors, the magnetic fields produced are single harmonic radio frequencies whose frequencies are the respective L-C(p) circuits resonant frequencies. The antenna is also used to receive the harmonic magnetic responses produced by the inductors of the circuits. The receiving antenna can be the same antenna used to produce the initial broadcast of energy Fig 2 L-C sensor frequency measurement bands. received by the L-C circuit or another antenna can be used. When the same antenna is used, it must be switched from a transmitting antenna to a receiving The interrogation method uses a scan-listen-compare antennna. A simple microprocessor can be used to technique. The interrogation logic is presented in Fig 3. identify the frequencies of the signals received by the The transmission and receiving antennae can be used or antenna. The measured frequencies are then correlated a single switching antenna can be used. Using two to measurement of physical properties. antennae provides a larger volumetric swath at which measurements can be taken which is approximately double that of a single antenna. The interrogation procedure goes as follows: 1. At the lower limit of a predetermined range, a radio frequency harmonic is transmitted for a predetermined time and then the transmission mode is swtiched off (i.e., the transmission antenna is turned off if two antennae are used or if a single antenna is used, it ceases transmission). 2. The receiving mode is then turned on (i.e., the receiving antenna is turned on if two antennae are used or if a single antenna is used, it begins receiving). The received response from the L-C sensor is rectified to determine its amplitude. The amplitude, A, and frequency, ω, are stored in i I memory. Fig 1 Schematic of L-C measurement acquisition method using a single radio frequency antenna and 3. The receiving mode is turned off and the multiple L-C sensing elements transmission mode is turned on. The transmitted radio frequency harmonic is then shifted by a predetermined amount. The harmonic is The L-C(p) circuit responses are superimposed. The L- transmitted for a predetermined time and then the C(p) circuits are designed (Fig. 2) such that their range transmission mode is turned off. of measurement frequencies do not overlap but the ranges are within a frequency range of the antenna. 4. The receiving mode is then turned on. The The range of resonant frequencies corresponds to received response from the L-C sensor is rectified physical property values that can be measured. An to determine it amplitude. The amplitude, A, and example would be that the lower frequency in the i frequency, ω, are stored in memory. measurement band, ωi(p), would correspond to the I lower limit of a strain measurement. This method 5. The current amplitude, A is compared to the two i, allows for any number of L-C sensing elements within previously attained amplitudes, A and A . If the i-1 i-2 the range of the antennae to be interrogated. previous amplitude, A , is greater than the current i-1 amplitude, A, and also greater than amplitude prior i to it, A , the previous amplitude, A , is the i-2 i-1 amplitude inflection. The amplitude inflection 4 American Institute of Aeronautics and Astronautics occurs when the excitation harmonic is equal to the The sweep of a single frequency is used because it resonant frequency of the L-C sensor. The concentrates all energy used to excite the L-C sensor at amplitude, A , and the corresponding frequency, that frequency. Fig 4 depicts the L-C sensor response i-1 ω, are cataloged for the L-C sensor for the current amplitude as the excitation frequency approaches the I frequency sweep. These values can be compared sensor resonant frequency. During each frequency to the values aquired during the next sweep. If an sweep for each sensor range, the current, A, and i amplitude inflection has not been identified, then previous two amplitudes (A and A ) and frequencies i-1 i-2 steps 3 and 4 are repeated. are stored. The amplitudes are compared to identify the 6. If amplitude inflection has been identified, the amplitude inflection. The frequency at which the harmonic sweep continues to the next L-C sensor. amplitude inflection occurs is the resonant frequency. The initial sweep is to ascertain all resonant frequencies and their corresponding amplitudes. Frequencies and amplitude values of successive sweeps can be compared to previous sweeps to ascertain if there is any change to measured property or if the antenna has moved with respect to the antenna. If the physical property has changed, the resonant frequency will be different from prior sweep. If a L-C sensor has moved with respect to the antenna, the amplitudes will be different (frequency will remain constant). The magnitude and sign of the difference can be used to determine how fast the sensor is moving and whether the sensor is moving toward the antenna or away from the antenna. Fig 3 L-C measurement acquisition method Fig 4. L-C sensor response to excitation radio interrogation logic frequency energy The initial frequency sweep can be used to identify and Examples and Application of L-C Sensors catalog all resonant peaks associated with all L-C sensors within its range of interrogation. The cataloged The L-C measurement acquisition method is applicable amplitudes and resonant frequencies for all L-C sensors for a variety of measurements sensors. The method has can be used to reduce the sweep time for successive been demonstrated for fluid-level and pressure sweeps. For example, the next sweep to update each measurements. Fig 5 shows an L-C(p) sensing element. resonant frequency can start and end a predetermined The inductor (L) is formed as a spiral of copper. Inter- proximity to the cataloged resonant and then skip to the digital electrodes have been used for the capacitor (C). next resonant range. The aforementioned capability The inductor and the capacitor have been deposited on allows L-C sensors to easily be added to measurement a thin dielectric film. The sensing element has been acquisition framework. used to measure pressure and fluid level of non-viscous fluids. A single antenna is used to power the L-C 5 American Institute of Aeronautics and Astronautics sensor and to receive its response. A wave generator is using 0.5 in increments. A fluid-level of 9 inches used to produce a single radio frequency harmonic. resulted in a frequency reduction of over 1 MHz from The excitation harmonic is tuned to the sensor’s that of the empty container. The fluid-level resonant frequency before force is applied. The measurements were acquired manually using the harmonic is kept constant while eight pounds of force is procedure presented in the previous section. applied to the L-C sensor shown in Fig 5. As the force is applied to the thin membrane, it causes the interdigital electrode separation distance to increase thus changing the resonant frequency. The response received by the antenna is shown in Fig 6 before and after the force was applied. The eight pounds of force resulted in the frequency response changing 0.5 MHz. When pressure is added, the response amplitude is decreased because the excitation frequency remained constant as the resonant frequency changed. The L-C sensor resonant frequency was measured before force was applied and with the force applied. However, having the excitation harmonic remain constant while the resonant frequency changed resulted in the lower a. Frequency response when no pressure is applied to response amplitude. This is also illustrated in Fig 4. capacitor The lower response level would reduce the distance at which changes in pressure level could be interrogated. The method presented in the prior section would eliminate the aforementioned shortcoming. CCaappaacciittoorr 00..55 MMHHzz 00..55 MMHHzz IInndduuccttoorr b. Frequency response when pressure is applied to capacitor Fig 6 L-C sensing element (Fig 3) frequency response to applied pressure. Fig 9 shows the RF response from multiple L-C(p) Fig 5 A L-C sensing element. The inductor (L) is sensing elements. In this example, a broadband of formed as a spiral of copper. Inter-digital electrodes radio frequency energy (1-10 MHz) excited the sensors. have been use for the capacitor (C ). The sensing Each sensor has a predetermined frequency range, Fig element can be used to measure pressure and fluid level 2, which is correlated to its measurement range. The of non-viscous fluids. resonant peaks shown are for a fluid-level measurement, ω (p), position measurement, ω (p), and 1 2 A L-C fluid-level sensor is shown in Fig 7. The sensor pressure measurement, ω (p). The range of consists of two capacitive plates electrically coupled to 3 frequencies (i.e., partition) for each measurement is an inductor. As the fluid fills the void between the annotated (arrows). plates, the effective dielectric increases thus changing the resonant frequency. The fluid sensor was excited The examples demonstrate the L-C sensors and their (powered) using the same method as the pressure respective measurements. To make this measurement sensor. Frequency measurements for a 9-inch fluid- method practical for vehicle applications, the distance level sensor are shown in Fig 8. As the level increases, between sensing elements and the interrogation the frequency decreases. Fluid level was increased antenna(e) needs to be more than 2 ft. The previous 6 American Institute of Aeronautics and Astronautics efficient. To facilitate non-obtrusive use of the measurement system, the antenna are developed as either thin-film deposited on a dielectric membrane or thin foil which can be placed on any existing nonconductive surface. To ascertain the effect that geometry would have on the electrical properties, two features were considered: antenna width and antenna diameter. Fig 10a shows a thin copper foil antenna adhered to a Plexiglas plate. The antenna trace width is initially 2.0 in. In first study, the antenna outer diameter remained a constant 18.0 inches. The inner diameter is reduced and measurements were taken when the antenna trace was at the following widths: Fig 7 L-C Fluid level sensor 2.0, 1.5, 1.0, 0.5, and 0.25 in. The inductance, DC resistance and Q were measured for each width. A current of 1 KHz was used for the inductance measurements and the Q measurements. Fig. 10b shows the other antennae used for parametric measurements. Six 0.5 in traces of copper foil are adherred to a Plexiglas plate. The outer diameters are 6, 8, 10, 12, 14 and 16 inches. The coaxially cable was individually electrically connected to each trace. The inductance, DC resistance and Q were measured for each width. Resistance measurements are shown in Fig 11 for both parametric changes to antenna width and diameter. As seen in Fig 11a, DC resistance decreased with increased trace width. Resistance increased Fig 8 Electrical resonance variation with fluid level as significantly as the width was reduced. The resistance measured by interrogation antenna doubled from 0.052 Ω to 0.118 Ω as the width was changed from 0.5 in to 0.25 in. The resistances of the wider traces were substantially less. For the traces wider than 1.0 in, the resistance decreased but not as ωω((pp)) ωω((pp)) ωω((pp)) much. Results from the DC resistance measurements 11 22 33 (Fig 11b) of the diameter variations show that the resistance increased approximately linearly with diameter. The measurement results indicate that to develop low resistance antennae, a wide trace would result in less applied power loss due to lower resistance. Inductance measurements are presented in Fig 12. The measurements have similar trends as the resistance Fig 9 Frequency response of three measurements. measurements. Inductance increases are more pronounced for narrower traces. Inductance also section discusses a method of concentrating energy into increases approximately linearly with increasing single harmonics to increase interrogation distance. diameter. Values of Q are presented in Fig 13. An Other methods to increase distance are to develop antenna’s electrical efficiency is dependent upon its Q energy efficient antenna(e) and L-C circuits. These (i.e., higher Q results in higher efficiency). The trace methods will be discussed in the next sections. width has a significant effect on Q. The increase of Q with increasing trace width is approximately linear. As Antenna Design Analysis the width is changed from 0.25 in to 2.0 in, Q changes by over a factor of 4 (Fig 13a). Changing outer Parametric measurements were performed to ascertain diameter from 6 in to 16 in results in Q changing by the influence of geometric properties on interrogation less than 0.02. antenna effectiveness. The measurement objective is to develop design criteria to make antenna more energy 7 American Institute of Aeronautics and Astronautics 2.0 in a. Antenna with constant outer diameter with variable b. Antennae with 0.5 in wide trace of copper foil with width various outer diameters Fig. 10 Antennae used for parametric studies a. DC resistance variation with antenna width b. DC resistance variation with antenna diameter Fig 11 DC resistance variation with antenna geometry. a. Inductance variation with antenna width b. Inductance variation with antenna diameter Fig 12 Inductance variation with antenna geometry 8 American Institute of Aeronautics and Astronautics a. Q variation with antenna width b. Q variation with antenna diameter Fig 13 Q variation with antenna geometry. results in higher Q for same trace width. Comparison Inductor Design and Analysis of the 5 in square with 0.25 in trace with the 3 in spiral with the 0.50 inch shows that increasing width An antenna is basically an inductor. Hence, results can be used as a method of producing a higher for antenna parametric measurements can be applied inductor Q. for the development of inductors. Five square spiral inductors such as the 5 in inductor showed in Fig 14 To quantify effective range for measurement were constructed to examine the effect that key acquisition, the inductors were coupled to capacitors. design features such perimeter size and trace width Two measurement configurations were used. In the had on inductance, DC resistance and Q. The first configuration, a switching antenna (12 in loop) inductor serves to relay the measurement. The was used with a transmission power level of 0.1 w. distance at which the magnetic inductor response can An inductor with a 5 in x 5 in square spiral with 0.75 be received is proportional the strength of the in trace coupled to a 504-pF capacitor achieved a – magnetic field created in the inductor. The magnetic 60dB response at 25 in distance from the antenna. field strength is dependent upon the current in the The inductor with the 3 in x 3 in square spiral with sensor. For the same applied energy, a lower 0.25 in trace coupled with a 826-pF capacitor resistance results in a higher current. Hence, to achieved a –60dB response at 22 in distance from increase the range of the L-C sensors, the sensor antenna. In second measurement configuration, a elements should have as low resistance as possible. transmission antenna (18 outer in diameter and 0.5 in trace) and receiving antenna (wire loop 24 in using Techniques used in the antenna analysis are used in 12 gauge copper wire) are used. They are positioned the development of inductor. Specifically, using 11 ft apart. The antennae are operated such that wider traces to reduce resistance. Fig 15 presents the when the transmission antenna is powered on to effect of trace width on DC resistance. Three 3-inch excite the L-C elements, the receiving antenna is off. square spiral inductors having widths of 0.02, 0.25 The transmission antenna used 1.5w of power. When and 0.50 inches were used. The resistance of the 0.02 the transmission antenna is switch off, the receiving in trace is 9.4 Ω. Resistance for the 0.25 and 0.5 in antenna is powered on allowing it to receive the L-C traces are 0.055 Ω and 0.023 Ω. The significantly element response. In this configuration, the sensing lower resistance of the wider traces demonstrates the elements presented in the section “Examples of L-S trace width is an effective design parameter. The Sensors” could be interrogated anywhere in a volume effects of trace width and inductor perimeter size on approximated by a cylinder whose longitudinal axis Q are shown in Fig 16. The values Q for the 3 in runs between the antenna centers and with diameter square spirals are shown. The value of Q increases approximately 4 ft. The length of the cylinder was approximately linearly with increasing trace width. the separation distance between the antennae. When The 5 in square spirals (0.25 in and 0.05 in trace) the antennae were separated by 9 ft, the same sensing show similar results. The larger size square spiral elements could be interrogated using 1.0 w of power. 9 American Institute of Aeronautics and Astronautics Fig 14 Five-inch square spiral inductor with 0.25 in trace and 0.25 in separation between traces Fig 15 Inductor DC resistance variation with trace width Fig 16 Inductor Q variation with trace width amplitude inflection. The frequency at which the amplitude inflection occurs is the resonant frequency. Concluding Remarks The initial sweep is used to ascertain all resonant frequencies and their corresponding amplitudes. A L-C measurement acquisition method has been Frequencies and amplitude values of successive described. The methodology was developed to sweeps can be compared to previous sweeps to increase the distance between an interrogation ascertain if there is any change to measured property antenna and a L-C sensor. The method facilitates or if the antenna has moved with respect to the multiple measurements having different dynamic antenna. If the physical property has changed, the characteristics. The sweep of a single frequency was resonant frequency will be different from prior used because it concentrates all energy used to excite sweep. If L-C sensor has moved with respect to the the L-C sensor into a single harmonic. The L-C antenna, the amplitudes will be different. The sensor response amplitude increases as the excitation magnitude and sign of the difference can be used to harmonic approaches the sensor resonant frequency. determine how fast the sensor is moving and whether The amplitudes are compared to identify the 10 American Institute of Aeronautics and Astronautics