Wireless Strain Measurement with a Micromachined Magnetoelastic Resonator Using Ringdown Frequency Locking

Abstract

Resonant magnetoelastic devices are widely used as anti-theft tags and are also being investigated for a range of sensing applications. The vast majority of magnetoelastic devices are operated at resonance, and rely upon an external interface to wirelessly detect the resonant frequency, and other characteristics. For micromachined devices, this detection method must accommodate diminished signal strength and elevated resonant frequencies. Feedthrough of the interrogating stimulus to the detector also presents a significant challenge. This paper describes a method of interrogating wireless magnetoelastic strain sensors using a new frequency-lock approach. Following a brief excitation pulse, the sensor ring-down is analyzed and a feedback loop is used to match the excitation frequency and the resonant frequency. Data acquisition hardware is used in conjunction with custom software to implement the frequency-lock loop. Advantages of the method include temporal isolation of interrogating stimulus from the sensor response and near real-time tracking of resonant frequencies. The method was investigated using a family of wireless strain sensors with resonant frequencies ranging from 120 to 240 kHz. Strain levels extending to 3.5 mstrain and sensitivities up to 14300 ppm/mstrain were measured with response times faster than 0.5 s. The standard deviation of the locked frequency did not exceed 0.1%.

I. Introduction

Magnetoelastic transducers can be wirelessly queried by applied electromagnetic fields, and are attractive for a number of applications. For example, magnetoelastic anti-theft tags are ubiquitous in the retail sector, with annual production numbering in the billions [1–3]. Magnetoelastic sensors are being explored as well. Sensors measuring mass loading, strain, viscosity, temperature, magnetic field among other physical parameters have been previously reported [4–9]. Many sensors based on magnetoelastic materials use a change in resonant frequencies to determine the measurand. Resonant frequency and quality factor measurements are also used for material characterization; for instance, to determine the stiffness, magnetomechanical coupling coefficient, or damping [10–12]. Hence, accurate measurement of resonances is an important element for technologies based on magnetoelastic materials.

Magnetoelastic materials exhibit coupling between magnetization and strain. This coupling manifests in the form of Joule magnetostriction and Villari effect. Joule magnetostriction is the phenomenon wherein an applied magnetic field results in material strain. Villari effect is the inverse of Joule magnetostriction, and is the material magnetization in response to applied deformation. This coupling allows resonances to be remotely excited by an oscillating magnetic field. The backscattered magnetic field, due to the induced vibrations, is detected by a receiving coil or antenna. There are three general challenges associated with this detection: avoiding feedthrough of the excitation signal into the detection circuit for the backscattered signal, accommodating diminished signal strength from microfabricated or distant resonators, and accommodating elevated resonant frequencies associated with microfabricated resonators. The resonant characteristics can be generally determined from the received voltage using either frequency domain or time domain methods.

In frequency domain detection methods, a range of frequencies is swept by the transmit coil, while the receive coil simultaneously detects the response from the device under test. The transmit and receive circuits are synchronized to operate at identical frequencies at a given instance of time. The voltage detected by the receive coil shows a maximum at the device resonant frequency [13]. A single coil can also be used for resonant frequency detection. The mutual induction between the coil and the device, and thus the effective impedance of the coil, is dependent on the frequency response of the device. The impedance of the coil exhibits a peak at the device resonant frequency [6].

In the time domain detection method, an incident magnetic impulse is used to excite the resonant device, following which the ring-down oscillations are measured. Excitation and detection can be performed using separate coils or a single coil switching between transmit and receive circuits. The ring-down occurs at the device resonant frequency and can be measured by using Fourier analysis or frequency counting techniques [14–16]. In this report, a frequency-locked loop approach is applied for measurement of resonant frequencies of a magnetoelastic strain sensor in the time domain (Fig. 1).

Fig. 1.

Detection of resonant frequency of magnetoelastic resonator using a frequency locked-loop.

An advantage of the time domain approach is the isolation of transmitted magnetic field from the receive circuit, which reduces the feedthrough. The receive circuit can be synchronized to measure the resonator response, while being deactivated during the transmit phase. Decoupling the magnetoelastic resonant response from the excitation field is useful in a multitude of ways. It enables the use of stronger excitation magnetic fields without the risk of damaging the receive circuit by overloading it. The resulting improvement in system performance is twofold: (i) the dimensional range of the excitation can be increased as the coils can now generate a stronger field over extended distances; and (ii) the resonators can now be driven to larger vibration amplitudes, enabling the generation of stronger signals at the receive coil. In addition, the decoupling isolates the comparatively weak resonant response of the resonators from the much stronger excitation magnetic field. Weak resonant responses are no longer superimposed on feedthrough of large magnitude, making the detection more robust. Because the strength of the sensor resonant response correlates to its size, the decoupling of excitation field from the sensor response also allows miniaturization of the sensors. Another advantage is the potentially faster response in tracking of changes in resonant frequencies. While the frequency domain approach requires sweeping through a range of frequencies, a time domain approach can provide the resonant frequency information with a single impulse response.

However, when the time domain approach is used with an impulse excitation, the incident magnetic field is distributed over a range of frequencies. Much of the excitation energy is outside the vicinity of the device resonant frequency and has a lower contribution towards building the vibration amplitudes prior to initiation of the ring-down. This does not maximize the response for the available stimulation power.

A time domain ring-down approach that can generate a higher amplitude ring-down response is one that uses tuned excitation, i.e. an excitation magnetic field that is a sinusoid of limited duration, at a frequency equal to the resonant frequency of the device. However, for sensing devices where the device resonant frequency is subject to change, a predetermined excitation frequency is very likely to be different from the device resonant frequency. In addition, small fluctuations in biasing DC magnetic fields and batch-to-batch variations between devices can lead to a non-uniformity in resonant frequencies across seemingly identical devices. In this scenario, the excitation frequency must be adjusted to track the device resonant frequency for strongest response.

A method of using the ring-down response of an LC resonant sensor to track the resonator frequency using a phase-locked loop (PLL) has been reported previously [17]. In applications where phase synchronization is not necessary, a frequency-locked loop (FLL) can be used to track a frequency of interest, which, in the case of a magnetoelastic sensor, is its resonant frequency. Analog and digital FLLs find wide use in wireless communication systems for carrier synchronization and frequency synthesis [18–20]; FLLs have also been demonstrated for frequency measurement applications [21–22]. By ignoring the phase differences between the target signal and the generated response signal, an FLL typically allows a larger lock-in frequency range than a PLL [18]. This is a desired feature because the elastic stiffness (and correspondingly, resonant frequencies) of magnetoelastic materials are highly dependent on the magnitude of biasing magnetic field, with variations of up to 90% of the nominal values in some situations [12],[23–24].

In this paper, an FLL is investigated for application to wireless magnetoelastic strain sensors. These sensors utilize the ΔE effect (i.e. change in Young’s modulus with applied strain) to transduce strain into change in sensor resonant frequency [25]. Real-time tracking of strain, as enabled by the use of the FLL, is useful in applications that present fast changing loading conditions. For instance, strain measurements in a biomechanical implant can be used to monitor its operation under stresses resulting from bodily motion. Such strain sensors can be integrated with artificial joints or orthopedic implants. While most FLLs operate on steady signals, the FLL implemented here detects a frequency difference between a transient ring-down signal and a steady excitation signal. This preserves the isolation between the excitation signal and the sensor response.

Section II describes the theory and modeling of the FLL. The design and fabrication of the prototype strain sensors and the interrogation test system are described in Section III. The results and discussion are described in Sections IV and V, respectively.

II. Theory and Modeling

The system level diagram for the approach used in this section is shown in Fig. 1. An excitation pulse of predetermined duration and frequency builds up the vibration of the magnetoelastic sensor, following which the excitation is turned off. The sensor is then allowed to ring-down at its resonant frequency. The frequency detector compares the excitation frequency with the resonant ring-down frequency and presents the difference between the two. To perform this operation, the measured ring-down signal from the receive coils is multiplied with two sinusoids at the excitation frequency that are in a quadrature phase relation with one another. If V_sig is the resonant ring-down response of the magnetoelastic sensor at frequency ω_s (as detected at the receive coil), and V_ex is the excitation signal at frequency ω_e (from the oscillator output):

$$V_{\mathit{\text{sig}}}=V_s(t)\text{ sin}({\omega }_{s}t+\varphi )$$ (1)

$$V_{\mathit{\text{ex}}}=V_e\text{ sin}({\omega }_{e}t)$$ (2)

where ϕ is the phase difference between the response and excitation signals, V_s(t) is the amplitude of the exponential envelope of the ring down response, and Ve is the amplitude of the excitation signal. Then the mixer outputs, after low pass filtering, are:

$$X=0.5V_s(t)V_e\text{ cos }\{({\omega }_s-{\omega }_e)t\}$$ (3)

$$Y=0.5V_s(t)V_e\text{ sin }\{({\omega }_s-{\omega }_e)t\}$$ (4)

The phase difference, Δθ(t), between the excitation signal and the sensor resonant response is tan⁻¹(Y/X). The frequency separation, ω_s − ω_e, between the excitation and the ring-down frequency is the time derivative of the phase difference. If the phase difference is calculated at intervals of Δt, then frequency separation is given as:

$${\omega }_s-{\omega }_e=\mathrm{\Delta }\omega =\frac{\mathrm{\Delta }\theta }{\mathrm{\Delta }t}=\frac{\theta (t+\mathrm{\Delta }t)-\theta (t)}{\mathrm{\Delta }t}$$ (5)

An average of ω_s − ω_e is measured for the duration of the ring-down and is the output of the frequency detector.

An accumulator adds the error signal (i.e., ω_s − ω_e) multiplied by a predetermined constant, k, to the excitation frequency, thereby adjusting the frequency of the oscillator for the next excitation pulse. In this manner, with each iteration of the loop, the excitation frequency is brought closer to the sensor resonant frequency. The process is continuously repeated, minimizing the frequency separation between the excitation and the resonant frequency.

An amplifier is used to generate the currents needed to drive the transmit coil. In addition, switches are used to gate the transmit pulses to the driving amplifier (Switch 1) and the received signal from the sensor to the frequency detector (Switch 2).

The duration of excitation pulse required for maximum ring-down response depends on the damping of the sensor. An underdamped resonator, as are the sensors used in this work, that is subject to higher damping takes less time to reach its peak vibration amplitude. For instance, Fig. 2 shows the MATLAB-simulated transient response amplitude of a resonator subject to an excitation magnetic field at a frequency equal to its resonant frequency. The sensor resonant frequency is assumed to be 50 kHz with a resonance quality factor of 200. Hence, for this resonator, it is expected that an excitation pulse of a duration of 10 ms will ensure that the resonator attains peak vibration amplitudes before the excitation is terminated, allowing the ring-down signal to be initiated from the maximum amplitude.

Fig. 2.

The MATLAB-simulated amplitude of ring-up response for a 50 kHz resonator with a quality factor of 200.

The ring-down response provides the mechanical quality factor of the resonant mode of the sensor. Assuming that a simple spring-mass-damper model can be applied, the amplitude of the ring-down, V_s(t) (or 0.5 V_s(t) V_e after downconversion) is proportional to $e^{-\frac{{\omega }_s}{2Q}t}$. The amplitude after the downconversion step can be evaluated from X and Y, using (3) and (4), respectively, and is equal to $\sqrt{X^2+Y^2}$. The quality factor of the resonance is determined by an exponential curve-fit to this amplitude, once the FLL is locked into the resonant frequency.

Each ring-down of the resonator (corresponding to one loop iteration) provides a single data point, or “sample”, of the difference between the excitation and the ring-down resonant frequency. This difference is used to correct the excitation frequency for the next loop iteration. The sampling rate of the FLL is the loop iteration rate which is measured in samples per second. Assuming that a proportional controller is used, the corrected excitation frequency is the sum of the previous excitation frequency and the error signal multiplied by gain k. Hence, the excitation frequency at the n^th iteration of the loop, ω_e(n), can be described by the difference equation:

$${\omega }_e(n)={\omega }_e(n-1)+k[{\omega }_s(n-1)-{\omega }_e(n-1)]$$ (6)

where ω_s(n − 1) is the sensor resonant frequency as of the (n − 1)^th iteration.

The signal flow block diagram in the z domain is shown in Fig. 3. The system transfer function is basically given by:

$$S(z)=\frac{{\mathrm{\Omega }}_e(z)}{{\mathrm{\Omega }}_s(z)}=\frac{k{z}^{-1}}{1-z^{-1}+k{z}^{-1}}$$ (7)

where Ω_e(z) and Ω_s(z) are the z-transforms of ω_e(n) and ω_s(n), respectively. However, the excitation frequency generator takes a minimum duration of time to respond to the error signal and change its frequency. Hence, the system transfer function is given by:

$$R(z)=\frac{kH(z)z^{-1}}{1-z^{-1}+kH(z)z^{-1}}$$ (8)

where H(z) represents the response of the frequency generator. This equation provides the values of k that result in a stable feedback loop. For instance, if the frequency generator response can be represented as a single-pole transfer function:

$$H(z)=\frac{z^{-1}(1-a)}{(1-a{z}^{-1})}$$ (9)

where a is defined by the unit step response which is given to be 1 − aⁿ, |a| < 1, n ≥ 0, then the overall system response is represented by:

$$R(z)=\frac{k(1-a)z^{-2}}{1-(a+1)z^{-1}+[a+k(1-a)]z^{-2}}$$ (10)

The parameter a determines the transient response of the frequency generator: a smaller value of a indicates a faster response.

Fig. 3.

The z-domain model of the frequency-locked loop.

III. Design and Fabrication

A. Prototype strain sensors

The magnetoelastic resonant strain sensors are doubly-anchored suspended structures. The sensors can be divided into three parts – a resonant strip, anchors, and one or more springs connecting the resonant strip to the anchors. Applied strain causes a change in the stiffness of the resonant strip through the ΔE effect, resulting in a change in the sensor resonant frequency. The springs limit the strain in the resonant strip, effectively increasing the dynamic range of the sensor. The sensors are fabricated from Metglas 2826MB (Fe₄₀Ni₃₈Mo₄B₁₈), a magnetoelastic alloy (available from Metglas Inc., Conway, SC). The detailed operation of these types of strain sensors was described in [25].

The four sensor designs used to assess the FLL-based ring-down method are shown in Fig. 4. The Type 1 and Type 2 sensors both measure 32 × 14 mm², and are 28 µm thick. Also, both sensors are designed for a dynamic range of 2 mstrain. The Type 1 sensor has the strain-limiting spring attached to one anchor. Narrow attachments to the second anchor limit the energy losses to the anchor by inducing an acoustic mismatch [26]. The Type 2 sensor has springs attached to both anchors, providing symmetric mode shapes and acoustic mismatches at both ends of the resonant strip. The Type 3 and Type 4 sensors both measure 21 × 8 mm², and are 28 µm thick. The Type 3 sensor is designed for a dynamic range of 2 mstrain, whereas the Type 4 sensor is designed for a dynamic range of 4 mstrain. The Type 3 sensor has the strain limiting spring attached to one anchor, whereas the Type 4 sensor has springs attached to both anchors; this difference results in the larger dynamic range for the Type 4 sensor.

Fig. 4.

Dimensions of the four prototype sensor designs (in mm).

Both transverse and longitudinal modes exist for the strain sensors, but the first longitudinal modes provides the strongest signal response. This is because these modes provide the largest unidirectional strain (i.e., tensile or compressive at a given instant of time) resulting in strongest magnetic field response. The strain sensors reported in this work are, hence, measured at the first longitudinal modes of each sensor.

The unstrained resonant frequencies are estimated using a coupled magnetic field-solid mechanics model in COMSOL Multiphysics (COMSOL AB, Stockholm, Sweden). The COMSOL-simulated resonant frequency for the Type 1 sensor is 122.8 kHz, while that for the Type 2 sensor is 118.2 kHz. Similarly, the simulated unstrained resonant frequencies for the Type 3 and Type 4 strain sensors are 218.7 kHz and 217.7 kHz, respectively. The corresponding resonant mode shapes, as simulated in COMSOL, are shown in Fig. 5.

Fig. 5.

COMSOL-simulated resonant frequencies and mode shapes for (a) Type 1, (b) Type 2, (c) Type 3, and (d) Type 4 strain sensors.

A biasing magnetic field is necessary for sensor operation in a region of maximum small-signal magnetostrictivity. Based on preliminary experiments, a biasing magnetic field of 2–5 G was determined to be sufficient. This magnetic biasing field for sensor operation was generated by Arnokrome 3 permanent magnets (Arnold Magnetic Technologies Corp., Rochester, NY). The appropriate sizing and spacing between the permanent magnets and the strain sensor for desired operation was estimated through magnetic field simulations in COMSOL Multiphysics. Based on these simulation studies, a 100-µm-thick magnet measuring 21 × 4 mm², was placed at a distance of 1–2 mm from the Type 1 and Type 2 sensors. Similarly, for the Type 3 and Type 4 designs, the biasing magnet measured 12 × 4 mm², and 100 µm thick.

The sensors were fabricated using photochemical machining (PCM) from 28-µm-thick foils of Metglas 2826MB at an external facility (Kemac Technology, Inc., Azusa, CA). The fabricated sensors are shown in Fig. 6. The permanent magnets were fabricated using microelectrodischarge machining (µEDM) from 100 µm thick foils of Arnokrome 3.

Fig. 6.

Strain sensors fabricated using PCM.

B. Test setup

The test setup consisted of a polypropylene cantilever, on the surface of which the strain sensors are affixed. A prescribed displacement of the cantilever tip resulted in a well-determined magnitude of strain on the cantilever surface. This strain-displacement relationship was confirmed using a commercial strain gage (SGD-5/350-LY13, Omega Engineering, Inc., Stamford, CT). The sensors were suspended between two supports – 600-µm-thick silicon blocks that were attached to the cantilever. The Arnokrome 3 permanent magnets were affixed underneath the cantilever. Cyanoacrylate adhesive was used for all attachments.

The transmit coil that generated the excitation magnetic field was 30 mm in diameter, 10 mm in length, and had 10 turns. The receive coil that detected the sensor response was wound coaxial to the transmit coil, was 10 mm in length, and had 10 turns. The strain sensor was located along the axis of the coils during testing, and the complete test setup is shown in Fig. 7(a).

Fig. 7.

(a) Test setup for sensor interrogation. The biasing magnet is affixed underneath the cantilever and is not visible in this image. (b) FLL implemented using NI USB-6341 device. (c) FLL implemented using NI PXI-6115 and NI PXI-5412.

C. FLL system implementation

The FLL was software-defined, and was implemented in a custom program written in National Instruments LabVIEW™ software. The custom program implements the frequency detector, accumulator, and the oscillator. One implementation of signal generation and acquisition was devised using a NI USB-6341 device (National Instruments Inc., Austin, TX) as shown in Fig. 7(b). The USB-6341 generated the sinusoidal excitation signal which was then amplified (amplifier Model 7500, Krohn-Hite Corp., Brockton, MA). An analog switch (TS5A22364, Texas Instruments Inc., Dallas, TX) gated the excitation signal to the transmit coil and the received ring-down sensor response from the receive coil. The switch was controlled by signals that were also generated by the USB-6341 device. Hardware limitations limited the maximum detectable frequency to approximately 200 kHz. Strain sensor Types 1 and 2 were tested using this approach.

A simpler implementation was also explored using an NI PXIe system with an integrated PXI-6115 data acquisition module and a PXI-5412 arbitrary waveform generator, as shown in Fig. 7(c). The FLL program was modified to generate a pulsed sinusoidal wave for excitation (from the arbitrary waveform generator), and also to isolate the sensor ring-down. No external switches were required. Strain sensor Types 3 and 4 were tested using this approach.

IV. Experimental Results

In the experiments, the excitation magnetic field was applied for a duration of 10 ms, following which the sensor ring-down was measured. As predicted in the approach illustrated in Fig. 2, a stimulus of this duration is sufficient for a resonator with a quality factor of around 200 and a resonant frequency of 50 kHz or higher. An exemplary ring-down response of the Type 1 strain sensor, as detected by the receive coils, is shown in Fig. 8. The ring-down is apparent for a duration of approximately 4 ms. Similar responses were observed, albeit at different frequencies, for Type 2, 3, and 4 sensors.

Fig. 8.

Ring-down response for the unstrained Type 1 strain sensor, measured as the voltage at the receive coil.

Typical strain dependencies of resonant frequencies for the four sensor types are shown in Fig. 9. A typical Type 1 sensor had an unstrained resonant frequency of 126.1 kHz. Under applied tensile strain of 1.5 mstrain, the resonant frequency increased to 128.3 kHz; this corresponds to a sensitivity of 11600 ppm/mstrain. A typical Type 2 sensor had an unstrained resonant frequency of 123.2 kHz. Under applied tensile strain of 2.1 mstrain, the resonant frequency increased to 126.9 kHz, corresponding to a sensitivity of 14300 ppm/mstrain. A typical Type 3 strain sensor had an unstrained resonant frequency of 227 kHz. Under an applied strain of 2.1 mstrain, the resonant frequency increased to 230.8 kHz, corresponding to a sensitivity of 8000 ppm/mstrain. Finally, a typical Type 4 strain sensor had an unstrained resonant frequency of 238.7 kHz. Under an applied strain of 3.5 mstrain, the resonant frequency increased to 242.7 kHz, corresponding to a sensitivity of 4800 ppm/mstrain.

Fig. 9.

Resonant frequency as a function of applied tensile strain for the different strain sensor types. (a) Type 1, (b) Type 2, (c) Type 1, and (d) Type 4.

The quality factors of the resonant responses of the four sensors can be estimated by curve-fitting to the ring-down response amplitude, as shown in Fig. 10. The fitting was performed on measurements taken in the absence of strain assuming an exponential decay of the form

$$V_s(t)=V_s(0)e^{-\frac{{\omega }_S}{2Q}t}.$$

The quality factor for a typical Type 1 sensor was 380. The other types had lower quality factors: 300, 250, and 280 for Type 2, 3, and 4, respectively. These results confirm that the 10 ms stimulus provided was sufficient to achieve steady state oscillation prior to initiation of the ring-down. Based on a calculation similar to that illustrated in Fig. 2, for the resonant frequencies presented in these experimental measurements, full excitation is achieved in only 4 ms despite the relatively high quality factors.

Fig. 10.

Quality factor estimation by curve-fit for the different strain sensor types. (a) Type 1, (b) Type 2, (c) Type 3, and (d) Type 4. The measurements are under no-strain conditions.

The step response of the measurement system was also measured (Fig. 11). An electromechanical solenoid actuator (SMT1632S, Jameco Electronics, Belmont, CA) was used to apply a rapid step displacement to the cantilever tip. The response time of the actuator is approximately 10 ms. An applied step of 0.8 mstrain resulted in a frequency shift of 1.25 kHz for the Type 1 sensor, and 1.5 kHz for the Type 2 sensor. Similarly, a 1.1 mstrain step resulted in a frequency shift of 2 kHz for the Type 3 sensor, whereas a 1.6 mstrain step resulted in a frequency shift of 2.1 kHz for the Type 4 sensor. These responses are consistent with those shown in Fig. 9 for quasi-static strains.

Fig. 11.

Response of the FLL to an applied step for the different strain sensor types. (a) Type 1, (b) Type 2, (c) Type 3, and (d) Type 4.

V. Discussion

A source of potential error in the FLL response is the emergence of additional resonant modes associated with the non-ideal out-of-plane deformation of the sensor under applied strain. The sensors were fabricated from Metglas 2826MB foil that is available in the form of rolls. As a result, the fabricated sensors have minor initial out-of-plane curvature. Under applied strain, this can cause out-of-plane deformation. Figure 12 shows the COMSOL-simulated out-of-plane deformation for an applied tensile strain of 2 mstrain. For this simulation, the structure was assumed to have an initial curvature that displaced the sensor mid-point by 100 µm out-of-plane with respect to the anchors. Such strain-induced deformations generate spurious modes that are spaced close to the frequency of the target sensor resonant modes. In such cases, the ring-down response is not an ideal exponentially decaying sinusoid. The resultant error term (ω_s − ω_e) has significant variation from iteration to iteration, manifesting as noise in the frequency lock. In addition, this can also limit the sensor dynamic range if increasing strain-induced deformation results in the amplitude of the spurious modes becoming comparable to the target resonant modes. In such a case, the FLL can lose its lock of the target mode, and instead lock onto the spurious mode.

Fig. 12.

Simulated out-of-plane deformation of the Type 1 sensor under an applied tensile strain of 2 mstrain. Anchors are not included to reduce simulation complexity.

Numerical simulations (performed in COMSOL™) can be used to compare the ring-down response of the sensors that are in non-deformed and deformed states. Figure 13 shows both the simulated ring-down response for the non-deformed Type 1 sensor under no applied strain as well as the ring-down response for the deformed sensor (as shown in Fig. 12). Arbitrary units for the displacement are used because the amplitude is highly dependent on the initial conditions as well as the experimental settings. The experimental ring-down receive coil voltage readings, shown in Fig. 14 for a strained Type 1 sensor, showed responses similar to the simulated response of the deformed sensor. Such measurements stand in contrast to an idealized ring-down response shown in Fig. 8. In future efforts, optimization of the anchor shape can reduce the sensor out-of-plane sensor deformation, reducing the non-ideality of the ring-down.

Fig. 13.

COMSOL-simulated ring-down displacement amplitudes (in arbitrary units) of a point at the end of the resonant strip of a Type 1 sensor in (a) non-deformed state, and (b) deformed state as characterized by Fig. 12.

Fig. 14.

Ring-down response for the Type 1 strain sensor, under applied tensile strain of 0.8 mstrain, measured as the voltage at the receive coil.

Additional future work may include the use of a custom application specific integrated circuit (ASIC) for improved overall system performance. The use of customized hardware to perform the functions performed in software in the current implementation can help by improving the processing time leading to overall improvement in the system response time as well as the measurement bandwidth.

VI. Conclusion

This work presents the design and implementation of an FLL-based readout approach for resonant magnetoelastic sensors. In addition to measurement of resonant frequencies and quality factors, the technique also allows real-time tracking of resonant frequencies. The entire system is implemented using data acquisition hardware running customized software. The system is applied for the measurement of wireless strain sensor responses, the performances of which are characterized in both frequency and time domains. Four strain sensor designs were used to investigate the capabilities of the FLL approach. The FLL was capable of tracking frequency changes of at least 3%, with resolution of better than 0.1%. The response time of the FLL to a step input was less than 0.5 s, which can enable near real-time tracking of strain for orthopedic or structural monitoring applications.