EP4731980A1

EP4731980A1 - Crack sensors and related systems and methods

Info

Publication number: EP4731980A1
Application number: EP24743133.1A
Authority: EP
Inventors: Brian L. Wardle; Luiz H. ACAUAN; Aniruddha Ghosh; Yosef Stein; Haim Primo
Original assignee: Analog Devices Inc; Massachusetts Institute of Technology
Current assignee: Analog Devices Inc; Massachusetts Institute of Technology
Priority date: 2023-06-21
Filing date: 2024-06-21
Publication date: 2026-04-29
Also published as: CN121794556A; WO2024263902A1

Abstract

The present disclosure is related to crack sensors, such as wireless crack sensors, and related systems and methods.

Description

CRACK SENSORS AND RELATED SYSTEMS AND METHODS

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application No. 63/509,513, filed June 21, 2023, and entitled “Crack Sensors and Related Systems and Methods,” which is incorporated herein by reference in its entirety for all purposes.

TECHNICAL FIELD

Crack sensors, such as wireless crack sensors, and related systems and methods are generally described.

SUMMARY

The present disclosure is related to crack sensors, such as wireless crack sensors, and related systems and methods. The subject matter of the present disclosure involves, in some cases, interrelated products, alternative solutions to a particular problem, and/or a plurality of different uses of one or more systems and/or articles.

According to certain embodiments, a sensor system is described. In some embodiments, the sensor system comprises a circuit comprising a first RLC circuit pathway and a second RLC circuit pathway, wherein the circuit is configured such that, when a crack propagates through the first RLC circuit pathway, the second RLC circuit pathway still produces a return signal.

In some embodiments, a sensor system comprises a single RLC circuit comprising a capacitor, an inductor, a first RLC circuit pathway comprising a first portion of the inductor, and a second RLC circuit pathway comprising a second portion of the inductor, wherein the first portion of the inductor and the second portion of the inductor are not identical but at least partially overlap with each other.

According to some embodiments, a method for operating a sensor system is described. In certain embodiments, the method comprises measuring, with the sensor system, an attribute of a signal of a circuit disposed in the sensor system, wherein the circuit comprises a first RLC circuit pathway and a second RLC circuit pathway, wherein the circuit is configured such that, when a crack propagates through the first RLC circuit pathway, the second RLC circuit pathway still produces a return signal. In some embodiments, the method comprises determining, with a processor, whether the crack has propagated through the first RLC circuit pathway based at least in part on a change in the attribute of the signal of the circuit.

In certain embodiments, a method for operating a sensor system comprises measuring, with the sensor system, an attribute of a signal of a single circuit disposed in the sensor system, wherein the single circuit comprises a capacitor, an inductor, a first RLC circuit pathway comprising a first portion of the inductor, and a second RLC circuit pathway comprising a second portion of the inductor, wherein the first portion of the inductor and the second portion of the inductor are not identical but at least partially overlap with each other. In some embodiments, the method comprises determining, with a processor, whether the crack has propagated through the first RLC circuit pathway based at least in part on a change in the attribute of the signal of the circuit.

Other advantages and novel features of the present disclosure will become apparent from the following detailed description of various non-limiting embodiments of the disclosure when considered in conjunction with the accompanying figures. In cases where the present specification and a document incorporated by reference include conflicting and/or inconsistent disclosure, the present specification shall control.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting embodiments of the present disclosure will be described by way of example with reference to the accompanying figures, which are schematic and are not intended to be drawn to scale unless otherwise indicated. In the figures, each identical or nearly identical component illustrated is typically represented by a single numeral. For purposes of clarity, not every component is labeled in every figure, nor is every component of each embodiment of the disclosure shown where illustration is not necessary to allow those of ordinary skill in the art to understand the disclosure.

FIG. 1A is a top-view schematic illustration of a circuit comprising a first RLC circuit pathway and a second RLC circuit pathway comprising a resistor, in accordance with certain embodiments.

FIG. IB is a top-view schematic illustration of the circuit of FIG. 1A, wherein the first RLC circuit pathway is represented as a dotted line. FIG. 1C is a top-view schematic illustration of the circuit of FIG. 1A, wherein the second RLC circuit pathway is represented as a dotted line.

FIG. 2A is a top-view schematic illustration of a circuit comprising a first RLC circuit pathway and a second RLC circuit pathway comprising an inductor, in accordance with certain embodiments.

FIG. 2B is a top-view schematic illustration of the circuit of FIG. 2A, wherein the first RLC circuit pathway is represented as a dotted line.

FIG. 2C is a top-view schematic illustration of the circuit of FIG. 2A, wherein the second RLC circuit pathway is represented as a dotted line.

FIG. 3 is a diagram of a RLC circuit pathway, in accordance with certain embodiments.

FIG. 4A is a schematic illustration of the fabrication of an inductor in which electronically conductive nanostructures are used to form the electronically conductive pathway of the inductor, in accordance with certain embodiments.

FIG. 4B is a schematic illustration of the fabrication of an interdigitated capacitor in which electronically conductive nanostructures are used to form the electrodes of the interdigitated capacitor, in accordance with certain embodiments.

FIGS. 5A-5D are a series of cross-sectional schematic illustrations showing the fabrication of a parallel-plate capacitor in which electronically conductive nanostructures are used to form the electrodes of the parallel-plate capacitor, in accordance with certain embodiments.

FIG. 6A is a top-view schematic illustration of the circuit of FIG. 1 A, wherein a crack has propagated through the first RLC circuit pathway.

FIG. 6B is a top-view schematic illustration of a circuit , wherein a crack has propagated through the first RLC circuit pathway from an interior of the circuit, in accordance with certain embodiments.

FIG. 6C is a top-view schematic illustration of a circuit configured to determine a location of a crack propagating through the first RLC circuit pathway, in accordance with certain embodiments.

FIG. 6D is a top-view schematic illustration of a circuit comprising compensating resistors electronically coupled to and external to an inductor, in accordance with certain embodiments. FIG. 7A is a top-view schematic illustration of the circuit of FIG. 2A, wherein a crack has propagated through the first RLC circuit pathway.

FIG. 7B is a top-view schematic illustration of a circuit, wherein a crack has propagated through the first RLC circuit pathway from an interior of the circuit, in accordance with certain embodiments.

FIG. 7C is a top-view schematic illustration of a circuit configured to determine a location of a crack propagating through the first RLC circuit pathway, in accordance with certain embodiments.

FIG. 7D is a top-view schematic illustration of a circuit comprising compensating inductors electronically coupled to and external to an inductor, in accordance with certain embodiments.

FIG. 8 is a top-view schematic illustration of a circuit comprising a first RLC circuit pathway, a second RLC circuit pathway comprising a resistor, and a third RLC circuit pathway comprising a resistor, wherein the third RLC circuit pathway is represented as a dotted line, in accordance with certain embodiments.

FIG. 9 is a top-view schematic illustration of a circuit comprising a first RLC circuit pathway, a second RLC circuit pathway comprising an inductor, and a third RLC circuit pathway comprising an inductor, wherein the third RLC circuit pathway is represented as a dotted line, in accordance with certain embodiments.

FIG. 10 is a top-view schematic illustration of the circuit of FIG. 8, wherein a crack has propagated through the second RLC circuit pathway.

FIG. 11 is a top-view schematic illustration of the circuit of FIG. 9, wherein a crack has propagated through the second RLC circuit pathway.

FIG. 12 is a top-view schematic illustration of a circuit comprising a first RLC circuit pathway, a second RLC circuit pathway comprising a resistor, a third RLC circuit pathway comprising a resistor, and a fourth RLC circuit pathway comprising a resistor, wherein the fourth RLC circuit pathway is represented as a dotted line, in accordance with certain embodiments.

FIG. 13 is a top-view schematic illustration of a circuit comprising a first RLC circuit pathway, a second RLC circuit pathway comprising an inductor, a third RLC circuit pathway comprising an inductor, and a fourth RLC circuit pathway comprising an inductor, wherein the fourth RLC circuit pathway is represented as a dotted line, in accordance with certain embodiments.

FIG. 14 is a top-view schematic illustration of the circuit of FIG. 12, wherein a crack has propagated through the third RLC circuit pathway.

FIG. 15 is a top-view schematic illustration of the circuit of FIG. 13, wherein a crack has propagated through the third RLC circuit pathway.

FIG. 16 is a block diagram showing an exemplary sensor system, in accordance with certain embodiments.

FIGS. 17A-17C are a schematic illustration depicting the concept of a change in an attribute of a signal of a circuit as a function of crack length, in accordance with certain embodiments.

FIG. 18 is a schematic illustration showing the measurement of a resonant frequency of a sensor, in accordance with some embodiments.

FIG. 19A is a top-view schematic illustration of a circuit comprising a first RLC circuit pathway and a second RLC circuit pathway, wherein the first RLC circuit pathway comprises a first capacitor and inductor, and the second RLC circuit pathway comprises a second capacitor and the inductor.

FIG. 19B is a top-view schematic illustration of the circuit of FIG. 19 A, wherein the first RLC circuit pathway is represented as a dotted line.

FIG. 19C is a top-view schematic illustration of the circuit of FIG. 19 A, wherein the second RLC circuit pathway is represented as a dotted line.

FIG. 19D is a top-view schematic illustration of the circuit of FIG. 19 A, wherein a crack has propagated through the first RLC circuit pathway.

FIG. 20A is a top-view schematic illustration of a circuit comprising a first inductor electronically coupled to a capacitor and a second inductor electronically coupled to the capacitor, wherein a first portion of the circuit comprises a first RLC circuit pathway and a second RLC circuit pathway comprising a resistor, and a second portion of the circuit comprises a first RLC circuit pathway and a second RLC circuit pathway comprising a resistor, in accordance with certain embodiments.

FIG. 20B is a top-view schematic illustration of a circuit comprising a first inductor electronically coupled to a capacitor and a second inductor electronically coupled to the capacitor, wherein a first portion of the circuit comprises a first RLC circuit pathway and a second RLC circuit pathway comprising an inductor, and a second portion of the circuit comprises a first RLC circuit pathway and a second RLC circuit pathway comprising an inductor, in accordance with certain embodiments.

FIG. 21A shows, according to some embodiments, a sensor electrical equivalent diagram of a resistance-based compensating circuit.

FIG. 21B shows, according to some embodiments, the resonance frequency of the circuit of FIG. 21A with no crack propagation.

FIG. 21C shows, according to some embodiments, the resonance frequency of the circuit of FIG. 21A with crack propagation through a first turn of an inductor of the circuit.

FIG. 21D shows, according to some embodiments, the resonance frequency of the circuit of FIG. 21A with crack propagation through the first four turns of an inductor of the circuit.

FIG. 21E shows, according to some embodiments, the resonance frequency of the circuit of FIG. 21A with no crack propagation, wherein the resonance frequency is used to calculate a 10% quality factor.

FIG. 21F shows, according to some embodiments, the resonance frequency of the circuit of FIG. 21A with crack propagation through the first two turns of an inductor of the circuit, wherein the resonance frequency is used to calculate a 10% quality factor.

FIG. 21G shows, according to some embodiments, the resonance frequency of the circuit of FIG. 21A with crack propagation through the first four turns of an inductor of the circuit, wherein the resonance frequency is used to calculate a 10% quality factor.

FIG. 22A shows, according to some embodiments, RLC circuit sensor decay as a function of quality factor for a 0.5 ohm compensating resistor.

FIG. 22B shows, according to some embodiments, RLC circuit sensor decay as a function of quality factor for a 1 ohm compensating resistor.

FIG. 22C shows, according to some embodiments, RLC circuit sensor decay as a function of quality factor for a 5 ohm compensating resistor.

FIG. 23A shows, according to some embodiments, a sensor electrical equivalent diagram of an inductance-based compensating circuit.

FIG. 23B shows, according to some embodiments, the resonance frequency of the circuit of FIG. 23A with no crack propagation. FIG. 23C shows, according to some embodiments, the resonance frequency of the circuit of FIG. 23A with crack propagation through a first turn of an inductor of the circuit.

FIG. 23D shows, according to some embodiments, the resonance frequency of the circuit of FIG. 23A with crack propagation through the first four turns of an inductor of the circuit.

FIG. 24A shows, according to some embodiments, the transfer function of crack propagation through the broken turns of an inductor to crack length.

FIG. 24B shows, according to some embodiments, the transfer function of sensor echo frequency to crack length.

FIG. 25A shows, according to some embodiments, the resonance frequency of a circuit with no cracks.

FIG. 25B shows, according to some embodiments, the resonance frequency of a circuit with a crack through the first turn of an inductor.

FIG. 26A shows a top-view schematic illustration of a circuit configured to determine a location of one or more cracks propagating from an exterior of the circuit to an interior of the circuit, in accordance with certain embodiments.

FIG. 26B shows a top-view schematic diagram of a circuit configured to determine a location of one or more cracks propagating from an interior of the circuit to an exterior of the circuit, in accordance with certain embodiments.

DETAILED DESCRIPTION

Crack sensors (e.g., wireless crack sensors), and related systems and methods, are generally described. In accordance with certain embodiments, the sensors comprise a single circuit comprising a first RLC circuit pathway and a second RLC circuit pathway. The first RLC circuit pathway can comprise an inductor and a capacitor electronically coupled to the inductor, and the second circuit pathway can comprise an inductor and a capacitor electronically coupled to the inductor. According to some embodiments, the second RLC circuit pathway may comprise a resistor and/or an inductor electronically coupled to the inductor of the first RLC circuit pathway.

The sensors may be configured such that, when a structural defect (e.g., a crack, a hole, etc.) propagates through the first RLC circuit pathway, the second RLC circuit pathway still produces a return signal. In some embodiments, for example, the structural defect may propagate through a portion of the inductor in the first RLC circuit pathway, therefore rendering the first RLC circuit pathway non-functional. The second RLC circuit pathway remains functional, in certain embodiments, even though the structural defect has propagated through the first RLC circuit pathway, such that the second RLC circuit pathway still produces a return signal. Advantageously, the configuration of first RLC circuit pathway and the circuit RLC circuit pathway ensure that the second RLC still produces a return signal when a crack propagates through the first RLC circuit pathway, in accordance with certain embodiments. Configuring the sensor in this manner allows the sensor to determine whether the structural defect has propagated through a portion of the sensor while maintaining sensor functionality.

In some embodiments, the structural defect may propagate from an exterior of the circuit towards an interior of the circuit. In other embodiments, the structural defect may propagate from an interior of the circuit towards an exterior of the circuit. The sensor system may advantageously be configured to determine a location of the structural defect in the circuit, in certain embodiments, based at least in part on the return signal of the second RLC circuit pathway.

In certain embodiments, the sensors may be disposed in a sensor system that is configured to measure an attribute of a signal (e.g., an oscillating signal) of the single circuit. The sensor system may, in some embodiments, comprise a processor configured to determine whether the structural defect has propagated through the first RLC circuit pathway based at least in part on a change in the attribute of the signal of the single circuit. Suitable signals of the single circuit that may be analyzed by the processor include, for example, a resonance frequency of the single circuit and/or a quality factor of the single circuit.

In accordance with certain embodiments, the sensors may comprise additional RLC circuit pathways (e.g., a third RLC circuit pathway, a fourth RLC circuit pathway, etc.). In some such embodiments, the sensors may be configured such that, when a structural defect propagates through additional RLC circuit pathways (e.g., the second, third, fourth, and/or additional circuit pathway), a subsequent RLC circuit pathway remains functional, i.e., still produces a return signal. In some embodiments, the electrically conductive sensor elements (e.g., the electronic pathway of the inductor, the electrodes of the capacitor, etc.) comprise nanocomposites (e.g., formed by arranging electronically conductive elongated nanostructures within a conductive or non-conductive matrix material).

Certain of the single circuit arrangements described herein can be used as wireless sensors. For example, the single circuits can be used, in some embodiments, as RLC resonators. In some embodiments, one can wirelessly interrogate a RLC resonator to determine whether the attribute of the signal of the single circuit has changed, an indication that a crack, hole, or other structural defect has propagated through a portion of the single circuit. As mentioned above, for example, in some embodiments, when a structural defect propagates through a RLC circuit pathway, a subsequent RLC circuit pathway remains functional and still produces a return signal. In some embodiments, the return signal of the subsequent RLC circuit pathway is used, at least in part, to determine and/or verify that the RLC circuit pathway has been compromised by propagation of the structural defect. The ability for the single circuit to continue providing a return signal after part of the single circuit has been compromised can greatly simplify the process of determining whether a defect is present because a verifiable signal is still provided after the defect has presented itself. In contrast, in systems in which no signal is present after the defect presents itself, the user could mistakenly believe that the system has malfunctioned for a reason other than the presence of the structural defect in the single circuit. Advantageously, in some embodiments, the sensor system can detect the structural defect while avoiding issues associated with the single circuit malfunctioning due to the structural defect.

In some embodiments, the single circuit can be an oscillator. The single circuit can be wirelessly interrogated, in some embodiments, and a return signal can be generated by the single circuit that is detected and analyzed by a processor to determine whether a structural defect (e.g., a crack, a hole, etc.) has propagated through a portion of the single circuit.

In some embodiments, the single circuit may be positioned on an article of which one wishes to monitor structural health. Examples of suitable articles include, but are not limited to, a component of a land system and/or vehicle, a water system and/or vehicle, an air system and/or vehicle, and/or a space system and/or vehicle. In some embodiments, the article is part of an airplane, a boat, a motor vehicle (e.g., motorcycle, car, truck, bus), a space vehicle (e.g., a rocket), a component of a building (e.g., a beam, a steel component, a concrete component, and the like), and the like.

The sensor systems can, in some embodiments, provide structural reinforcement between two layers of a composite. In this way, in accordance with certain embodiments, the sensor systems can perform better than certain other non-invasive sensor solutions because the sensors add mechanical reinforcement. In some embodiments, one or more components of the circuit (e.g., one or more components of the first RLC circuit pathway and/or one or more components of the second RLC circuit pathway) can comprise elongated nanostructures that can be used to reinforce an interface between the circuit component and a region of a solid body (e.g., one or more layers of a solid body on or within which the circuit is positioned). In certain embodiments, one or more components of the circuit (e.g., one or more components of the first RLC circuit pathway and/or one or more components of the second RLC circuit pathway) can comprise elongated nanostructures that can be used to reinforce an interface between two solid bodies that are positioned on opposite sides of the circuit component. In some embodiments, the nanostructures can be used to mechanically reinforce one or more interfaces between a circuit element and an adjacent layer of a multi-layer laminate. Mechanically reinforcing the interface between, for example, the capacitor electrodes(s) and the adjacent layer(s) and/or between the inductor and the adjacent layer(s) can provide advantageous structural reinforcement to the article with which the circuit system has been incorporated. In some embodiments, a component of the circuit penetrates into an adjacent layer to provide mechanical reinforcement. For example, in some embodiments, one or more electrodes of the capacitor of the circuit comprises patterned elongated nanostructures that serve an electronic function of the capacitor and that penetrate into an adjacent layer to mechanically reinforce an interface between the electrode(s) of the capacitor and the adjacent layer (or two adjacent layers each on opposite sides of the circuit). In certain embodiments, one or more portions of the inductor of the circuit comprises patterned elongated nanostructures that serve an electronic function of the inductor and that penetrate into an adjacent layer to mechanically reinforce an interface between the inductor and the adjacent layer (or two adjacent layers each on opposite sides of the circuit). Non-limiting examples of the use of electronically conductive nanostructures embedded in matrices to form circuit components and provide structural reinforcement are described, for example, in International Patent Application Publication No. WO 2019/118706, published on June 20, 2019, filed on December 13, 2018, as International Application No.

PCT/US2018/065422, and entitled “Structural Electronics Wireless Sensor Nodes” and in U.S. Patent Application No. 16/900,159, filed on June 12, 2020, published as U.S. Patent Publication No. 2020/0309674 on October 1, 2020, and entitled “Structural Electronics Wireless Sensor Nodes,” each of which is incorporated herein by reference in its entirety for all purposes. It should be understood that, while nanostructures within the circuit can be used to provide mechanical reinforcement within a composite article in accordance with certain embodiments, not all embodiments are so limited, and in other cases, the circuit elements do not provide mechanical reinforcement.

In certain embodiments, the circuit comprises a first RLC circuit pathway. FIG. 1A is a top-view schematic illustration of circuit 100a comprising a first RLC circuit pathway, in accordance with certain embodiments. As shown in FIG. 1A, the first RLC circuit pathway comprises inductor 106 and capacitor 108 electronically coupled to inductor 106 via electronically conductive pathway 114. Electronically conductive pathway 114 may, in some embodiments, comprise metal, carbon, or any other suitable electronically conductive material.

Inductor 106 can assume any of a variety of suitable configurations. In the embodiment illustrated in FIG. 1A, inductor 106 comprises an electronically conductive pathway arranged in a spiral shape. Other inductor shapes and/or configurations are also possible.

As described in further detail below, in some embodiments, the inductor can comprise electronically conductive nanostructures (e.g., electronically conductive elongated nanostructures, such as carbon nanotubes) embedded within a conductive or non-conductive (e.g., electrically insulating) matrix. In certain embodiments, the electronically conductive nanostructures serve an electronic function of the inductor.

The inductor may have any of a variety of suitable dimensions. Referring to FIG. 1A, for example, inductor 106 has first dimension 120 and second dimension 122, wherein second dimension 122 is perpendicular to first dimension 120. The first dimension of the inductor may be any of a variety of suitable values. In certain embodiments, for example, the first dimension of the inductor is greater than or equal to 10 micrometers, greater than or equal to 100 micrometers, greater than or equal to 1 millimeter, greater than or equal to 1 centimeter, or greater than or equal to 10 centimeters. In some embodiments, the first dimension of the inductor is less than or equal to 1 meter, less than or equal to 10 centimeters, less than or equal to 1 centimeter, less than or equal to 1 millimeter, or less than or equal to 100 micrometers. Combinations of the above recited ranges are possible (e.g., the first dimension of the inductor is greater than or equal to 10 micrometers and less than or equal to 1 meter, the first dimension of the inductor is greater than or equal to 1 millimeter and less than or equal to 1 centimeter). Other ranges are also possible.

The second dimension of the inductor (e.g., perpendicular to the first dimension of the inductor) may be any of a variety of suitable values. According to some embodiments, for example, the second dimension of the inductor is greater than or equal to 10 micrometers, greater than or equal to 100 micrometers, greater than or equal to 1 millimeter, greater than or equal to 1 centimeter, or greater than or equal to 10 centimeters. In certain embodiments, the second dimension of the inductor is less than or equal to 1 meter, less than or equal to 10 centimeters, less than or equal to 1 centimeter, less than or equal to 1 millimeter, or less than or equal to 100 micrometers. Combinations of the above recited ranges are possible (e.g., the second dimension of the inductor is greater than or equal to 10 micrometers and less than or equal to 1 meter, the second dimension of the inductor is greater than or equal to 1 millimeter and less than or equal to 1 centimeter). Other ranges are also possible.

Capacitor 108 can assume any of a variety of suitable configurations. In the embodiment illustrated in FIG. 1A, capacitor 108 is an interdigitated capacitor comprising first electrode 116 and second electrode 118. Other shapes and/or configurations for the capacitor are also possible. In some embodiments, for example, the capacitor may be a parallel-plate capacitor (e.g., a circular- shaped parallel-plate capacitor, a square-shaped parallel-plate capacitor, etc.). In certain embodiments, the parallel-plate capacitor comprises a first electrode, a second electrode, and a conductive or non-conductive material between the first electrode and the second electrode. Examples of conductive materials for use within the parallel-plate capacitor include, but are not limited to, conductive polymers, metals, or combinations thereof. Examples of non-conductive materials for use within the parallel-plate capacitor include, but are not limited to, polymers (e.g., epoxy resin (e.g., EPON resin), paramethylstyrene (PMS), para-methoxyamphetamine (PMA), polyimide (e.g., Kapton®), polyether ether ketone (PEEK), polyether ketone ketone (PEKK), bis-maleimide (BMI), cyanate ester, and the like), metal and/or metalloid oxides, glasses, ceramics, or any combinations of two or more of these materials.

As described in further detail below, in certain embodiments, the capacitor can comprise electronically conductive nanostructures (e.g., electronically conductive elongated nanostructures, such as carbon nanotubes) embedded within a conductive or non-conductive (e.g., electrically insulating) matrix. In some embodiments, the electronically conductive nanostructures serve an electronic function of the capacitor.

In the embodiment shown in FIG. 1A, inductor 106 is electronically coupled to capacitor 108. In particular, electronically conductive pathway 114 electronically couples first end 124 of inductor 104 to first electrode 116 of capacitor 108, and second end 126 of inductor 106 is electronically coupled (e.g., directly electronically coupled) to second electrode 118 of capacitor 108. The second end of the inductor may, in certain embodiments, be electronically coupled to the second electrode of the capacitor via an electronically conductive pathway (e.g., an electronically conductive pathway 114), such that there is no direct electronic connection between the second end of the inductor and the second electrode of the capacitor.

According to some embodiments, when inductor 106 is electronically coupled to capacitor 108, then inductor 106 and capacitor 108 can form a RLC circuit pathway (e.g., a first RLC circuit pathway), such as the RLC circuit pathway illustrated in FIG. 3. In some embodiments, a dedicated resistor can be incorporated into the RLC circuit pathway. In other embodiments, the intrinsic electrical resistivity of the circuit elements and/or the electronically conductive pathways coupling the circuit elements to each other can serve as the resistor of the RLC circuit pathway.

FIG. IB is a top-view schematic illustration of circuit 100a, wherein the first RLC circuit pathway is represented as a dotted line. As shown in FIG. IB, the first RLC circuit pathway comprises, in certain embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through inductor 106, through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. IB, the first RLC circuit pathway does not include resistor 110 (which is shown in solid line).

In some embodiments, the first RLC circuit pathway may be configured to produce a return signal. In certain embodiments, for example, the circuit may be a resonator and the first RLC circuit pathway may produce a return signal in response to a suitable input signal. Any of a variety of suitable input signals may be utilized. In some embodiments, for example, the sensor system is a wireless sensor system and the input signal comprises electromagnetic radiation. In other embodiments, the sensor system is a wired sensor system and the input signal comprises power (e.g., voltage, current) from a power supply. As described herein in greater detail, the return signal of the first RLC circuit pathway may be transmitted to and analyzed by a processor.

In certain embodiments, circuit 100a comprises a second RLC circuit pathway. Referring to FIG. 1C, for example, second RLC circuit pathway comprises first portion 128 of inductor 106, resistor 110 electronically coupled to inductor 106, second portion 130 of inductor 106, and capacitor 108 electronically coupled to inductor 106 via electronically conductive pathway 114.

According to certain embodiments, resistor 110 is a portion of the second RLC circuit pathway, as resistor 110 functions as a compensating circuit element that electronically couples a first portion (e.g., a first finger) of inductor 106 to a second portion (e.g., a second finger) of inductor 106. Although resistor 110 is shown in FIG. 1A as being positioned substantially perpendicular to the arms of inductor 106, resistor 110 may be positioned at an angle (e.g., a 45° angle) between the arms of inductor 106. Resistor 110 can assume any of a variety of suitable configurations. In some embodiments, for example, resistor 110 can comprise electronically conductive nanostructures (e.g., electronically conductive elongated nanostructures, such as carbon nanotubes) embedded within a conductive or non-conductive (e.g., electrically insulating) matrix. In certain embodiments, the electronically conductive nanostructures serve an electronic function of resistor 110. According to certain embodiments, resistor 110 comprises metal, carbon, or any other suitable electronically conductive material.

Resistor 110 may have any of a variety of suitable resistances. In certain embodiments, resistor 110 has a resistance of greater than or equal to 0.1 ohms, greater than or equal to 1 ohm, greater than or equal to 10 ohms, greater than or equal to 100 ohms, greater than or equal to 1 kiloohm, greater than or equal to 10 kiloohms, or greater than or equal to 100 kiloohms. In some embodiments, resistor 110 has a resistance of less than or equal to 1 megaohm, less than or equal to 100 kiloohms, less than or equal to 10 kiloohms, less than or equal to 1 kiloohm, less than or equal to 100 ohms, less than or equal to 10 ohms, or less than or equal to 1 ohm. Combinations of the above recited ranges are possible (e.g., resistor 110 has a resistance greater than or equal to 0.1 ohm and less than or equal to 1 megaohm, resistor 110 has a resistance greater than or equal to 100 ohms and less than or equal to 1 kiloohm). Other ranges are also possible.

According to some embodiments, when inductor 106 is electronically coupled to resistor 110 and capacitor 108, then inductor 106, resistor 110, and capacitor 108 can form a RLC circuit pathway (e.g., a second RLC circuit pathway), such as the RLC circuit pathway illustrated in FIG. 3.

FIG. 1C is a top-view schematic illustration of circuit 100a, wherein the second RLC circuit pathway is represented as a dotted line. As shown in FIG. 1C, the second RLC circuit pathway comprises, in some embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106 (the first portion shown in dotted lines in FIG. 1C), through resistor 110, through second portion 130 of inductor 106 (the second portion shown in dotted line in FIG. 1C), through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 1C, the second RLC circuit pathway does include resistor 110 (which is shown in dotted line).

According to some embodiments, as shown in FIGS. 1B-1C, at least a portion of the second RLC circuit pathway may overlap with at least a portion of the first RLC circuit pathway. In certain embodiments, for example, the same capacitor (e.g., capacitor 108) is used in both the first RLC circuit pathway and the second RLC circuit pathway. In some embodiments, at a least a portion of the inductor (e.g., inductor 106) is used in both the first RLC circuit pathway and the second RLC circuit pathway.

Referring to FIGS. 1B-1C, for example, the second RLC circuit pathway comprises electronically conductive pathway 114, first end 124 of inductor 106, first portion 128 of inductor 106, second portion 130 of inductor 106, and second end 126 of inductor 106 that overlaps with the first RLC circuit pathway. In fact, as shown in FIGS. 1B-1C, all of the second RLC circuit pathway except for resistor 110 overlaps with the first RLC circuit pathway. Also, as shown in FIGS. 1B-1C, some, but not all, of the first RLC circuit pathway overlaps with the second RLC circuit pathway.

In certain embodiments, the first RLC circuit pathway comprises at least a portion of the inductor, and the second RLC circuit pathway comprises at least a portion of the inductor. Referring to FIGS. 1B-1C, for example, the first RLC circuit pathway comprises inductor 106, and the second RLC circuit pathway comprises first portion 128 of inductor 106 and second portion 130 of inductor 106. In some embodiments, the portion of the inductor in the first RLC circuit pathway and the portion of the inductor in the second RLC circuit pathway are not identical but at least partially overlap. Referring, for example, to FIGS. 1B-1C, inductor 106 in the first RLC circuit pathway and first portion 128 and second portion 130 of inductor 106 in the second RLC circuit pathway are not identical but at least partially overlap.

According to certain embodiments, at least 10%, at least 20%, at least 30%, at least 40%, at least 50%, at least 60%, at least 70%, at least 80%, or at least 90% of the surface area of the electronically conductive pathway of the portion of the inductor in the first RLC circuit pathway may overlap with the surface area of the electronically conductive pathway of the portion of the inductor in the second RLC circuit pathway. In some embodiments, less than 99%, less than or equal to 90%, less than or equal to 80%, less than or equal to 70%, less than or equal to 60%, less than or equal to 50%, less than or equal to 40%, less than or equal to 30%, or less than or equal to 20% of the surface area of the electronically conductive pathway of the portion of the inductor in the first RLC circuit pathway may overlap with the surface area of the electronically conductive pathway of the portion of the inductor in the second RLC circuit pathway.

As explained in further detail herein, the second RLC circuit pathway may be configured to produce a return signal, in accordance with certain embodiments. In certain embodiments, for example, the circuit may be a resonator and the second RLC circuit pathway may produce a return signal in response to a suitable input signal. Any of a variety of suitable input signals may be utilized. In some embodiments, for example, the sensor system is a wireless sensor system and the input signal comprises electromagnetic radiation. In other embodiments, the sensor system is a wired sensor system and the input signal comprises power (e.g., voltage, current) from a power supply. The return signal of the second RLC circuit pathway may, in some embodiments, be different than the return signal of the first RLC circuit pathway. As described herein in greater detail, the return signal of the second RLC circuit pathway may be transmitted to and analyzed by a processor.

FIG. 2A is a top-view schematic illustration of circuit 100b comprising a first RLC circuit pathway and a second RLC circuit pathway comprising inductor 106’, in accordance with certain embodiments. Circuit 100b corresponds to circuit 100a of FIGS. 1A-1C, except circuit 100b comprises inductor 106’ in place of resistor 110.

According to some embodiments, circuit 100b comprises a first RLC circuit pathway comprising inductor 106 and capacitor 108 electronically coupled to inductor 106 via electronically conductive pathway 114.

In certain embodiments, when inductor 106 is electronically coupled to capacitor 108, then inductor 106 and capacitor 108 can form a RLC circuit pathway (e.g., a first RLC circuit pathway), such as the RLC circuit pathway illustrated in FIG. 3. In some embodiments, a dedicated resistor can be incorporated into the RLC circuit pathway. In other embodiments, the intrinsic electrical resistivity of the circuit elements and/or the electronically conductive pathways coupling the circuit elements to each other can serve as the resistor of the RLC circuit pathway.

FIG. 2B is a top-view schematic illustration of circuit 100b, wherein the first RLC circuit pathway is represented as a dotted line. As shown in FIG. 2B, the first RLC circuit pathway comprises, in some embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through inductor 106, through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 2B, the first RLC circuit pathway does not include inductor 106’ (which is shown in solid line).

According to certain embodiments, circuit 100b comprises a second RLC circuit pathway comprising first portion 128 of inductor 106, inductor 106’ electronically coupled to inductor 106, second portion 130 of inductor 106, and capacitor 108 electronically coupled to inductor 106 via electronically conductive pathway 114.

According to certain embodiments, inductor 106’ is a portion of the second RLC circuit pathway, as inductor 106’ functions as a compensating circuit element that electronically couples a first portion (e.g., a first finger) of inductor 106 to a second portion (e.g., a second finger) of inductor 106. Although inductor 106’ is shown in FIG. 2B as being positioned substantially perpendicular to the arms of inductor 106, inductor 106’ may be positioned at an angle (e.g., a 45° angle) between the arms of inductor 106.

Inductor 106’ can assume any of a variety of suitable configurations. In some embodiments, inductor 106’ can comprise electronically conductive nanostructures (e.g., electronically conductive elongated nanostructures, such as carbon nanotubes) embedded within a conductive or non-conductive (e.g., electrically insulating) matrix. In certain embodiments, the electronically conductive nanostructures serve an electronic function of inductor 106’. According to certain embodiments, inductor 106’ comprises metal, carbon, or any other suitable electronically conductive material.

Inductor 106’ may have any of a variety of suitable inductances. In certain embodiments, inductor 106’ has an inductance of greater than or equal to 10 nanohenries, greater than or equal to 100 nanohenries, greater than or equal to 1 microhenry, greater than or equal to 10 microhenries, greater than or equal to 100 microhenries, greater than or equal to 1 millihenry, greater than or equal to 10 millihenries, or greater than or equal to 100 millihenries. In some embodiments, inductor 106’ has an inductance of less than or equal to 1 henry, less than or equal to 100 millihenries, less than or equal to 10 millihenries, less than or equal to 1 millihenry, less than or equal to 100 microhenries, less than or equal to 10 microhenries, less than or equal to 1 microhenry, or less than or equal to 100 nanohenries. Combinations of the above-recited ranges are possible (e.g., inductor 106’ has an inductance of greater than or equal to 10 nanohenries and less than or equal to 1 henry, inductor 106’ has an inductance of greater than or equal to 100 microhenries and less than or equal to 1 millihenry). Other ranges are also possible.

In certain embodiments, when inductor 106 is electronically coupled to inductor 106’ and capacitor 108, then inductor 106, inductor 106’, and capacitor 108 can form a RLC circuit pathway (e.g., a second RLC circuit pathway), such as the RLC circuit pathway illustrated in FIG. 3. In some embodiments, a dedicated resistor can be incorporated into the RLC circuit pathway. In other embodiments, the intrinsic electrical resistivity of the circuit elements and/or the electronically conductive pathways coupling the circuit elements to each other can serve as the resistor of the RLC circuit pathway. FIG. 2C is a top-view schematic illustration of circuit 100b, wherein the second RLC circuit pathway is represented as a dotted line. As shown in FIG. 2C, the second RLC circuit pathway comprises, in certain embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106 (the first portion shown in dotted lines in FIG. 2C), through inductor 106’, through second portion 130 of inductor 106 (the second portion shown in dotted line in FIG. 2C), through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 2C, the second RLC circuit pathway does include inductor 106’ (which is shown in dotted line).

According to some embodiments, as shown in FIGS. 2B-2C, at least a portion of the second RLC circuit pathway may overlap with at least a portion of the first RLC circuit pathway. In certain embodiments, for example, the same capacitor (e.g., capacitor 108) is used in both the first RLC circuit pathway and the second RLC circuit pathway. In some embodiments, at least a portion of the inductor (e.g., inductor 106) is used in both the first RLC circuit pathway and the second RLC circuit pathway.

Referring to FIGS. 2B-2C, for example, the second RLC circuit pathway comprises electronically conductive pathway 114, first end 124 of inductor 106, first portion 128 of inductor 106, second portion 130 of inductor 106, and second end 126 of inductor 106 that overlaps with the first RLC circuit pathway. In fact, as shown in FIGS. 2B-2C, all of the second RLC circuit pathway except for inductor 106’ overlaps with the first RLC circuit pathway. Also, as shown in FIGS. 2B-2C, some, but not all, of the first RLC circuit pathway overlaps with the second RLC circuit pathway.

In some embodiments, as described above, nanostructures can be incorporated into one or more elements of the circuit (e.g., into an inductor and/or a capacitor). In some embodiments, the nanostructures can serve an electronic function of the circuit components. For example, in some embodiments, the nanostructures are electronically conductive and can be embedded in a conductive or non-conductive matrix to impart electronic conductivity to the circuit element.

FIG. 4A is a schematic illustration of the fabrication of an inductor in which electronically conductive nanostructures are used to form the electronically conductive pathway of the inductor, in accordance with certain embodiments. In certain embodiments, substrate 401a is provided, and patterned with active growth material 402a, such as a catalyst. The patterning may be performed, for example, using lithography masking techniques. According to some embodiments, a forest of vertically aligned patterned nanostructures 404a are grown on substrate 401a, followed by knocking down the forest of vertically aligned patterned nanostructures 404a (e.g., using a roller), drop-casting electrically insulating material 410a, and spin-coating 412a, thereby providing inductor 106 comprising forest of substantially parallel patterned nanostructures 404a embedded in electrically insulating material 410a (e.g., a structural polymer matrix).

FIG. 4B is a schematic illustration of the fabrication of an interdigitated capacitor in which electronically conductive nanostructures are used to form the electrodes of the capacitor, in accordance with certain embodiments. In certain embodiments, substrate 401b is provided, and patterned with active growth material 402b, such as a catalyst. The patterning may be performed, for example, using lithography masking techniques. According to some embodiments, a forest of vertically aligned patterned nanostructures 404b are grown on substrate 401b, followed by knocking down the forest of vertically aligned patterned nanostructures 404b (e.g., using a roller), drop-casting electrically insulating material 410b, and spin-coating 412b, thereby providing first electrode 116 and/or second electrode 118 of capacitor 108. In certain embodiments, first electrode 116 and/or second electrode 118 of capacitor 108 comprise forest of substantially parallel patterned nanostructures 404b embedded in electrically insulating material 410b (e.g., a structural polymer matrix).

FIGS. 5A-5D are a series of cross-sectional schematic illustrations showing the fabrication of a parallel-plate capacitor in which electronically conductive nanostructures are used to form the electrodes of the parallel-plate capacitor, in accordance with certain embodiments. In FIG. 5A, a collection of elongated nanostructures 501 has been formed on substrate 401c (e.g., a Kapton substrate), for example, using catalytic growth of carbon nanotubes. The collection of elongated nanostructures has been infused with a non-conductive material 502a (e.g., EPON). The elongated nanostructures can provide electrical conductivity, such that the combination of the elongated nanostructures 501 and non-conductive material 502a forms the first electrode of the parallel-plate capacitor. In FIG. 5B, additional non-conductive material 502b (e.g., EPON) has been placed over elongated nanostructures 501 and non-conductive material 502a. In FIG. 5C, non- conductive material 502b has been reformed in the shape of layer. In one non-limiting embodiment, non-conductive material 502b is a layer of Kapton film with epoxy (e.g., having a thickness of less than 50 micrometers, or less than 10 micrometers). In FIG. 5D, a second electrode comprising electronically conductive elongated nanostructures 501 embedded in non-conductive material layer 502c has been added to the top of the stack from FIG. 5C. Additional substrate 401d may also be included. Optionally, the stack may be cured, for example, using a hot press, to form the final parallel-plate capacitor. Optionally, substrate 401c and/or substrate 401d may be omitted or removed from the capacitor.

Non-limiting examples of the use of electronically conductive nanostructures embedded in non-conductive matrices to form circuit components are described, for example, in International Patent Application Publication No. WO 2019/118706, published on June 20, 2019, filed on December 13, 2018, as International Application No. PCT/US2018/065422, and entitled “Structural Electronics Wireless Sensor Nodes” and in U.S. Patent Application No. 16/900,159, filed on June 12, 2020, published as U.S. Patent Publication No. 2020/0309674 on October 1, 2020, and entitled “Structural Electronics Wireless Sensor Nodes,” each of which is incorporated herein by reference in its entirety for all purposes.

Any of a variety of suitable nanostructures can be used in association with the embodiments described herein. The term “nanostructure” is used herein in a manner consistent with its ordinary meaning in the art and refers to a structure that has a characteristic dimension, such as a cross-sectional diameter, or other appropriate dimension, that is greater than or equal to 1 nm and less than 1 micrometer. In some embodiments, the nanostructure has at least one characteristic dimension of less than 750 nm, less than 500 nm, less than 250 nm, less than 100 nm, less than 75 nm, less than 50 nm, less than 25 nm, less than 10 nm, or, in some cases, less than 5 nm.

In some embodiments, the nanostructures are elongated nanostructures (e.g., having an aspect ratio of at least 10, and in some embodiments, at least 100; at least 1,000; at least 10,000; at least 100,000; or more). In some embodiments, the elongated nanostructure is a nanofiber, a nanowire, a nanorod, or the like. In certain aspects, the nanostructures are electrically conductive. In certain embodiments, the nanostructures comprise carbon-based nanostructures (i.e., nanostructures that are at least 50 atomic percent (at%) carbon and, in some cases, can be at least 60 at%, at least 70 at%, at least 80 at%, at least 90 at%, at least 95 at%, at least 99 at%, or more carbon). In certain embodiments, the nanostructures comprise carbon nanotubes (CNTs). The term “carbon nanotube” is used herein in a manner consistent with its ordinary meaning in the art and refers to a substantially cylindrical molecule or nanostructure comprising a fused network of primarily six-membered rings (e.g., six-membered aromatic rings) comprising primarily carbon atoms. Further details regarding CNTs are described below. In some embodiments, the nanostructures comprise metal. In some embodiments the metal is a conducting metal. For example, the nanostructure may comprise silicon (Si), germanium (Ge), gold (Au), metal oxides (e.g., I112O3, SnCE, ZnO), and the like.

Additional examples of nanostructures that can be used include, but are not limited to, metal nanowires, conductive particles, buckyballs, graphene flakes, and the like.

In some embodiments, one or more circuit elements (e.g., the capacitor, the inductor) can comprise electronically conductive nanostructures embedded in a conductive or non-conductive matrix. Examples of conductive matrices includes, but are not limited to, conductive polymers, metals, or combinations thereof. Example of non- conductive matrices include, but are not limited to, polymers (e.g., epoxy resin (e.g., EPON resin), paramethylstyrene (PMS), para-methoxyamphetamine (PMA), polyimide (e.g., Kapton®), polyether ether ketone (PEEK), polyether ketone ketone (PEKK), bis- maleimide (BMI), cyanate ester, and the like), metal and/or metalloid oxides, glasses, ceramics, or any combinations of two or more of these materials.

In some embodiments, the first RLC circuit pathway is configured to produce a return signal unless and until the first RLC circuit pathway is broken (e.g., via a structural defect, such as a crack, hole, etc.). According to certain embodiments, the circuits described herein are configured such that, when a crack propagates through the first RLC circuit pathway, the second RLC circuit pathway still produces a return signal. In some embodiments, for example, the circuit is configured such that the second RLC circuit pathway still produces a return signal when a crack propagates through a portion (e.g., a finger) of the inductor in the first RLC circuit pathway. As a result of the second RLC circuit pathway being configured to produce a return signal even though the first RLC circuit pathway becomes non-functional (e.g., due to a crack), the circuits described herein advantageously may be used as a sensor (e.g., a crack sensor) to determine whether a crack has propagated through the first RLC circuit pathway.

FIG. 6A is, in accordance with certain embodiments, a top-view schematic illustration of circuit 100a comprising a first RLC circuit pathway and a second RLC circuit pathway comprising resistor 110, wherein crack 602a has propagated through the first RLC circuit pathway (e.g., through a portion of inductor 106 in the first RLC circuit pathway). In some embodiments, as shown in FIG. 6A, the second RLC circuit pathway (e.g., comprising an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106, through resistor 110, through second portion 130 of inductor 106, through second end 126 of inductor 106, and to second electrode 118 of capacitor 108), represented as a dotted line, is configured to produce a return signal even though crack 602a has propagated through the first RLC circuit pathway (e.g., through a portion of inductor 106 in the first RLC circuit pathway).

FIG. 7A is, in accordance with certain embodiments, a top-view schematic illustration of circuit 100b comprising a first RLC circuit pathway and a second RLC circuit pathway comprising inductor 106’, wherein crack 602a has propagated through the first RLC circuit pathway (e.g., through a portion of inductor 106 in the first RLC circuit pathway). As shown in FIG. 7A, the second RLC circuit pathway (e.g., comprising an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106, through inductor 106’, through second portion 130 of inductor 106, through second end 126 of inductor 106, and to second electrode 118 of capacitor 108), represented as a dotted line, is configured to produce a return signal even though crack 602a has propagated through the first RLC circuit pathway (e.g., through a portion of inductor 106 in the first RLC circuit pathway).

Although the crack shown in FIGS. 6A-7A propagates from an exterior of the circuit towards an interior of the circuit, embodiments are also envisioned in which the crack propagates from the interior of the circuit towards the exterior of the circuit. According to certain embodiments, sensor systems configured to detect a crack propagating from an interior of the circuit to an exterior of the circuit may be useful in embodiments where the circuit is disposed over a rivet head, such that the sensor system is able to detect a crack emanating from the rivet head.

FIG. 6B shows, for example, a top-view schematic illustration of circuit 100a’ comprising a first RLC circuit pathway (as shown, for example, in FIG. IB) and a second RLC circuit pathway comprising resistor 110, wherein the second RLC circuit pathway is represented as a dotted line. As shown in FIG. 6B, crack 602a’ has propagated through the first RLC circuit pathway (e.g., through a portion of inductor 106 in the first RLC circuit pathway). The second RLC circuit pathway in FIG. 6B comprises, in some embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106 (the first portion shown in dotted lines in FIG. 6B), through resistor 110, through second portion 130 of inductor 106 (the second portion shown in dotted line in FIG. 6B), through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 6B, the second RLC circuit pathway does include resistor 110 (which is shown in dotted line). The second RLC circuit pathway in FIG. 6B is configured to produce a return signal even though crack 602a’ has propagated through the first RLC circuit pathway (e.g., through a portion of the inductor in the first RLC circuit pathway).

FIG. 7B shows, for example, a top-view schematic illustration of circuit 100b’ comprising a first RLC circuit pathway (as shown, for example, in FIG. 2B) and a second RLC circuit pathway comprising inductor 106’, wherein the second RLC circuit pathway is represented as a dotted line. As shown in FIG. 7B, crack 602a’ has propagated through the first RLC circuit pathway (e.g., through a portion of inductor 106 in the first RLC circuit pathway). The second RLC circuit pathway in FIG. 7B comprises, in some embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106 (the first portion shown in dotted lines in FIG. 7B), through inductor 106’, through second portion 130 of inductor 106 (the second portion shown in dotted line in FIG. 6B), through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 7B, the second RLC circuit pathway does include inductor 106’ (which is shown in dotted line). The second RLC circuit pathway in FIG. 7B is configured to produce a return signal even though crack 602a’ has propagated through the first RLC circuit pathway (e.g., through a portion of the inductor in the first RLC circuit pathway).

According to certain embodiments, the sensor systems described herein may be configured to determine a location of one or more cracks in the circuit. In certain embodiments, for example, the circuit may comprise a first compensating circuit element and a second compensating circuit element electronically coupling a first portion of the first RLC circuit pathway (e.g., a first portion of an inductor of the first RLC circuit pathway) to a second portion of the first RLC circuit pathway (e.g., a second portion of the inductor of the first RLC circuit pathway). In some embodiments, the return signal of the second RLC circuit pathway may depend on whether the second RLC circuit pathway comprises the first compensating circuit element or the second compensating circuit element, and the sensor system may be configured to determine the location of the crack based at least in part on the return signal of the second RLC circuit pathway.

FIG. 6C shows, for example, a top view schematic illustration of circuit 100a” comprising a first RLC circuit pathway (as shown, for example, in FIG. IB) and a second RLC circuit pathway comprising resistor 110’ or resistor 110”. In some embodiments, a sensor system comprising circuit 100a” is configured to determine a location of the crack depending on where the crack propagates through the first RLC circuit pathway (e.g., through the inductor of the first RLC circuit pathway). In certain embodiments, for example, if the crack propagates through inductor 106 at first location 132, then the second RLC circuit pathway comprises compensating resistor 110’ . In other embodiments, if the crack propagates through inductor 106 at second location 134, then the second RLC circuit pathway comprises compensating resistor 110”.

Compensating resistors 110’ and 110” may have different resistances, in some embodiments. In some such embodiments, the return signal of the second RLC circuit pathway may differ depending on whether the second RLC circuit pathway comprises resistor 110’ or resistor 110”. As explained in further detail herein, in some embodiments, the return signal may be detected and analyzed (e.g., by a processor), and the sensor system may determine a location of the crack based on the analysis. In some embodiments, for example, the resonance frequency and/or quality factor of the return signal of the second RLC circuit pathway can be used to identify a region of the circuit in which the crack has formed.

FIG. 7C shows, for example, a top view schematic illustration of circuit 100b” comprising a first RLC circuit pathway (as shown, for example, in FIG. 2B) and a second RLC circuit pathway comprising inductor 106a or inductor 106b. In some embodiments, a sensor system comprising circuit 100b” is configured to determine a location of the crack depending on where the crack propagates through the first RLC circuit pathway (e.g., through the inductor of the first RLC circuit pathway). In certain embodiments, for example, if the crack propagates through inductor 106 at first location 132, then the second RLC circuit pathway comprises compensating inductor 106a. In other embodiments, if the crack propagates through inductor 106 at second location 134, then the second RLC circuit pathway comprises compensating inductor 106b.

Compensating inductors 106a and 106b may have different inductances, in some embodiments. In some such embodiments, the return signal of the second RLC circuit pathway may differ depending on whether the second RLC circuit pathway comprises inductor 106a or inductor 106b. As explained in further detail herein, in some embodiments, the return signal may be detected and analyzed (e.g., by a processor), and the sensor system may determine a location of the crack based on the analysis. In some embodiments, for example, the resonance frequency and/or quality factor of the return signal of the second RLC circuit pathway can be used to identify a region of the circuit in which the crack has formed.

Although FIGS. 6C and 7C show two compensating circuit elements (e.g., resistor 110’ and resistor 110” in FIG. 6C, inductor 106a and inductor 106b in FIG. 7C) electronically coupling a first finger of the inductor to a second finger of the inductor, the circuit may comprise more than two compensating circuit elements (e.g., three compensating circuit elements, four compensating circuit elements, five compensating circuit elements, etc.) electronically coupling the first finger of the inductor to the second finger of the inductor.

Although the compensating circuit elements shown in FIGS. 6C and 7C (e.g., resistor 110’ and resistor 110” in FIG. 6C, inductor 106a and inductor 106b in FIG. 7C) are shown as being positioned perpendicular to the arms of the inductor, the compensating circuit elements may be positioned at an angle (e.g., a 45° angle) between - 1 - the arms of inductor 106, according to some embodiments. Configuring the compensating circuit elements in this manner may advantageously result in a sensor system that is configured to determine an angle range of where the crack propagates through the inductor.

As described above, the sensor systems described herein may be configured to determine a location of one or more cracks in the circuit. In certain embodiments, for example, the circuit comprises a plurality of circuit elements electronically coupled to the inductor and external to the inductor. FIG. 6D is, in accordance with certain embodiments, a top-view schematic illustration of circuit 100a”’ comprising compensating resistors 110’, 110”, and 110”’, wherein each compensating resistor is electronically coupled to inductor 106 and external to inductor 106. In some embodiments, compensating resistors 110’, 110”, and 110” may be out-of-plane of inductor 106. In other embodiments, compensating resistors 110’, 110”, and 110” may be in-plane with inductor 106.

In some embodiments, circuit 100a’” is configured such that, when a crack propagates through a portion of the first RLC circuit pathway in any of quadrants I, II, and/or III, the second RLC circuit pathway comprising a respective compensating resistor in quadrants I, II, and/or III is still configured to produce a return signal. For example, in some embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrant I (e.g., from an exterior of circuit 100a’” to an interior of circuit 100a’”, from an interior of circuit 100a’” to an exterior of circuit 100a’”), the second RLC circuit pathway comprising compensating resistor 110’ is still configured to produce a return signal. In certain embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrant II (e.g., from an exterior of circuit 100a”’ to an interior of circuit 100a”’, from an interior of circuit 100a’” to an exterior of circuit 100a’”), the second RLC circuit pathway comprising compensating resistor 110” is still configured to produce a return signal. In some embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrant III (e.g., from an exterior of circuit 100a”’ to an interior or circuit 100a”’, from an interior of circuit 100a”’ to an exterior of circuit 100a”’), the second RLC circuit pathway comprising compensating resistor 110”’ is still configured to produce a return signal. In some embodiments, a sensor system comprising circuit 100a’” is configured determine a location of more than one crack in circuit 100a”’. In certain embodiments, for example, when a crack propagates through a portion of the first RLC circuit pathway in quadrants I and II, the second RLC circuit pathway comprising compensating resistors 110’ and 110’ ’ is still configured to produce a return signal. In some embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrants I and III, the second RLC circuit pathway comprising compensating resistors 110’ and 110”’ is still configured to produce a return signal. In certain embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrants II and III, the second RLC circuit pathway comprising compensating resistors 110” and 110’” is still configured to produce a return signal. In some embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrants I, II, and III, the second RLC circuit pathway comprising compensating resistors 110’, 110”, and 110”’ is still configured to produce a return signal.

As explained in further detail herein, in some embodiments, the return signal (e.g., of the second RLC circuit pathway) may be detected and analyzed (e.g., by a processor), and the sensor system may determine a location of the crack, such as a quadrant of the circuit in which the crack has propagated, based on the analysis. In some embodiments, for example, compensating resistors 110’, 110”, and/or 110”’ may have different resistances. In some such embodiments, the return signal of the second RLC circuit pathway may differ depending on whether the second RLC circuit pathway comprises resistor 110’, resistor 110”, and/or resistor 110”’. As explained in further detail herein, the return signal of the second RLC circuit pathway may be detected and analyzed (e.g., by a processor), and the sensor system may determine a location, such as a quadrant of the circuit in which the crack has propagated, based on the analysis. In some embodiments, the sensor system may determine an angle range of where the crack propagates through the inductor.

FIG. 7D is, in accordance with certain embodiments, a top-view schematic illustration of circuit 100b’” comprising compensating inductors 106a, 106b, and 106c, wherein each compensating inductor is electronically coupled to inductor 106 and external to inductor 106. In some embodiments, compensating inductors 106a, 106b, and 106c may be out-of-plane of inductor 106. In other embodiments, compensating inductors 106a, 106b, and 106c may be in-plane with inductor 106.

In some embodiments, circuit 100b’” is configured such that, when a crack propagates through a portion of the first RLC circuit pathway in any of quadrants I, II, and/or III, the second RLC circuit pathway comprising a respective compensating inductor in quadrants I, II, and/or III is still configured to produce a return signal. For example, in some embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrant I (e.g., from an exterior of circuit 100b’” to an interior of circuit 100b”’, from an interior of circuit 100b’” to an exterior of circuit 100b’”), the second RLC circuit pathway comprising compensating inductor 106a is still configured to produce a return signal. In certain embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrant II (e.g., from an exterior of circuit 100b”’ to an interior of circuit 100b’”, from an interior of circuit 100b”’ to an exterior of circuit 100b”’), the second RLC circuit pathway comprising compensating inductor 106b is still configured to produce a return signal. In some embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrant III (e.g., from an exterior of circuit 100b”’ to an interior or circuit 100b”’, from an interior of circuit 100b”’ to an exterior of circuit 100b’”), the second RLC circuit pathway comprising compensating inductor 106c is still configured to produce a return signal.

In some embodiments, a sensor system comprising circuit 100b’” is configured determine a location of more than one crack in circuit 100b”’. In certain embodiments, for example, when a crack propagates through a portion of the first RLC circuit pathway in quadrants I and II, the second RLC circuit pathway comprising compensating inductors 106a and 106b is still configured to produce a return signal. In some embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrants I and III, the second RLC circuit pathway comprising compensating inductors 106a and 106c is still configured to produce a return signal. In certain embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrants II and III, the second RLC circuit pathway comprising compensating inductors 106b and 106c is still configured to produce a return signal. In some embodiments, when a crack propagates through a portion of the first RLC circuit pathway in quadrants I, II, and III, the second RLC circuit pathway comprising compensating inductors 106a, 106b, and 106c is still configured to produce a return signal.

As explained in further detail herein, in some embodiments, the return signal (e.g., of the second RLC circuit pathway) may be detected and analyzed (e.g., by a processor), and the sensor system may determine a location of the crack, such as a quadrant of the circuit in which the crack has propagated, based on the analysis. In some embodiments, for example, compensating inductors 106a, 106b, and/or 106c may have different inductances. In some such embodiments, the return signal of the second RLC circuit pathway may differ depending on whether the second RLC circuit pathway comprises inductor 106a, inductor 106b, and/or inductor 106c. As explained in further detail herein, the return signal of the second RLC circuit pathway may be detected and analyzed (e.g., by a processor), and the sensor system may determine a location, such as a quadrant of the circuit in which the crack has propagated, based on the analysis. In some embodiments, the sensor system may determine an angle range of where the crack propagates through the inductor.

Although FIGS. 6D and 7D show a circuit comprising three compensating circuit elements electronically coupled to the inductor and external to the inductor, the circuits described herein may comprise any suitable number of compensating circuit elements electronically coupled to the inductor and external to the inductor (e.g., four compensating circuit elements, five compensating circuit elements, ten compensating circuit elements, etc.). In accordance with certain embodiments, the number of circuit quadrants may change depending on the number of compensating circuit elements electronically coupled to and external to the inductor.

The interior angle of each comer of each quadrant of the circuit (see, e.g., interior angle 602 in FIGS. 6D and 7D) may by any of a variety of suitable angles. In some embodiments, for example, the interior angle of each corner of each quadrant of the circuit is greater than or equal to 15°, greater than or equal to 30°, greater than or equal to 45°, greater than or equal to 60°, or greater than or equal to 75°. In certain embodiments, the interior angle of each corner of each quadrant of the circuit is less than or equal to 90°, less than or equal to 75°, less than or equal to 60°, less than or equal to 45°, or less than or equal to 30°. Combinations of the above recited ranges are possible (e.g., the interior angle of each corner of each quadrant of the circuit is greater than or equal to 15° and less than or equal to 90°, the interior angle of each comer of each quadrant of the circuit is greater than or equal to 45° and less than or equal to 60°). Other ranges are also possible.

According to certain embodiments, the circuits described herein may comprise a third RLC circuit pathway. FIG. 8 is, in accordance with certain embodiments, a topview schematic illustration of circuit 100c comprising a first RLC circuit pathway, a second RLC circuit pathway comprising resistor 110a, and a third RLC circuit pathway comprising resistor 110b. The third RLC circuit pathway in FIG. 8 is represented as a dotted line. As shown in FIG. 8, the third RLC circuit pathway comprises first portion 128 of inductor 106, resistor 110a electronically coupled to inductor 106, resistor 110b electronically coupled to inductor 106, second portion 130 of inductor 106, and capacitor 108 electronically coupled to inductor 106 via electronically conductive pathway 114.

According to certain embodiments, resistor 110b is a portion of the third RLC circuit pathway, as resistor 110b functions as a compensating circuit element that electronically couples the second portion (e.g., the second finger) of inductor 106 to a third portion (e.g., a third finger) of inductor 106.

Resistor 110a and resistor 110b may be configured as described above with respect to resistor 110 in reference to FIGS. 1A-1C.

According to some embodiments, when inductor 106 is electronically coupled to resistor 110a, resistor 110b, and capacitor 108, then inductor 106, resistor 110a, resistor 110b, and capacitor 108 can form a RLC circuit pathway (e.g., a third RLC circuit pathway), such as the RLC circuit pathway illustrated in FIG. 3.

As shown in FIG. 8, the third RLC circuit pathway comprises, in some embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106 (the first portion shown in dotted lines in FIG. 8), through resistor 110b, through resistor 110a, through second portion 130 of inductor 106 (the second portion shown in dotted line in FIG. 8), through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 8, the third RLC circuit pathway does include resistor 110a and resistor 110b (which are shown in dotted line). FIG. 9 is, in accordance with certain embodiments, a top-view schematic illustration of circuit lOOd comprising a first RLC circuit pathway, a second RLC circuit pathway comprising inductor 106’, and a third RLC circuit pathway comprising inductor 106”. The third RLC circuit pathway in FIG. 9 is represented as a dotted line. As shown in FIG. 9, the third RLC circuit pathway comprises first portion 128 of inductor 106, inductor 106’ electronically coupled to inductor 106, inductor 106” electronically coupled to inductor 106, second portion 130 of inductor 106, and capacitor 108 electronically coupled to inductor 106 via electronically conductive pathway 114.

According to certain embodiments, inductor 106” is a portion of the third RLC circuit pathway, as inductor 106” functions as a compensating circuit element that electronically couples the second portion (e.g., the second finger) of inductor 106 to a third portion (e.g., a third finger) of inductor 106.

Inductor 106” may be configured as described above with respect to inductor 106’ in reference to FIGS. 2A-2C.

According to some embodiments, when inductor 106 is electronically coupled to inductor 106’, inductor 106”, and capacitor 108, then inductor 106, inductor 106’, inductor 106”, and capacitor 108 can form a RLC circuit pathway (e.g., a third RLC circuit pathway), such as the RLC circuit pathway illustrated in FIG. 3. In some embodiments, a dedicated resistor can be incorporated into the RLC circuit pathway. In other embodiments, the intrinsic electrical resistivity of the circuit elements and/or the electronically conductive pathways coupling the circuit elements to each other can serve as the resistor of the RLC circuit pathway.

As shown in FIG. 9, the third RLC circuit pathway comprises, in some embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106 (the first portion shown in dotted lines in FIG. 9), through inductor 106”, through inductor 106’, through second portion 130 of inductor 106 (the second portion shown in dotted line in FIG. 9), through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 9, the third RLC circuit pathway does include inductor 106’ and inductor 106” (which are shown in dotted line). According to some embodiments, at least a portion of the third RLC circuit pathway may overlap with at least a portion of the second RLC circuit pathway. In certain embodiments, for example, the same capacitor (e.g., capacitor 108) is used in both the first RLC circuit pathway and the second RLC circuit pathway. In some embodiments, at least a portion of the inductor (e.g., inductor 106) is used in both the first RLC circuit pathway and the second RLC circuit pathway.

Referring to FIG. 8, for example, third RLC circuit pathway comprises electronically conductive pathway 114, first end 124 of inductor 106, first portion 128 of inductor 106, resistor 110a, second portion 130 of inductor 106, and second end 126 of inductor 106 that overlaps with the second RLC circuit pathway. In fact, as shown in FIG. 8, all of the third RLC circuit pathway except for resistor 110b overlaps with the second RLC circuit pathway. Also, as shown in FIG. 8, some, but not all, of the second RLC circuit pathway overlaps with the third RLC circuit pathway.

Referring to FIG. 9, in some embodiments, third RLC circuit pathway comprises electronically conductive pathway 114, first end 124 of inductor 106, first portion 128 of inductor 106, inductor 106’, second portion 130 of inductor 106, and second end 126 of inductor 106 that overlaps with the second RLC circuit pathway. In fact, as shown in FIG. 9, all of the third RLC circuit pathway except for inductor 106” overlaps with the second RLC circuit pathway. Also, as shown in FIG. 9, some, but not all, of the second RLC circuit pathway overlaps with the third RLC circuit pathway.

As explained in further detail herein, the third RLC circuit pathway may be configured to produce a return signal, in accordance with certain embodiments. In certain embodiments, for example, the circuit may be a resonator and the third RLC circuit pathway may produce a return signal in response to a suitable input signal. Any of a variety of suitable input signals may be utilized. In some embodiments, for example, the sensor system is a wireless sensor system and the input signal comprises electromagnetic radiation. In other embodiments, the sensor system is a wired sensor system and the input signal comprises power (e.g., voltage, current) from a power supply. The return signal of the third RLC circuit pathway may, in some embodiments, be different than the return signal of the first RLC circuit pathway and the second RLC circuit pathway. As described herein in greater detail, the return signal of the third RLC circuit pathway may be transmitted to and analyzed by a processor. In some embodiments, the second RLC circuit pathway is configured to produce a return signal unless and until the second RLC circuit pathway is broken (e.g., via a crack). According to certain embodiments, the circuits described herein are configured such that, when a crack propagates through the second RLC circuit pathway, the third RLC circuit pathway still produces a return signal. In some embodiments, for example, the circuits are configured such that the third RLC circuit pathway still produces a return signal when a crack propagates through a portion (e.g., a finger) of the inductor in the second RLC circuit pathway. As a result of the third RLC circuit pathway being configured to produce a return signal even though the second RLC circuit pathway becomes non-functional (e.g., due to a crack), the circuits described herein advantageously may be used as a sensor (e.g., a crack sensor) to determine whether a crack has propagated through the second RLC circuit pathway.

FIG. 10 is, in accordance with certain embodiments, a top-view schematic illustration of circuit 100c comprising a first RLC circuit pathway, a second RLC circuit pathway comprising resistor 110a, and a third RLC circuit pathway comprising resistor 110b, wherein crack 602b has propagated through the second RLC circuit pathway (e.g., through a portion of inductor 106 in the second RLC circuit pathway). As shown in FIG. 10, the third RLC circuit pathway (e.g., comprising an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106, through resistor 110b, through resistor 110a, through second portion 130 of inductor 106, through second end 126 of inductor 106, and to second electrode 118 of capacitor 108), represented as a dotted line, is configured to produce a return signal even though crack 602b has propagated through the second RLC circuit pathway (e.g., through a portion of inductor 106 in the second RLC circuit pathway).

FIG. 11 is, in accordance with certain embodiments, a top-view schematic diagram illustration of circuit lOOd comprising a first RLC circuit pathway, a second RLC circuit pathway comprising inductor 106’, and a third RLC circuit pathway comprising inductor 106”, wherein crack 602b has propagated through the second RLC circuit pathway (e.g., through a portion of inductor in the second RLC circuit pathway). As shown in FIG. 11, the third RLC circuit pathway (e.g., comprising an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106, through inductor 106”, through inductor 106’, through second portion 130 of inductor 106, through second end 126 of inductor 106, and to second electrode 118 of capacitor 108), represented as a dotted line, is configured to produce a return signal even though crack 602b has propagated through the second RLC circuit pathway (e.g., through a portion of inductor 106 in the second RLC circuit pathway).

According to some embodiments, the circuits described herein may comprise a fourth RLC circuit pathway. FIG. 12 is, in accordance with certain embodiments, a topview schematic illustration of circuit 100c comprising a first RLC circuit pathway, a second RLC circuit pathway comprising resistor 110a, a third RLC circuit pathway comprising resistor 110b, and a fourth RLC circuit pathway comprising resistor 110c. The fourth RLC circuit pathway in FIG. 12 is represented as a dotted line. As shown in FIG. 12, the fourth RLC circuit pathway comprises first portion 128 of inductor 106, resistor 110a electronically coupled to inductor 106, resistor 110b electronically coupled to inductor 106, resistor 110c electronically coupled to inductor 106, second portion 130 of inductor 106, and capacitor 108 electronically coupled to inductor 106 via electronically conductive pathway 114.

According to certain embodiments, resistor 110c is a portion of the fourth RLC circuit pathway, as resistor 110c functions as a compensating circuit element that electronically couples the third portion (e.g., the third finger) of inductor 106 to a fourth portion (e.g., a fourth finger) of inductor 106.

Resistor 110c may be configured as described above with respect to resistor 110 in reference to FIGS. 1A-1C.

According to some embodiments, when inductor 106 is electronically coupled to resistor 110a, resistor 110b, resistor 110c, and capacitor 108, then inductor 106, resistor 110a, resistor 110b, resistor 110c, and capacitor 108 can form a RLC circuit pathway (e.g., a fourth RLC circuit pathway), such as the RLC circuit pathway illustrated in FIG. 3.

As shown in FIG. 12, the fourth RLC circuit pathway comprises, in certain embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106 (the first portion shown in dotted lines in FIG. 12), through resistor 110c, through resistor 110b, through resistor 110a, through second portion 130 of inductor 106 (the second portion shown in dotted line in FIG. 12), through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 12, the fourth RLC circuit pathway does include resistor 110a, resistor 110b, and resistor 110c (which are shown in dotted line).

FIG. 13 is, in accordance with certain embodiments, a top-view schematic illustration of circuit lOOf comprising a first RLC circuit pathway, a second RLC circuit pathway comprising inductor 106’, a third RLC circuit pathway comprising inductor 106”, and a fourth RLC circuit pathway comprising inductor 106’”. The fourth RLC circuit pathway in FIG. 13 is represented as a dotted line. As shown in FIG. 13, the fourth RLC circuit pathway comprises first portion 128 of inductor 106, inductor 106’ electronically coupled to inductor 106, inductor 106” electronically coupled to inductor 106, inductor 106”’ electronically coupled to inductor 106, second portion 130 of inductor 106, and capacitor 108 electronically coupled to inductor 106 via electronically conductive pathway 114.

According to certain embodiments, inductor 106”’ is a portion of the fourth RLC circuit pathway, as inductor 106”’ functions as a compensating circuit element that electronically couples the third portion (e.g., the third finger) of inductor 106 to a fourth portion (e.g., a fourth finger) of inductor 106.

Inductor 106’” may be configured as described above with respect to inductor 106’ in reference to FIGS. 2A-2C.

According to some embodiments, when inductor 106 is electronically coupled to inductor 106’, inductor 106”, inductor 106’”, and capacitor 108, then inductor 106, inductor 106’, inductor 106”, inductor 106’”, and capacitor 108 can form a RLC circuit pathway (e.g., a fourth RLC circuit pathway), such as the RLC circuit pathway illustrated in FIG. 3. In some embodiments, a dedicated resistor can be incorporated into the RLC circuit pathway. In other embodiments, the intrinsic electrical resistivity of the circuit elements and/or the electronically conductive pathways coupling the circuit elements to each other can serve as the resistor of the RLC circuit pathway.

As shown in FIG. 13, the fourth RLC circuit pathway comprises, in certain embodiments, an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106 (the first portion shown in dotted line in FIG. 13), through inductor 106”’, through inductor 106”, through inductor 106’, through second portion 130 of inductor 106 (the second portion shown in dotted line in FIG. 13), through second end 126 of inductor 106, and to second electrode 118 of capacitor 108. As shown in FIG. 13, the fourth RLC circuit pathway does include inductor 106’, inductor 106”, and inductor 106”’ (which are shown in dotted line).

According to some embodiments, at least a portion of the fourth RLC circuit pathway may overlap with at least a portion of the third RLC circuit pathway. In certain embodiments, for example, the same capacitor (e.g., capacitor 108) is used in both the first RLC circuit pathway and the second RLC circuit pathway. In some embodiments, at least a portion of the inductor (e.g., inductor 106) is used in both the first RLC circuit pathway and the second RLC circuit pathway.

Referring to FIG. 12, for example, fourth RLC circuit pathway comprises electronically conductive pathway 114, first end 124 of inductor 106, first portion 128 of inductor 106, resistor 110b, resistor 110a, second portion 130 of inductor 106, and second end 126 of inductor 106 that overlaps with the third RLC circuit pathway. In fact, as shown in FIG. 12, all of the fourth RLC circuit pathway except for resistor 110c overlaps with the third RLC circuit pathway. Also, as shown in FIG. 12, some, but not all, of the third RLC circuit pathway overlaps with the fourth RLC circuit pathway.

Referring to FIG. 13, in some embodiments, fourth RLC circuit pathway comprises electronically conductive pathway 114, first end 124 of inductor 106, first portion 128 of inductor 106, inductor 106”, inductor 106’, second portion 130 of inductor 106, and second end 126 of inductor 106 that overlaps with the third RLC circuit pathway. In fact, as shown in FIG. 13, all of the fourth RLC circuit pathway except for inductor 106’” overlaps with the third RLC circuit pathway. Also, as shown in FIG. 13, some, but not all, of the third RLC circuit pathway overlaps with the fourth RLC circuit pathway.

As explained in further detail herein, the fourth RLC circuit pathway may be configured to produce a return signal, in accordance with certain embodiments. In certain embodiments, for example, the circuit may be a resonator and the fourth RLC circuit pathway may produce a return signal in response to a suitable input signal. Any of a variety of suitable input signals may be utilized. In some embodiments, for example, the sensor system is a wireless sensor system and the input signal comprises electromagnetic radiation. In other embodiments, the sensor system is a wired sensor system and the input signal comprises power (e.g., voltage, current) from a power supply. The return signal of the fourth RLC circuit pathway may, in some embodiments, be different than the return signal of the first RLC circuit pathway, the return signal of the second RLC circuit pathway, and the return signal of the third RLC circuit pathway. As described herein in greater detail, the return signal of the fourth RLC circuit pathway may be transmitted to and analyzed by a processor.

In some embodiments, the third RLC circuit pathway is configured to produce a return signal unless and until the third RLC circuit pathway is broken (e.g., via a crack). According to certain embodiments, the circuits described herein are configured such that, when a crack propagates through the third RLC circuit pathway, the fourth RLC circuit pathway still produces a return signal. In some embodiments, for example, the circuits are configured such that the fourth RLC circuit pathway still produces a return signal when a crack propagates through a portion (e.g., a finger) of the inductor in the third RLC circuit pathway. As a result of the fourth RLC circuit pathway being configured to produce a return signal even though the third RLC circuit pathway becomes nonfunctional (e.g., due to a crack), the circuits described herein advantageously may be used as a sensor (e.g., a crack sensor) to determine whether a crack has propagated through the third RLC circuit pathway.

FIG. 14 is, in accordance with certain embodiments, a top-view schematic diagram of circuit lOOe comprising a first RLC circuit pathway, a second RLC circuit pathway comprising resistor 110a, a third RLC circuit pathway comprising resistor 110b, and a fourth RLC circuit pathway comprising resistor 110c, wherein crack 602c has propagated through the third RLC circuit pathway. As shown in FIG. 14, the fourth RLC circuit pathway (e.g., comprising an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106, through resistor 110c, through resistor 110b, through resistor 110a, through second portion 130 of inductor 106, through second end 126 of inductor 106, and to second electrode 118 of capacitor 108), represented as a dotted line, is configured to produce a return signal even though crack 602c has propagated through the third RLC circuit pathway (e.g., through a portion of inductor 106 in the third RLC circuit pathway).

FIG. 15 is, in accordance with certain embodiments, a top-view schematic diagram of circuit lOOf comprising a first RLC circuit pathway, a second RLC circuit pathway comprising inductor 106’, a third RLC circuit pathway comprising inductor 106”, and a fourth RLC circuit pathway comprising inductor 106’”, wherein crack 602c has propagated through the third RLC circuit pathway. As shown in FIG. 15, the fourth RLC circuit pathway (e.g., comprising an electronically conductive pathway from first electrode 116 of capacitor 108, through electronically conductive pathway 114, through first end 124 of inductor 106, through first portion 128 of inductor 106, through inductor 106”’, through inductor 106”, through inductor 106’, through second portion 130 of inductor 106, through second end 126 of inductor 106, and to second electrode 118 of capacitor 108), represented as a dotted line, is configured to produce a return signal even though crack 602c has propagated through the third RLC circuit pathway (e.g., through a portion of inductor 106 in the third RLC circuit pathway).

Although four RLC circuit pathways are described herein and shown in the accompanying figures, a circuit may comprise more than four RLC circuit pathways (e.g., five RLC circuit pathways, ten RLC circuit pathways, twenty RLC circuit pathways, fifty RLC circuit pathways, etc.), depending on the size of the inductor. In some such embodiments, each RLC circuit pathway may be configured as described herein, such that, when a crack propagates through the “n” RLC circuit pathway, the “n+1” RLC circuit pathway still produces a return signal, wherein n is greater than or equal to 4.

According to some embodiments, a circuit described herein may comprise more than one inductor electronically coupled to a capacitor. FIG. 20A is a top-view schematic illustration of circuit lOOh comprising first inductor 106d electronically coupled to capacitor 108 and second inductor 106e electronically coupled to capacitor 108, wherein first portion 138 of circuit lOOh comprises a first RLC circuit pathway and a second RLC circuit pathway comprising resistor 1 lOd, and second portion 140 of circuit lOOh comprises a first RLC circuit pathway and a second RLC circuit pathway comprising resistor 1 lOe. In the embodiment shown in FIG. 20A, electronically conductive pathway 114d electronically couples first end 124a of first inductor 106d to first end 138a of first electrode 116 of capacitor 108, and second end 126a of first inductor 106d is electronically coupled to first end 138b of second electrode 118 of capacitor 108. Also in the embodiment shown in FIG. 20A, electronically conductive pathway 114e electronically couples first end 124b of second inductor 106e to second end 136b of second electrode 118 of capacitor 108, and second end 126b of second inductor 106e is electronically coupled to second end 136a of second electrode 118 of capacitor 108.

In some embodiments, the first RLC circuit pathway of first portion 138 of circuit lOOh comprises first inductor 106d and capacitor 108 electronically coupled to first inductor 106d via electronically conductive pathway 114d, and the second RLC circuit pathway of first portion 138 of circuit lOOh comprises first portion 128a of first inductor 106d, resistor 1 lOd electronically coupled to first inductor 106d, second portion 130a of first inductor 106d, and capacitor 108 electronically coupled to first inductor 106d via electronically conductive pathway 114d. In certain embodiments, the first RLC circuit pathway of second portion 140 of circuit lOOh comprises second inductor 106e and capacitor 108 electronically coupled to second inductor 106e via electronically conductive pathway 114e, and the second RLC circuit pathway of second portion 140 of circuit lOOh comprises first portion 128b of second inductor 106e, resistor I lOe electronically coupled to second inductor 106e, second portion 130b of second inductor 106e, and capacitor 108 electronically coupled to second inductor 106e via electronically conductive pathway 114e.

Although the embodiment shown in FIG. 20A shows that first portion 138 and second portion 140 of circuit lOOh each comprise a first RLC circuit pathway and a second RLC circuit pathway, first portion 138 and/or second portion 140 of circuit lOOh may comprise additional RLC circuit pathways (e.g., a third RLC circuit pathway, a fourth RLC circuit pathway, etc.), wherein each additional RLC circuit pathway comprises a compensating inductor, in accordance with certain embodiments.

FIG. 20B is a top-view schematic illustration of circuit lOOi comprising first inductor 106d electronically coupled to capacitor 108 and second inductor 106e electronically coupled to capacitor 108, wherein first portion 138 of circuit lOOi comprises a first RLC circuit pathway and a second RLC circuit pathway comprising inductor 106f, and second portion 140 of circuit lOOi comprises a first RLC circuit pathway and a second RLC circuit pathway comprising inductor 106g. In the embodiment shown in FIG. 20B, electronically conductive pathway 114d electronically couples first end 124a of first inductor 106d to first end 138a of first electrode 116 of capacitor 108, and second end 126a of first inductor 106d is electronically coupled to first end 138b of second electrode 118 of capacitor 108. Also in the embodiment shown in FIG. 20B, electronically conductive pathway 114e electronically couples first end 124b of second inductor 106e to second end 136b of second electrode 118 of capacitor 108, and second end 126b of second inductor 106e is electronically coupled to second end 136a of second electrode 118 of capacitor 108.

In some embodiments, the first RLC circuit pathway of first portion 138 of circuit lOOi comprises first inductor 106d and capacitor 108 electronically coupled to first inductor 106d via electronically conductive pathway 114d, and the second RLC circuit pathway of first portion 138 of circuit lOOi comprises first portion 128a of first inductor 106d, inductor 106f electronically coupled to first inductor 106d, second portion 130a of first inductor 106d, and capacitor 108 electronically coupled to first inductor 106d via electronically conductive pathway 114d. In certain embodiments, the first RLC circuit pathway of second portion 140 of circuit lOOi comprises second inductor 106e and capacitor 108 electronically coupled to second inductor 106e via electronically conductive pathway 114e, and the second RLC circuit pathway of second portion 140 of circuit lOOi comprises first portion 128b of second inductor 106e, inductor 106g electronically coupled to second inductor 106e, second portion 130b of second inductor 106e, and capacitor 108 electronically coupled to second inductor 106e via electronically conductive pathway 114e.

Although the embodiment shown in FIG. 20B shows that first portion 138 and second portion 140 of circuit lOOi each comprise a first RLC circuit pathway and a second RLC circuit pathway, first portion 138 and/or second portion 140 of circuit lOOi may comprise additional RLC circuit pathways (e.g., a third RLC circuit pathway, a fourth RLC circuit pathway, etc.), wherein each additional RLC circuit pathway comprises a compensating inductor, in accordance with certain embodiments.

Although the embodiments shown in FIGS. 20A-20B show two inductors electronically coupled to a capacitor, more than two inductors (e.g., three inductors, four inductors, etc.) electronically coupled to the capacitor are possible. In some embodiments, a circuit comprising more than one inductor (e.g., two inductors, three inductors, four inductors, etc.) electronically coupled to a capacitor advantageously increases the surface area of the sensor system when disposed on an article of which one wishes to monitor structural health.

According to certain embodiments, the first RLC circuit pathway may comprise an inductor and a first capacitor electronically coupled to the inductor, and the second RLC circuit pathway may comprise the inductor and a second capacitor electronically coupled to the inductor. FIG. 19A is a top-view schematic illustration of circuit 100g comprising a first RLC circuit pathway and a second RLC circuit pathway, wherein the first RLC circuit pathway comprises inductor 106 and first capacitor 108a electronically coupled to inductor 106, and the second RLC circuit pathway comprises inductor 106 and second capacitor 108b electronically coupled to inductor 106.

In some embodiments, a first electrode of first capacitor 108a may be electronically coupled to second end 126 of inductor 106 via electronically conductive pathway 114a, and a second electrode of first capacitor 108a may be electronically coupled to first portion 128 of inductor 106 via electronically conductive pathway 114b. In certain embodiments, a first electrode of second capacitor 108b may be electronically coupled to second portion 130 of inductor 106 via electronically conductive pathway 114b, and a second electrode of second capacitor 108b may be electronically coupled to first end 124 of inductor 106 via electronically conductive pathway 114c.

As explained elsewhere herein, capacitor 108 a and/or capacitor 108b may be an interdigitated capacitor, in certain embodiments. In other embodiments, capacitor 108a and/or capacitor 108b may be a parallel-plate capacitor.

FIG. 19B is a top-view schematic illustration of circuit 100g, wherein the first RLC circuit pathway is represented as a dotted line. As shown in FIG. 19B, the first RLC circuit pathway comprises, in some embodiments, first portion 128 of inductor 106 and capacitor 108a electronically coupled to inductor 106 via electronically conductive pathways 114a and 114b. In certain embodiments, for example, the first RLC circuit pathway comprises an electronically conductive pathway from a first electrode of capacitor 108a, through electronically conductive pathway 114a, through second end 126 of inductor 106, through first portion 128 of inductor 106, through electronically conductive pathway 114b, and to the second electrode of capacitor 108a. FIG. 19C is a top-view schematic illustration of circuit 100g, wherein the second RLC circuit pathway is represented as a dotted line. As shown in FIG. 19C, the second RLC circuit pathway comprises, in some embodiments, second portion 130 of inductor 106 and capacitor 108b electronically coupled to inductor 106 via electronically conductive pathways 114b and 114c. In certain embodiments, for example, the second RLC circuit pathway comprises an electronically conductive pathway from a first electrode of capacitor 108b, through electronically conductive pathway 114b, through second portion 130 of inductor 106, through first end 124 of inductor 106, through electronically conductive pathway 114c, and to the second electrode of capacitor 108b.

According to certain embodiments, different capacitors are used in each of the first RLC circuit pathway and the second RLC circuit pathway. Referring to FIGS. 19B- 19C, for example, capacitor 108a is used in the first RLC circuit pathway and capacitor 108b is used in the second RLC circuit pathway. In some embodiments, different portions of the inductor are used in the first RLC circuit pathway and the second RLC circuit pathway. Referring to FIGS. 19B-19C, for example, first portion 128 of inductor 106 is used in the first RLC circuit pathway, and second portion 130 of inductor 106 is used in the second RLC circuit pathway.

Referring to FIGS. 19B-19C, in some embodiments, the second RLC circuit pathway comprises electronically conductive pathway 114b that overlaps with the first RLC circuit pathway.

FIG. 19D is a top-view schematic illustration of circuit 100g, wherein crack 602d has propagated through the first RLC circuit pathway (e.g., through a portion of inductor 106 in the first RLC circuit pathway). In some embodiments, as shown in FIG. 19D, the second RLC circuit pathway, represented as a dotted line, is configured to produce a return signal even though crack 602d has propagated through the first RLC circuit pathway.

According to certain embodiments, the circuits described herein may be disposed in a sensor system. FIG. 16 is a block diagram showing an exemplary sensor system 800, in accordance with certain embodiments. As shown in FIG. 16, sensor system 800 comprises circuit 100.

In some embodiments, sensor system 800 is configured to measure an attribute of a signal of circuit 100 (e.g., a return signal of one or more of the RLC circuit pathways of the circuit). The signal of circuit may, in some embodiments, be an oscillating signal of the circuit. Suitable attributes of the signal of the circuit are described herein in further detail.

In some embodiments, sensor system 800 comprises an optional energy storage module 802. Energy storage module 802 is, in certain embodiments, a power supply that provides power to at least some components of sensor system 800. In some embodiments, energy storage module 802 may be connected to an external power supply (not shown in FIG. 16) that provides a suitable power supply (e.g., a voltage and/or current) for operation of sensor system 800, although such an external power connection is not required. Energy storage module 802 may be included in some embodiments wherein the sensor system is a wired sensor system. In certain embodiments wherein the sensor system is a wireless sensor system, energy storage module 802 may not be included in sensor system 800.

According to certain embodiments, energy storage module 802 is configured to store electrical energy and to provide power to at least a portion of the circuit. In one embodiment, energy storage module 802 may comprise a battery or capacitor for storing energy. In another embodiment, energy storage module 802 may additionally comprise one or more energy harvesters (not shown in FIG. 16) to recharge a battery or capacitor, such that the sensor system 800 can operate for a prolonged period of time without the need to be connected to an external power source such as a power outlet to recharge the battery or capacitor inside the energy storage module 802. The energy harvester may be a mechanical harvester that converts mechanical-acoustic energy such as vibration or human motion into electricity, a thermoelectric harvester that converts temperature gradient such as temperature difference between different parts of the sensor system 800 into electricity, a solar energy or photovoltaic harvester that converts ambient light into electricity, and/or an electrochemical energy harvester that converts electrochemical potential differences in the system environment into electricity.

In some embodiments, sensor system 800 comprises processor 804. The processor may be configured, in certain embodiments, to determine whether the structural defect (e.g., crack, hole, etc.) has propagated through the first RLC circuit pathway, the second RLC circuit pathway, and/or the third RLC circuit pathway based at least in part on a change in the attribute of the signal of the circuit. Examples of processors that could be used include, for example, commercially available processors such as one of the series x86; Celeron, Pentium, and Core processors, available from Intel; similar devices from AMD and Cyrix; the 680X0 series microprocessors available from Motorola; and the PowerPC microprocessor from IBM. Many other processors are also available.

Any suitable communication protocol may be used for processor 804 to communicate with circuit 100. In some embodiments, for example, processor 804 may receive one or more signals of the circuit from wireless communication module 806. In other embodiments, processor 804 may be a local processor attached to circuit 100. In yet other embodiments, processor 804 may be based on the cloud and communicate with circuit 100 using a wired or wireless interface.

According to some embodiments, the change in the attribute of the signal of the circuit is based on a change in an inductance of the circuit. Referring, for example, to FIGS. 6 A and 7 A, as crack 602a propagates through a portion of inductor 106 in the first RLC circuit pathway, the inductance of circuits 100a and 100b may change. In certain embodiments, an attribute of a signal of circuits 100a and 100b may change due to the change in the inductance of circuits 100a and 100b. In certain embodiments, the change in the inductance of circuits 100a and 100b may be a stepwise change in inductance. Referring to FIG. 6A, for example, the inductance of circuit 100a may, in some embodiments, change by a first amount as crack 602a propagates through the first RLC circuit pathway and resistor 110a becomes part of the second RLC circuit pathway. Referring to FIG. 7A, in certain embodiments, the inductance of circuit 100b may change by a first amount as crack 602b propagates through the first RLC circuit pathway and inductor 106’ becomes part of the second RLC circuit pathway.

In another embodiment, referring to FIGS. 10-11, as crack 602b propagates through a portion of inductor 106 in the second RLC circuit pathway, the inductance of circuits 100c and lOOd may change. In some such embodiments, an attribute of a signal of circuits 100c and lOOd may change due to the change in the inductance of circuits 100c and lOOd. In certain embodiments, the change in the inductance of circuits 100c and lOOd may be a stepwise change in inductance. Referring to FIG. 10, for example, the inductance of circuit 100c may, in some embodiments, change by a first amount as crack 602b propagates through the first RLC circuit pathway and resistor 110a becomes part of the second RLC circuit pathway. In certain embodiments, the inductance of circuit 100c may change by a second amount as crack 602b propagates through the second RLC circuit pathway and resistor 110b becomes part of the third RLC circuit pathway. Referring to FIG. 11, in certain embodiments, the inductance of circuit lOOd may change by a first amount as crack 602b propagates through the first RLC circuit pathway and inductor 106’ becomes part of the second RLC circuit pathway. In some embodiments, the inductance of circuit lOOd may change by a second amount as crack 602d propagates through the second RLC circuit pathway and inductor 106” becomes part of the third RLC circuit pathway.

In yet another embodiment, referring to FIGS. 14-15, as crack 602c propagates through a portion of inductor 106 in the third RLC circuit pathway, the inductance of circuits 100c and lOOf may change. In some such embodiments, an attribute of a signal of circuits 100c and lOOf may change due to the change in the inductance of circuits 100c and lOOf. In certain embodiments, the change in the inductance of circuits 100c and lOOf may be a stepwise change in inductance. Referring to FIG. 14, for example, the inductance of circuit 100c may, in some embodiments, change by a first amount as crack 602c propagates through the first RLC circuit pathway and resistor 110a becomes part of the second RLC circuit pathway. In certain embodiments, the inductance of circuit 100c may change by a second amount as crack 602b propagates through the second RLC circuit pathway and resistor 110b becomes part of the third RLC circuit pathway. In some embodiments, the inductance of circuit 100c may change by a third amount as crack 602b propagates through the third RLC circuit pathway and resistor 110c becomes part of the fourth RLC circuit pathway. Referring to FIG. 11, in certain embodiments, the inductance of circuit lOOf may change by a first amount as crack 602b propagates through the first RLC circuit pathway and inductor 106’ becomes part of the second RLC circuit pathway. In some embodiments, the inductance of circuit lOOf may change by a second amount as crack 602d propagates through the second RLC circuit pathway and inductor 106” becomes part of the third RLC circuit pathway. In certain embodiments, the inductance of circuit lOOf may change by a third amount as crack 602b propagates through the third RLC circuit pathway and inductor 106’” becomes part of the fourth RLC circuit pathway. In certain embodiments, the change in the attribute of the signal of the circuit comprises a change in a resonance frequency of the circuit.

The resonance frequency of the circuit may be any of a variety of suitable frequencies. In certain embodiments, for example, the circuit has a resonance frequency of greater than or equal to 10 Hz, greater than or equal to 100 Hz, greater than or equal to 1 kHz, greater than or equal to 10 kHz, greater than or equal to 100 kHz, greater than or equal to 1 MHz, or greater than or equal to 10 MHz. In some embodiments, the circuit has a resonance frequency of less than or equal to 100 MHz, less than or equal to 10 MHz, less than or equal to 1 MHz, less than or equal to 100 kHz, less than or equal to 10 kHz, less than or equal to 1 kHz, or less than or equal to 100 Hz. Combinations of the above recited ranges are possible (e.g., the circuit has a resonance frequency greater than or equal to 10 Hz and less than or equal to 10 MHz, the circuit has a resonance frequency greater than or equal to 10 kHz and less than or equal to 100 MHz). Other ranges are also possible.

The change in the resonance frequency of the circuit may be any of a variety of suitable values. In certain embodiments, for example, the change in the resonance frequency of the circuit is greater than or equal to 1%, greater than or equal to 5%, greater than or equal to 10%, greater than or equal to 15%, greater than or equal to 20%, greater than or equal to 25%, greater than or equal to 30%, greater than or equal to 35%, greater than or equal to 40%, or greater than or equal to 45%. In some embodiments, the change in the resonance frequency of the circuit is less than or equal to 50%, less than or equal to 45%, less than or equal to 40%, less than or equal to 35%, less than or equal to 30%, less than or equal to 25%, less than or equal to 20%, less than or equal to 15%, less than or equal to 10%, or less than or equal to 5%. Combinations of the above recited range are possible (e.g., the change in the resonance frequency of the circuit is greater than or equal to 1% and less than or equal to 50%, the change in the resonance frequency of the circuit is greater than or equal to 20% and less than or equal to 30%). Other ranges are also possible.

The percentage change in the resonance frequency of the circuit is measured by subtracting the initial resonance frequency from the final resonance frequency, dividing the absolute value of that difference by the initial resonance frequency, and multiplying the result by 100%. Stated mathematically, the percentage change in resonance frequency (%ARF) is calculated as follows: where RFi is the resonance frequency in a first state (e.g., before crack propagation) and RF is the resonance frequency in a second, later state (e.g., after crack propagation).

In certain embodiments wherein the crack has propagated through the first RLC circuit pathway, the change in the resonance frequency of the circuit is measured by calculating the percent change between: (i) the resonance frequency of the circuit prior to the crack propagating through the first RLC circuit pathway; and (ii) the resonance frequency of the circuit after the crack has propagated through the first RLC circuit pathway. In some embodiments wherein the crack has propagated through the second RLC circuit pathway, the change in the resonance frequency of the circuit is measured by calculating the percent change between: (i) the resonance frequency of the circuit prior to the crack propagating through the second RLC circuit pathway; and (ii) the resonance frequency of the circuit after the crack has propagated through the second RLC circuit pathway. In some embodiments wherein the crack has propagated through the third RLC circuit pathway, the change in the resonance frequency of the circuit is measured by calculating the percent change between: (i) the resonance frequency of the circuit prior to the crack propagating through the third RLC circuit pathway; and (ii) the resonance frequency of the circuit after the crack has propagated through the third RLC circuit pathway.

According to some embodiments, the change in the resonance frequency of the circuit is proportional to a length of the crack through the first RLC circuit pathway, the second RLC circuit pathway, and/or the third RLC circuit pathway. In certain embodiments, for example, the change in the resonance frequency of the circuit is proportional to a length of the crack through one or more portions (e.g., one or more fingers) of the inductor in the first RLC circuit pathway, the second RLC circuit pathway, and/or the third RLC circuit pathway.

FIGS. 17A-17C are a schematic illustration depicting the concept of a change in an attribute of a signal of a circuit as a function of crack length, in accordance with certain embodiments. Additional circuit components have been removed from FIGS. 17A-17C for clarity.

Referring to FIG. 17A, in some embodiments, as crack 602 propagates through a first portion (e.g., a first finger) of inductor 106 in the first RLC circuit pathway, the resonance frequency of a circuit comprising inductor 106 changes by a first amount. Referring to FIG. 17B, in some embodiments, as crack 602 propagates through a second portion (e.g., a second finger) of inductor 106 in the second RLC circuit pathway, the resonance frequency of a circuit comprising inductor 106 changes by a second amount, wherein the second amount is greater than the first amount. Referring to FIG. 17C, in certain embodiments, as crack 602 propagates through a third potion (e.g., a third finger) of inductor 106 in the third RLC circuit pathway, the resonance frequency of a circuit comprising inductor 106 changes by a third amount, wherein the third amount is greater than the second amount.

In some embodiments, the change in the attribute of the signal of the circuit comprises a change in a quality factor (or Q factor) of the circuit. As used herein, the phrase “quality factor” is given its ordinary meaning in the art and refers to a ratio of the initial energy stored in an oscillator to the energy lost in one cycle of oscillation. In certain embodiments, the quality factor is calculated using the following equation: wherein f_r is the resonant frequency and d/'is the resonance width or full width at half maximum (FWHM).

According to certain embodiments, to account for small quality factor values (i.e., less than 1), a 10% quality factor or a 20% quality factor can be calculated according to the equation above, wherein zl/is the resonance width or full width at 90% or 80% of the maximum, respectively.

The quality factor of the circuit may be any of a variety of suitable values. In certain embodiments, for example, the circuit has a quality factor greater than or equal to 0.1, greater than or equal to 0.5, greater than or equal to 1, greater than or equal to 5, greater than or equal to 10, greater than or equal to 15, greater than or equal to 20, or greater than or equal to 25. In some embodiments, the circuit has a quality factor less than or equal to 50, less than or equal to 25, less than or equal to 20, less than or equal to 15, less than or equal to 10, less than or equal to 5, less than or equal to 1, or less than or equal to 0.5. Combinations of the above recited ranges are possible (e.g., the circuit has a quality factor greater than or equal to 0.5 and less than or equal to 50, the circuit has quality factor greater than or equal to 5 and less than or equal to 10). Other ranges are also possible.

The change in the quality factor of the circuit may be any of a variety of suitable values. In certain embodiments, for example, the change in the quality factor of the circuit is greater than or equal to 1%, greater than or equal to 5%, greater than or equal to 10%, greater than or equal to 15%, greater than or equal to 20%, greater than or equal to 25%, greater than or equal to 30%, greater than or equal to 35%, greater than or equal to 40%, or greater than or equal to 45%. In some embodiments, the change in the quality factor of the circuit is less than or equal to 50%, less than or equal to 45%, less than or equal to 40%, less than or equal to 35%, less than or equal to 30%, less than or equal to 25%, less than or equal to 20%, less than or equal to 15%, less than or equal to 10%, or less than or equal to 5%. Combinations of the above recited range are possible (e.g., the change in the quality factor of the circuit is greater than or equal to 1% and less than or equal to 50%, the change in the quality factor of the circuit is greater than or equal to 20% and less than or equal to 30%). Other ranges are also possible.

The percentage change in the quality factor of the circuit is measured by subtracting the initial quality factor from the final quality factor, dividing the absolute value of that difference by the initial quality factor, and multiplying the result by 100%. Stated mathematically, the percentage change in quality factor (%AQ) is calculated as follows: where Qi is the quality factor in a first state (e.g., before crack propagation) and Qf is the quality factor in a second, later state (e.g., after crack propagation).

In certain embodiments wherein the crack has propagated through the first RLC circuit pathway, the change in the quality factor of the circuit is measured by calculating the percent change between: (i) the quality factor of the circuit prior to the crack propagating through the first RLC circuit pathway; and (ii) the quality factor of the circuit after the crack has propagated through the first RLC circuit pathway. In some embodiments wherein the crack has propagated through the second RLC circuit pathway, the change in the quality factor of the circuit is measured by calculating the percent change between: (i) the quality factor of the circuit prior to the crack propagating through the second RLC circuit pathway; and (ii) the quality factor of the circuit after the crack has propagated through the second RLC circuit pathway. In some embodiments wherein the crack has propagated through the third RLC circuit pathway, the change in the quality factor of the circuit is measured by calculating the percent change between: (i) the quality factor of the circuit prior to the crack propagating through the third RLC circuit pathway; and (ii) the quality factor of the circuit after the crack has propagated through the third RLC circuit pathway.

According to certain embodiments, the change in the quality factor of the circuit is proportional to a length of the crack through the first RLC circuit pathway. According to some embodiments, the change in the quality factor of the circuit is proportional to a length of the crack through the first RLC circuit pathway, the second RLC circuit pathway, and/or the third RLC circuit pathway. In certain embodiments, for example, the change in the quality factor of the circuit is proportional to a length of the crack through one or more portions (e.g., one or more fingers) of the inductor in the first RLC circuit pathway, the second RLC circuit pathway, and/or the third RLC circuit pathway.

Referring to FIG. 17A, in some embodiments, as crack 602 propagates through a first portion (e.g., a first finger) of inductor 106 in the first RLC circuit pathway, the quality factor of a circuit comprising inductor 106 changes by a first amount. Referring to FIG. 17B, in some embodiments, as crack 602 propagates through a second portion (e.g., a second finger) of inductor 106 in the second RLC circuit pathway, the quality factor of a circuit comprising inductor 106 changes by a second amount, wherein the second amount is greater than the first amount. Referring to FIG. 17C, in certain embodiments, as crack 602 propagates through a third potion (e.g., a third finger) of inductor 106 in the third RLC circuit pathway, the quality factor of a circuit comprising inductor 106 changes by a third amount, wherein the third amount is greater than the second amount.

The crack may have any of a variety of suitable lengths. In certain embodiments, for example, the crack has a length greater than or equal to 10 micrometers, greater than or equal to 100 micrometers, greater than or equal to 1 millimeter, greater than or equal to 1 centimeter, greater than or equal to 10 micrometers, or greater than or equal to 1 meter. In certain embodiments, the crack has a length less than or equal to 10 meters, less than or equal to 1 meter, less than or equal to 10 centimeters, less than or equal to 1 centimeter, less than or equal to 1 millimeter, or less than or equal to 100 micrometers. Combinations of the above recited ranges are possible (e.g., the crack has a length greater than or equal to 10 micrometers and less than or equal to 10 meters, the crack has a length greater than or equal to 1 millimeter and less than or equal to 1 centimeter). Other ranges are also possible.

Referring to FIG. 16, according to certain embodiments, sensor system 800 is a wireless sensor system. In some embodiments, for example, sensor system 800 comprises wireless communication module 806. Wireless communication module 806 may be configured, in some embodiments, to wirelessly communicate information external to sensor system 800. In some embodiments, for example, wireless communication module 806 may be configured to send a signal (e.g., a wireless signal) to circuit 100.

One or more components of sensor system 800 may be disposed in a housing (not shown in FIG. 16). For example, circuit 100, energy storage module 802, processor 804, and/or wireless communication module 806 may be housed in a housing. Optionally or additionally, processor 804 may be provided outside the housing, for example, as a remote processor in the cloud that is coupled to circuit 100 and/or wireless communication module 806 using any suitable communication means.

As noted above, in some embodiments, the circuits described herein can be used as RLC circuits (e.g., wireless RLC circuits). FIG. 18 is a schematic illustration showing one mode of operation, in which resonant inductive pulse-echo methods are employed.

The idea of the pulse-echo non-invasive sensor architecture, in accordance with certain embodiments, is to keep the embedded sensing circuit as simple as possible and move the complexity to the reader. The measurement approach is, in accordance with certain embodiments, “pulse echo.” In such embodiments, a reader can apply a drive waveform to power the resonator. In some embodiments, the drive waveform is subsequently removed for detection. After removing the drive waveform, the circuit can generate a signal (e.g., a decaying signal in a frequency of the inductor and capacitor), which can be used to determine a mechanical characteristic of the circuit. In some embodiments, determining the mechanical characteristic of the circuit comprises determining whether a mechanical transformation has occurred in the circuit; determining the type of mechanical transformation that has occurred in the circuit; determining whether a structural defect (e.g., a crack, a hole, etc.) is present within the circuit; and/or determining the type of structural defect that is present in the circuit. For example, in accordance with some embodiments, if a mechanical transformation has occurred in the circuit, the signal that is returned to the reader by the circuit exhibits a change in the resonance frequency of the circuit and/or a change in the quality factor of the circuit; but if a mechanical transformation has not occurred in the circuit, the signal that is returned to the reader by the sensor does not exhibit a change in the resonance frequency of the circuit and/or a change in the quality factor of the circuit. As one example, the reader can use, in some embodiments, ADC to sample the information and can perform a finite Fourier transform (FFT) to estimate the change in the resonance frequency of the circuit and/or the change in the quality factor of the circuit, and can map the change in the resonance frequency of the circuit and/or the change in the quality factor of the circuit to a mechanical transformation. Any of a variety of mechanical transformations and/or structural defects of the circuit may be detected using the sensor system, including cracks, holes, and the like.

According to certain embodiments, a method for operating a sensor system is described. In some embodiments, the method comprises applying energy to a portion of a sensor system (e.g., a circuit of a sensor system). For example, in certain embodiments, the sensor system is a wireless sensor system and the applying comprises applying electromagnetic radiation (e.g., a drive waveform) from a reader to the circuit of the wireless sensor system. In other embodiments, the sensor system is a wired sensor system and the applying comprises applying power (e.g., voltage and/or current) from a power supply (e.g., an energy storage module) to the circuit of the wired sensor system. As a result of applying energy to the circuit, the circuit may produce a signal, in some embodiments. According to certain embodiments, the signal of the circuit may be produced from a RLC circuit pathway (e.g., a first RLC circuit pathway, a second RLC circuit pathway, a third RLC circuit pathway, a fourth RLC circuit pathway). The signal may be a return signal that is returned to the reader, in some embodiments. In certain embodiments, the method comprises measuring, with a sensor system, an attribute of the signal of the circuit disposed in the sensor system. In some embodiments, for example, the measuring comprises measuring the attribute of the signal with a reader. According to some embodiments, the measuring comprises a “pulse echo” approach, as shown in FIG. 18 and described herein in greater detail. In certain embodiments, the attribute of the signal may be a resonance frequency of the circuit and/or a quality factor of the circuit.

In some embodiments, the method comprises measuring, with a sensor system, a change in the attribute of the signal of the circuit disposed in the sensor system. According to some embodiments, for example, the attribute of the signal of the circuit may change due to a structural defect (e.g., a crack) propagating through a portion of the circuit. In accordance with certain embodiments, the sensor system may be configured to measure: (i) a first signal (e.g., a first return signal of a first RLC circuit pathway) prior to the structural defect propagating through a portion of the circuit (e.g., a first RLC circuit pathway); and (ii) a second signal (e.g., a second return signal of a second RLC circuit pathway) after the structural defect has propagated through the portion of the circuit (e.g., the first RLC circuit pathway). In some embodiments, the method comprises transmitting signals to and/or receiving signals (e.g., the first signal and the second signal) with a processor. In some embodiments, the processor can be used to compare a property of the first signal (e.g., a quality factor and/or a resonance frequency, for example, prior to a defect propagating through the circuit) to a corresponding property of the second signal (e.g., a quality factor and/or a resonance frequency, for example, after a defect propagates through the circuit)

According to certain embodiments, the method comprises determining, with the processor, whether a structural defect (e.g., a crack) has propagated through a RLC circuit pathway of the circuit based at least in part on a change in the attribute of the signal of the circuit. In some embodiments, for example, the processor may be configured to determine the change in the attribute of the signal of the circuit by calculating a percent change between: (i) the attribute of the signal prior to the structural defect propagating through the portion of the circuit (e.g., a first RLC circuit pathway); and (ii) the attribute of the signal after the structural defect has propagated through the portion of the circuit (e.g., the first RLC circuit pathway). In certain embodiments, the method comprises determining, with the processor, a location of the crack based at least in part on the return signal of the second RLC circuit pathway. According to some embodiments, for example, the circuit may comprise a first compensating circuit element and a second compensating circuit element electronically coupling a first portion of the first RLC circuit pathway (e.g., a first portion of an inductor of the first RLC circuit pathway) to a second portion of the first RLC circuit pathway (e.g., a second portion of the inductor of the first RLC circuit pathway). A property of the return signal of the second RLC circuit pathway may, in some embodiments, depend on whether the second RLC circuit pathway comprises the first compensating circuit element or the second compensating circuit element or both. For example, in some such embodiments, the return signal has a first resonance frequency profile when both the first and second RLC circuit pathways are active, a second resonance frequency profile when just the first RLC circuit pathway is active (e.g., because a crack has propagated through the second RLC circuit pathway), and a third resonance frequency profile when just the second RLC circuit pathway is active (e.g., because a crack has propagated through the first RLC circuit pathway). In some such embodiments, the processor may be configured to determine the location of the crack based at least in part on the resonance frequency profile of the return signal. For example, if the resonance frequency profile of the return signal is consistent with only the first RLC circuit pathway being active, the processor can determine that the defect is present somewhere in the second RLC circuit pathway, and if the resonance frequency profile of the return signal is consistent with only the second RLC circuit pathway being active, the processor can determine that the defect is present somewhere in the first RLC circuit pathway.

As another example, in some such embodiments, the return signal has a first quality factor profile when both the first and second RLC circuit pathways are active, a second quality factor profile when just the first RLC circuit pathway is active (e.g., because a crack has propagated through the second RLC circuit pathway), and a third quality factor profile when just the second RLC circuit pathway is active (e.g., because a crack has propagated through the first RLC circuit pathway). In some such embodiments, the processor may be configured to determine the location of the crack based at least in part on the quality factor profile of the return signal. For example, if the quality factor profile of the return signal is consistent with only the first RLC circuit pathway being active, the processor can determine that the defect is present somewhere in the second RLC circuit pathway, and if the quality factor profile of the return signal is consistent with only the second RLC circuit pathway being active, the processor can determine that the defect is present somewhere in the first RLC circuit pathway.

One example of a sensor comprising a resistance-based compensating circuit for detecting crack propagation through a portion of the circuit is shown in FIG. 21A and described with respect to FIGS. 21A-21D. FIG. 21A shows, according to some embodiments, a sensor electrical equivalent diagram of a resistance-based compensating circuit. The circuit had a resonance frequency of 1 MHz and a quality factor of 0.862 with no crack propagation through a portion of the circuit, wherein the quality factor was determined according to the following equation: wherein f_r is the resonance frequency and //, -f_a is Af or the resonance width or full width at half maximum, with // = 1 MHz, /;, = 0.7 MHz, and//, = 1.86 MHz (see FIG. 21B). When a crack propagated through the first turn of the inductor, the turn of the inductor was replaced by a 1 ohm resistor, resulting in a resonance frequency of 1.09 MHz and a quality factor of 0.712, with /; = 1.09 MHz, /;, = 0.66 MHz, and//, = 2.19 MHz (see FIG. 21C). As the crack propagated through the next three turns of the inductor, each turn of the inductor was replaced by a 1 ohm resistor, resulting in a resonance frequency of 1.12 MHz and a quality factor of 0.516, with /; = 1.12 MHz, /;, = 0.63 MHz, and//, = 2.8 MHz (see FIG. 21D).

To account for the low quality factors described with reference to FIGS. 21B- 21D, a 10% quality factor was determined according to the following equation:

> fr Qw% —

Jb J a wherein f_r is the resonance frequency and//, -f_a is the resonance width or full width at 90% of the maximum.

The circuit had a resonance frequency of 1.05 MHz and a 10% quality factor of 1.615 with no crack propagation through a portion of the circuit, with /; = 1.05 MHz, /;, = 0.821 MHz, and //, = 1.47 MHz (see FIG. 21E). When a crack propagated through the first two turns of the inductor, each turn of the inductor was replaced by a 1 ohm resistor, resulting in a resonance frequency of 1.11 MHz and a 10% quality factor of 1.434, with f_r= 1.11 MHz, fa = 0.826 MHz, and/z> = 1.6 MHz (see FIG. 21F). As the crack propagated through the next two turns of the inductor, each turn of the inductor was replaced by a 1 ohm resistor, resulting in a resonance frequency of 1.19 MHz and a quality factor of 0.997, with /i = 1.19 MHz,/_a = 0.816 MHz, and/z> = 2.01 MHz (see FIG. 21G).

The RLC circuit sensor decay as a function of quality factor is shown in FIGS. 22A-22C for compensating resistors with various resistances. FIG. 22A shows the RLC circuit sensor decay as a function of quality factor with a RLC circuit comprising an inductor having an inductance of 1 microhenry, a capacitor having a capacitance of 0.03 microfarads, and a resistor having a resistance of 0.5 ohms. FIG. 22B shows the RLC circuit sensor decay as a function of quality factor with a RLC circuit comprising an inductor having an inductance of 1 microhenry, a capacitor having a capacitance of 0.03 microfarads, and a resistor having a resistance of 1 ohm. FIG. 22C shows the RLC circuit sensor decay as a function of quality factor with a RLC circuit comprising an inductor having an inductance of 1 microhenry, a capacitor having a capacitance of 0.03 microfarads, and a resistor having a resistance of 5 ohms.

An example of a sensor comprising an inductance-based compensating circuit for detecting crack propagation through a portion of the circuit is shown in FIG. 23A and described with respect to FIGS. 23A-23D. FIG. 23A shows, according to some embodiments, a sensor electrical equivalent diagram of an inductance-based compensating circuit. The circuit had a resonance frequency of 1.01 MHz with no crack propagation through a portion of the circuit (see FIG. 23B). When a crack propagated through the first turn of the inductor, the turn of the inductor was replaced by a 200 nH inductor, resulting in a resonance frequency of 961.24 kHz (see FIG. 23C). Since the circuit inductor broke due to the crack, the total inductance of the circuit increased, reflecting a lower resonance frequency. As the crack propagated through the next three turns of the inductor, each turn of the inductor was replaced by a 200 nH inductor, resulting in a resonance frequency of 853.29 kHz (see FIG. 23D).

An example of a sensor comprising a circuit for detecting crack propagation through a portion of the circuit, wherein the change in the resonance frequency of the circuit is proportional to a length of the crack through the inductor of the circuit, is described with respect to FIGS. 24A-24B and FIGS. 25A-25B. FIG. 24A shows, according to some embodiments, the transfer function of crack propagation through the turns of the inductor to crack length. FIG. 24B shows, according to some embodiments, the transfer function of the sensor echo frequency to crack length. FIG. 25A shows, according to some embodiments, the resonance frequency of a circuit with no cracks. As shown in FIG. 25A, the circuit had a resonance frequency of 1.01 MHz. FIG. 25B shows, according to some embodiments, the resonance frequency of a circuit with a crack through the first turn of an inductor. As shown in FIG. 25B, the circuit had a resonance frequency of 961.24 kHz.

An example of a sensor comprising an inductance-based compensating circuit for determining a location of one or more cracks propagating from an exterior of the circuit to an interior of the circuit is shown in FIG. 26A. As shown in FIG. 26A, circuit lOOj comprises inductor 106 and capacitor 108 electronically coupled to inductor 106. In certain embodiments, circuit lOOj comprises compensating inductors 106a, 106b, 106c, and 106d electronically coupled to inductor 106 via electronically conductive pathways. As shown in FIG. 26A, when crack 602a propagates from an exterior of circuit lOOj to an interior of circuit lOOj, e.g., through a portion of the first RLC circuit pathway in quadrant I, the second RLC circuit pathway comprising inductor 106a is still configured to produce a return signal. In certain embodiments, when crack 602b propagates from an exterior of circuit lOOj to an interior of circuit lOOj, e.g., through a portion of the first RLC circuit pathway in quadrant III, the second RLC circuit pathway comprising inductor 106c is still configured to produce a return signal. As explained in further detail herein, in some embodiments, the return signal (e.g., of the second RLC circuit pathway) may be detected and analyzed (e.g., by a processor), and the sensor system may determine a location of the crack, such as a quadrant of the circuit in which the crack has propagated, based on the analysis. In some embodiments, the sensor system may determine an angle range of where the crack propagates through the inductor.

An example of a sensor comprising an inductance-based compensating circuit for determining a location of one or more cracks propagating from an interior of the circuit to an exterior of the circuit is shown in FIG. 26B. As shown in FIG. 26B, circuit 100k comprises inductor 106 and capacitor 108 electronically coupled to inductor 106. In certain embodiments, circuit 100k comprises compensating inductors 106a, 106b, 106c, and 106d electronically coupled to inductor 106 via electronically conductive pathways. As shown in FIG. 26B, when crack 602a propagates from an interior of circuit 100k to an exterior of circuit 100k, e.g., through a portion of the first RLC circuit pathway in quadrant II, the second RLC circuit pathway comprising inductor 106b is still configured to produce a return signal. In certain embodiments, when crack 602b propagates from an interior of circuit 100k to an exterior of circuit 100k, e.g., through a portion of the first RLC circuit pathway in quadrant IV, the second RLC circuit pathway comprising inductor 106d is still configured to produce a return signal. As explained in further detail herein, in some embodiments, the return signal (e.g., of the second RLC circuit pathway) may be detected and analyzed (e.g., by a processor), and the sensor system may determine a location of the crack, such as a quadrant of the circuit in which the crack has propagated, based on the analysis. In some embodiments, the sensor system may determine an angle range of where the crack propagates through the inductor.

While several embodiments of the present invention have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the functions and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the present invention. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the teachings of the present invention is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific embodiments of the invention described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, the invention may be practiced otherwise than as specifically described and claimed. The present invention is directed to each individual feature, system, article, material, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, and/or methods, if such features, systems, articles, materials, and/or methods are not mutually inconsistent, is included within the scope of the present invention.

The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified unless clearly indicated to the contrary. Thus, as a non-limiting example, a reference to “A and/or B,” when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A without B (optionally including elements other than B); in another embodiment, to B without A (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of’ or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of.” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

Some embodiments may be embodied as a method, of which various examples have been described. The acts performed as part of the methods may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include different (e.g., more or less) acts than those that are described, and/or that may involve performing some acts simultaneously, even though the acts are shown as being performed sequentially in the embodiments specifically described above.

Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.

In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of’ and “consisting essentially of’ shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.

Claims

CLAIMS What is claimed is:

1. A sensor system, comprising: a circuit comprising: a first RLC circuit pathway; and a second RLC circuit pathway; wherein the circuit is configured such that, when a crack propagates through the first RLC circuit pathway, the second RLC circuit pathway still produces a return signal.

2. A sensor system, comprising: a single RLC circuit comprising: a capacitor; an inductor; a first RLC circuit pathway comprising a first portion of the inductor; and a second RLC circuit pathway comprising a second portion of the inductor, wherein the first portion of the inductor and the second portion of the inductor are not identical but at least partially overlap with each other.

3. The sensor system of claim 2, wherein the first RLC circuit pathway and the second RLC circuit pathway ensure that, when a crack propagates through the first RLC circuit pathway, the second RLC circuit pathway still produces a return signal, the return signal produced by the second RLC circuit pathway being different from a return signal produced the single RLC circuit prior to the crack propagating through the first RLC circuit pathway.

4. The sensor system of any one of claims 1-3, wherein the sensor system is a wireless sensor system.

5. The sensor system of any one of claims 1-4, wherein the first RLC circuit pathway comprises an inductor comprising elongated nanostructures that serve an electronic function of the inductor.

6. The sensor system of any one of claims 1-5, wherein the first RLC circuit pathway comprises a capacitor comprising elongated nanostructures that serve an electronic function of the capacitor.

7. The sensor system of any one of claims 5-6, wherein an inductor of the second RLC circuit pathway is electronically coupled to the inductor of the first RLC circuit pathway.

8. The sensor system of any one of claims 5-7, wherein a resistor of the second RLC circuit pathway is electronically coupled to the inductor of the first RLC circuit pathway.

9. The sensor system of any one of claims 5-8, wherein the circuit is configured such that, when the crack propagates through the inductor of the first RLC circuit pathway, the second RLC circuit pathway still produces the return signal.

10. The sensor system of any one of claims 1-9, wherein the sensor system is configured to measure an attribute of a signal of the circuit.

11. The sensor system of claim 10, further comprising a processor configured to determine whether the crack has propagated through the first RLC circuit pathway based at least in part on a change in the attribute of the signal of the circuit.

12. The sensor system of claim 11, wherein the processor is configured to determine a location of the crack based on the return signal of the second RLC circuit pathway.

13. The sensor system of any one of claims 10-12, wherein the signal of the circuit is an oscillating signal of the circuit.

14. The sensor system of any one of claims 11-13, wherein the change in the attribute of the signal of the circuit is based on a change in an inductance of the circuit.

15. The sensor system of any one of claims 11-14, wherein the change in the attribute of the signal of the circuit comprises a change in a resonance frequency of the circuit.

16. The sensor system of claim 15, wherein the change in the resonance frequency of the circuit is proportional to a length of the crack through the first RLC circuit pathway.

17. The sensor system of any one of claims 11-16, wherein the change in the attribute of the signal of the circuit comprises a change in a quality factor of the circuit.

18. The sensor system of claim 17, wherein the change in the quality factor of the circuit is proportional to a length of the crack through the first RLC circuit pathway.

19. The sensor system of any one of claims 1-18, further comprising an energy storage module configured to store electrical energy and to provide power to at least a portion of the circuit.

20. The sensor system of any one of claims 1-19, wherein the circuit further comprises a third RLC circuit pathway, and wherein the circuit is configured such that, when the crack propagates through the second RLC circuit pathway, the third RLC circuit pathway still produces a return signal.

21. The sensor system of claim 20, wherein the circuit further comprises a fourth RLC circuit pathway, and wherein the circuit is configured such that, when the crack propagates through the third RLC circuit pathway, the fourth RLC circuit pathway still produces a return signal.

22. The sensor system of any one of claims 1-21, wherein the crack propagates from an exterior of the circuit towards an interior of the circuit.

23. The sensor system of any one of claims 1-21, wherein the crack propagates from an interior of the circuit towards an exterior of the circuit.

24. The sensor system of claim 1, wherein: the sensor system is a wireless sensor system, wherein the wireless sensor system is configured to measure an attribute of an oscillating signal of the circuit; the first RLC circuit pathway comprises an inductor and a capacitor electronically coupled to the inductor; the inductor has a first dimension greater than or equal to 10 micrometers and less than or equal to 1 meter; the inductor has second dimension greater than or equal to 10 micrometers and less than or equal to 1 meter, wherein the second dimension is perpendicular to the first dimension; and the wireless sensor system further comprises: a processor configured to determine whether the crack has propagated through the first RLC circuit pathway based at least in part on a change in the attribute of the oscillating signal of the circuit, wherein the change in the attribute of the oscillating signal of the circuit comprises a change in a resonance frequency of the circuit and/or a change in a quality factor of the circuit.

25. A method for operating a sensor system, comprising: measuring, with the sensor system, an attribute of a signal of a circuit disposed in the sensor system, wherein the circuit comprises: a first RLC circuit pathway; and a second RLC circuit pathway, wherein the circuit is configured such that, when a crack propagates through the first RLC circuit pathway, the second RLC circuit pathway still produces a return signal; and determining, with a processor, whether the crack has propagated through the first RLC circuit pathway based at least in part on a change in the attribute of the signal of the circuit.

26. A method for operating a sensor system, comprising: measuring, with the sensor system, an attribute of a signal of a single circuit disposed in the sensor system, wherein the single circuit comprises: a capacitor; an inductor; a first RLC circuit pathway comprising a first portion of the inductor; and a second RLC circuit pathway comprising a second portion of the inductor, wherein the first portion of the inductor and the second portion of the inductor are not identical but at least partially overlap with each other; and determining, with a processor, whether the crack has propagated through the first RLC circuit pathway based at least in part on a change in the attribute of the signal of the circuit.

27. The method of claim 26, wherein the first RLC circuit pathway and the second RLC circuit pathway ensure that, when the crack propagates through the first RLC circuit pathway, the second RLC circuit pathway still produces a return signal, the return signal produced by the second RLC circuit pathway being different from a return signal produced the single RLC circuit prior to the crack propagating through the first RLC circuit pathway.

28. The method of any one of claims 25-27, wherein the sensor system is a wireless sensor system.

29. The method of any one of claims 25-28, further comprising providing, with an energy storage module configured to store electrical energy, power to at least a portion of the circuit.

30. The method of any one of claims 25-29, wherein the signal of the circuit is an oscillating signal of the circuit.

31. The method of any one of claims 25-30, further comprising receiving signals representing the change in the attribute of the signal of the circuit with the processor.

32. The method of any one of claims 25-31, wherein the change in the attribute of the signal of the circuit is based on a change in an inductance of the circuit.

33. The method of any one of claims 25-32, wherein the change in the attribute of the signal of the circuit comprises a change in a resonance frequency of the circuit.

34. The method of claim 33, wherein the change in the resonance frequency of the circuit is proportional to a length of the crack through the first RLC circuit pathway.

35. The method of any one of claims 25-34, wherein the change in the attribute of the signal of the circuit comprises a change in a quality factor of the circuit.

36. The method of claim 35, wherein the change in the quality factor of the circuit is proportional to a length of the crack through the first RLC circuit pathway.

37. The method of any one of claims 25-36, further comprising determining, with the processor, a location of the crack based at least in part on the return signal of the second RLC circuit pathway.