Enhanced RF response of 3D-printed wireless LC sensors using dielectrics with high permittivity

LC sensors consist of an inductor (L) and a capacitor (C), which are connected to each other and are in resonance with each other. Each sensor has its own resonant frequency, which is related to its inductance and capacitance. In order to detect the resonant frequency of an LC sensor, an external readout coil that is connected to a vector network analyzer (VNA) is placed on top of the sensor, to interact with the magnetic field that comes from the inductor of the sensor. The readout coil will have a mutual inductance with the inductor of the sensor. Therefore, the signature signal directly related to mutual inductance can be transferred from the sensor to the VNA. The resonant frequency of an LC sensor with the capacitance of C_S and the inductance of L_S can be expressed as equation (1).

$$\begin{equation}f = \frac{1}{{2\pi \sqrt {{C_{\text{S}}}{L_{\text{S}}}} }}.\end{equation} \tag{ 1 }$$

As a means of achieving sensors with different resonant frequencies, three compact sensors with differing capacitance have been designed. As shown in figure 1(a), the three sensors have 3.75 turns of the inductor on the outside, which is connected to the curved and interdigitated capacitor (IDC) at the center. The width of the inductor and each finger of the IDC is 300 µm, and the gap between the inductor's turns and the capacitor's fingers is 300 µm. The outer diameter of the sensor is 18 mm. In order to have differing capacitances in the three sensors, a different number of paired fingers of capacitors has been selected. LC sensor #1 has two pairs of curved electrodes, LC sensor #2 has three and LC sensor #3 has four pairs of capacitor electrodes. By having a greater number of paired fingers of the capacitor, capacitance is increased. Therefore, based on equation (1), the resonant frequency is decreased.

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Both inductors and IDC capacitors have been designed to have circular shapes to achieve a compact design. As a demonstration, the number of inductor's turns and capacitor's fingers have been controlled to achieve a resonant frequency in the range of 1–4 GHz. As a result, three sensors have three different resonant frequencies, which are required to distinguish each sensor in different locations. Circular designs of the LC sensors demonstrate reliable mechanical behavior that leads to consistent electromagnetic behavior depending on the strain change.

To have a closed LC circuit, the inductor must be connected to both electrodes of the capacitor. Since the inductor is outside the capacitor in the proposed design, a bridge between the inductor and the capacitor is required to complete the closed circuit. Figure 1(b) shows the DIW-based 3D printing method for the fabrication of an LC sensor with a bridge for connecting the capacitor to the inductor, so that the circuit can be closed. This ability of DIW-based 3D printing, which allows a bridge to be printed on top of the inductor in a different layer will make the fabrication process faster than constructive methods and help to save conductive material. A 3D CAD model of LC sensors has been designed and converted into a tool path, and the 3D printer moves the nozzle based on the designed tool path. By applying pressure to the syringe, the conductive ink is dispensed from the nozzle and makes the desired path. Parameters, such as dispensing pressure, the movement speed of the nozzle, and the distance between the nozzle and the surface, determine the width and quality of printed patterns. The dispensing pressure affects the amount of dispensing material in such a way that higher pressure leads to more dispensing material and larger width of the prints. In addition, the printhead's moving speed needs to be optimized so that the dispensing materials have enough time to adhere to the substrate and not to be dragged with the nozzle. Finally, the vertical gap between the nozzle and the substrate needs to be less than the nozzle width to make the dispensing material fully adhere to the surface. The optimal printing parameters including dispensing pressure, speed and the vertical gap were initially selected based on trial and error to obtain reliable 3D-printed patterns.

The printed sample is shown in figure 1(c), in which the bridge area is focused. The conductive ink that has been used is 'Voltera's conductor 2 ink', which has a resistivity of 1.265 × 10⁻⁷ Ωm. After printing the LC sensors with conductive ink on a polyimide substrate, the samples were cured thermally at 120 °C for 30 min to achieve fully dried and conductive traces.

In order to find the resonant frequencies of the LC sensors by experiment, an external readout coil is employed. The coil antenna is connected to the Sub Miniature version A (SMA) adapter and then connected to the VNA with a cable. The SMA connector has an impedance of 50 Ω and is designed to function in the frequency range of 0–12 GHz. The resonant frequency of the sensor is obtained via electromagnetic coupling between the readout coil and the inductor of the LC sensor. For a single port measurement system with a coil antenna, the input return loss (S11) parameter and reflection coefficient are measured in the desired frequency range. The frequency at which S11 is the minimum is close to the resonant frequency. Therefore, with this method the resonant frequency of the LC can be measured.

In this study, FEA that mimics the real experimental situation has been conducted for the characterization of LC sensors for the validation and characterization of the sensor design. The ANSYS high-frequency structure simulator (HFSS) has been used for the S11 simulation of the resonant frequencies of LC sensors. The conductive material used in the simulation setup for the sensors is bulk silver with a resistivity of 1.6 × 10⁻⁸ Ωm.

Figure 2(a) shows the ANSYS HFSS interface of the simulation setup. A circular coil antenna 2 cm in diameter has been connected to the SMA and placed on top of the LC sensor with 5 mm. After conducting a simulation, the S11 coefficient has been found at different frequencies. The plot of S11 versus frequency has been obtained, as shown in figure 2(b). The blue line is for LC 1, which has two pairs of capacitor fingers, showing that the minimum value of S11 is around 2.76 GHz, which is indicated as the resonant frequency of LC 1. The orange line is for LC 2 with three pairs of capacitor fingers, showing that the resonant frequency is around 2.74 GHz. The red line is for LC 3 with four pairs of capacitor fingers, showing that the resonant frequency is around 2.72. Results show that the three sensors have different resonant frequencies. Moreover, since LC 1 has the minimum capacitance among the other sensors, it has the highest resonant frequency, and LC 3 has the lowest resonant frequency among them due to its maximum capacitance in line with the theoretical expectation from equation (1).

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Figure 2(c) shows the simulation results of resonant frequency changes in applied strain for LC sensor #3. Due to the circular shape of the LC sensors, the resonant frequency does not change drastically by applying the strain in both the x and y directions up to 0.5%.

To find the resonant frequency with different location information, the transmission coefficient (S21) is measured in the desired frequency range. The frequency at which S21 is minimum is close to the resonant frequency. For the simulation of transmission coefficient (S21), sensors with polyimide substrate have been placed on top of the L-shaped transmission line (stripline) with 3.5 mm width on top of the printed circuit board (PCB) substrate, as shown in figure 2(d) in such a way that their inductors cover the strip line and communicate with the strip line with mutual inductance. The length of the L-shaped tag is 105 mm, and the width of the tag is 75 mm. A copper plate has been attached at the bottom of the PCB, which acts as a ground. Signals from the first port move along the strip line and the signature signal, which has the information of the LC sensor will be transferred back to the VNA via the second port for analysis.

For the simulation, each sensor has been placed on the strip line individually, and the results have been collected. In addition, three sensors were placed on the strip line together, and these results have also been collected, as shown in figure 2(e). For the individual case, LC 1 has a resonant frequency of 2.22 GHz. The resonant frequencies of LC 2 and LC 3 are 1.82 and 1.61 GHz, respectively. The results from the bottom graph, which are for all LC sensors together on the transmission line, show that for LC 1 and LC 2, the resonant frequencies match the individual cases. The difference in resonant frequency is around 50 MHz for LC 3, which may come from the interaction among the magnetic fields of the three sensors. All the LC sensors can still be identified individually. Moreover, the discrepancy between the S11 and S21 results comes from the difference in mutual inductance between the LC sensors and coil antenna in the S11 measurement and the mutual inductance between the LC sensors and transmission line in the S21 measurement. From the S11 and S21 measurements, it has been confirmed that each sensor has its resonant frequency, which varies from other sensors. Therefore, when each sensor is placed at a different location it has its specific location-based information that is different to other locations with a sensor.

After we confirmed the FEA simulation, an experimental method was chosen to verify the communication between the LC sensors and the strip line. As shown in figure 3(a), an L-type strip line has been fabricated on top of the tag with a 3.5 mm width of copper sheets as a transmission line. Two ends of the strip line have been connected to SMA connectors. On the other side of the tag, a copper plate has been used to act as a ground. Two SMA connectors have been connected to the VNA input and output ports to conduct the measurement of the S21 coefficient. The VNA used in this study is the 'Rohde and Schwarz ZND Vector Network Analyzer' with a frequency range of 100 kHz–4.5 GHz.

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One sensor at a time has been placed on top of the strip line in such a way that its inductor is placed exactly on top of the strip line so that there can be mutual inductance between them. After completing the setup, the VNA applied the excitation from one port and received the signal from another port. The S21 graph has been obtained, as shown in figure 3(b). The blue line is the result of placing LC 1 on the strip line, the orange line is for LC 2, and the red line is for LC 3. All three results from the three sensors are shown in one graph for comparison. The minimum number of S21 coefficients for LC 1 is at 3.09 GHz frequency, which is considered to be its resonant frequency. LC 2 has a resonant frequency of 2.48 GHz, and the resonant frequency of LC 3 has been found to be 2.05 GHz.

The behavior of decreasing resonant frequencies by having a sensor with a larger capacitance has been proved by the S21 measurement. It was expected that results from the experiment would not completely match the results from the FEA simulation because the properties of the material used in fabrication are different to the material parameters used in the simulation. For instance, the conductivity of the silver conductive ink used for the fabrication is different to the conductivity of bulk silver in the FEA simulation. There are two main reasons for the FEA characterization of designed LC sensors. First, we find that the resonant frequency trend in the 1–4 GHz range (by increasing the fingers of the IDC capacitor, the resonant frequency decreases). Next, it is confirmed that the LC sensor and the transmission line can communicate, and the transmission line can transfer the signature signal that is demonstrated in figures 2(d) and (e). Moreover, by FEA simulation, it has been confirmed that by having different LC sensors on top of the transmission line, each sensor shows its own resonant frequency with a minimum influence on the other sensors. Thus, the value mismatch between the simulation and experimental results does not affect the objective of the study.

Figure 4(a) shows a schematic of the wireless detection system. Signals come from one port of the VNA that leads to the transmitter (Tx) reader antenna. This antenna transmits the signal from one side, and the receiver (Ry) tag antenna that is connected to the strip line receives the signals. The Rx tag antenna transmits the signals to the strip line, and the signals go through the strip line, while the LC sensors placed on top of the strip line signature the signal with their resonant frequencies. Signature signals go through the transmitter (Ty) tag antenna, and this antenna transmits the signal to the VNA receiver (Rx) reader antenna and then to the VNA to collect the signals for the S21 versus frequency graph.

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The photo image of the experimental setup is shown in figure 4(b). The tag size is 105 mm by 75 mm. Commercial antennas have been used as reader antennas, and monopole antennas with a diameter of 3 cm have been printed as tag antennas.

A tag with an L-type strip line and two monopole antennas have been fabricated using a DIW-based 3D printing method with conductive ink on top of a polyimide substrate, which is then thermally cured to be fully conductive, and finally attached to a copper plate ground on the other side.

Figure 4(c) shows the results of placing one sensor at a time on top of the strip line for a working distance of 5 mm. As shown in the graph, the resonant frequencies of the three LC sensors are different to each other and distinguishable, and the tag without any sensors shows wireless communication. From the graph, LC 1 has a resonant frequency of 3.69 GHz, LC 2 has a resonant frequency of 3.61 GHz, and the resonant frequency of LC 3 is 3.49 GHz. The same experiment has been conducted for LC 1 at different working distances from 1–10 cm, and results have been provided in figures S1 and S2 in the supporting data. Resonant frequencies of tags without LC sensors and with LC 1 in different working distances have been collected from the S21 versus frequency graphs, as shown in figure 4(d). For each working distance, signals were detectable, and the resonant frequency has been found from the S21 versus frequency graph. For the working distance beyond 10 cm, it was hard to distinguish a minimum S21 for finding the resonant frequency of the sensor, which means that the proposed system with these types of antennas has a maximum working distance of 10 cm, which is a significant improvement in the case of the working distance of the LC sensor.

The designed LC sensors have been improved by applying high dielectric constant materials on top of the LC. In order to determine the effect of the dielectric constant of dielectrics on the communication between LC sensors and strip lines, FEA simulations with ANSYS HFSS have been conducted for four different dielectric materials with thicknesses ranging from 1–5 mm. Figure 5(a) shows the S21 results with different dielectric material thicknesses for poly(methyl methacrylate) (PMMA), epoxy, Al₂O₃ and TiO₂ in the case of LC 3.

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The simulation setup interface of ANSYS is shown in figure S3, and the relative permittivity (dielectric constant) of four dielectric materials is provided in table S1 in the supporting data. As shown in the graph, by increasing the thickness of the dielectric material, the intensity of S21 decreases. For PMMA and epoxy, the intensity of S21 goes to 0 with a thickness over 4 mm, which means that the resonant frequency cannot be found. From table S1, the dielectric constants of PMMA and epoxy are 3.4 and 4.4, respectively. With Al₂O₃, which has a dielectric constant of 9.8 (higher than PMMA and epoxy), it has a higher permittivity. Consequently, the magnetic field from the inductor of the sensor can reach the strip line, and they can communicate up to 5 mm thickness of Al₂O₃. Figure S4 in the supporting data shows the graph drawn from the simulation of the relationship between the absolute value of the S21 coefficient in resonant frequency and Al₂O₃ thickness between the LC sensor and the strip line for the three LC sensors.

Another dielectric material that has been chosen for this part is TiO₂ due to its high dielectric constant, which is 86. As shown in figure 5(a), for TiO₂ as a dielectric between the LC sensor and strip line, the intensity of the S21 coefficient in the resonant frequency of the sensor is much higher than that of other materials from 1 mm to 5 mm thickness. Its high permittivity allows proper electromagnetic communication between the LC sensor and the strip line. Resonant frequencies of the three LC sensors for the mentioned dielectric materials are provided in figure S5 in the supporting data.

In section C, LC 1 has been used for wireless measurement at different distances between the tag and VNA transmitter and receiver antennas. Figure 5(b) shows the schematic of the wireless setup with different working distances. Since wireless measurement has been conducted for LC 1, it has been noted that finding a resonant frequency for a relatively longer working distance (>6 cm) is challenging, and the bandwidth at the resonant frequency increasesd, which means that the quality factor decreases with increasing the working distance. Therefore, dielectric material paste that contains TiO₂ has been prepared, and after applying it to the sensor, its effect on wireless communication has been studied. To make the 3D printable dielectric paste, the urethane triacrylate oligomer was mixed with nano-fibrillated cellulose with phenylbis phosphine oxide as a photo-initiator. This paste is UV curable by light with a wavelength of 400 nm.

After making the paste, 40 wt. % of the TiO₂ powder has been added to the paste, and the paste was mixed with a speed mixer to achieve a homogeneous 3D printable paste. TiO₂ has been chosen due to its high dielectric constant and permittivity to make a dielectric paste with a high dielectric constant. The dielectric constant of the paste has been measured for different wt. % of TiO₂ and the results are provided in figure S6 in the supporting data. For the paste with 40 wt. % of TiO₂, the measured permittivity is around 43 F m⁻¹. Therefore, this dielectric paste has been used for further preparation of the three LC sensors. Figure S7 shows the fabricated LC sensor #3 with dielectric paste on the capacitor part.

Figure 5(c) shows the S21 measurement results for the working distance of 5 mm for the three LC sensors without dielectric material and with dielectric paste on their capacitor. The blue line represents LC 1, the orange line LC 2 and the green line LC3. Solid lines result from sensors without dielectrics and dotted lines result from sensors with dielectric paste. As shown in the graph, the resonant frequency of each LC sensor decreases by adding the dielectric material on top of its capacitor. By increasing the dielectric constant between the layers of the capacitor, the capacitance increases so the resonant frequency decreases as expected based on equation (1).

In order to determine the effect of dielectric materials with high permittivity on wireless communication of the LC sensors, LC sensor #3 has been demonstrated with S21 wireless measurement for both with and without dielectric material at different detection distances, as shown in figure 5(d). Orange points are data coming from LC 3 without dielectric material, and blue points are for LC 3 with the dielectric material. For the LC sensor without dielectric material, the quality factor decreases from 18 to 0 as the working distance increases from 1 to 7 cm, which means that the resonant frequency cannot be found at a working distance beyond 7 cm. In this case, the decrease in the quality factor is 2.852 cm⁻¹. However, for the LC sensor with TiO₂ dielectric material, by increasing the working distance, the quality factor decreased from 13.78 to 3.11 as the working distance increased from 1 to 10 cm, and the decreasing rate of the quality factor is 1.111 cm⁻¹, which means that by having the dielectric material with high dielectric constant, the wireless communication is more reliable for a relatively longer working distance because of the fact that the dielectric material with high permittivity helps the electromagnetic communication of the LC sensor with the strip line. Although the quality factor decreases by increasing the capacitance after applying the dielectric material to the capacitor, the rate of decrease in the quality factor by increasing the working distance is twice less than the rate for LC sensors without dielectric material. The maximum working distance that we could achieve with TiO₂ was 10 cm. For working distances more than 10 cm, the quality factor drops to zero, and the resonant frequency is not distinguishable.