Adaptive Radio Frequency Sensor Enabled by Electromechanically Controlled Stretchable Rectifying Antenna Systems

Traditionally, radio frequency detection or ambient spectrum sensing has required high-performance spectrum analyzers and RF signal analyzers, leading to relatively high costs due to the need for a local oscillator and signal mixer. To overcome this challenge, we propose a low-cost, substantially simplified solution utilizing a stretchable rectenna, a microcontroller unit (MCU), and feedback control systems. By exploiting the dynamic correlation between the resonant frequency and the tensile ratio of the stretchable antenna, the incoming frequency can be determined by recording the maximum rectifier DC power output as a function of the electromechanically controlled tension ratio of the stretchable antenna. Our measured results indicate that a frequency measurement range of 1.8 GHz to 2.5 GHz can be achieved through careful design of the stretchable antenna and broadband rectifier. We have experimentally demonstrated an over-the-air far-field frequency sensing system based on this concept, showcasing significant advantages in power consumption, cost-effectiveness, and simplicity when compared to state-of-the-art RF spectrum analyzers.

Swept spectrum analyzers function by sweeping a sinusoidal signal across an RF (radio frequency) spectrum, measuring the response of the system under test at each frequency point.This process involves a local oscillator, whose output signal mixes with the input signal of the analyzer.The resulting signal, after passing through a filter, is amplified and sent to a detector, which graphically represents the input signal's amplitude as a function of frequency [8], [9].However, these RF signal analyzers often come with high costs and substantial sizes, especially when designed for wide frequency and dynamic ranges.
To facilitate low-cost RF frequency sensing, two primary design methodologies are prevalent for frequency measurement: fixed and reconfigurable designs [19], [20], [21], [22].In both methods, bit information for frequency measurement is gathered by transmitting the output signal to an Analog-to-Digital (A/D) converter, enabling the estimation of the frequency interval.The design of a fixed frequency measurement system depends on the number of frequency discriminator circuits used.Here, the signal is amplified, split by a power divider, and then fed into a specific discriminator, which produces the bits for frequency identification.The accuracy of the measurement improves with an increased number of discriminator circuits [23], [24], [25].For instance, a microstrip structure-based frequency measurement system is proposed in [26], utilizing a 16-way Wilkinson power divider and 15 filters to achieve highresolution frequency measurements in the 2 GHz ∼ 4 GHz range.Similarly, a 7-bit discriminator for 2 GHz ∼ 4 GH frequency measurements is introduced in [27], which employs band-stop filters across multiple channels to generate the necessary secondary system code.While these fixed designs offer higher accuracy, with a measurement error of around 15 MHz, they are complex and large due to the use of numerous components.Their implementation also involves multiple amplifiers, leading to increased power consumption.
In contrast, a 2-bit reconfigurable frequency measurement device is developed in [28], which detects frequency by switching two delay lines via PIN tubes and allocating unknown signals to four predefined sub-bands, covering a frequency range of 1 GHz ∼ 4 GHz.Additionally, [29] proposes a reconfigurable frequency discriminator using fractal delay lines based on fractal geometry, capable of identifying eight different sub-bands within 2.7 GHz ∼ 4.5 GHz, aiming for a compact design.Furthermore, a reconfigurable bandwidth frequency measurement circuit is described in [30], which employs a varactor diode to vary the voltage, thereby reconfiguring the bandwidth and frequency measurements across four states.This design offers a simpler structure and a broader measurement range but has lower resolution, with a maximum error of 525 MHz in [30].
From these examples, it's evident that while fixed designs provide high resolution, their large size and complex structure make them unsuitable for integration into rectenna systems.Conversely, reconfigurable designs are simpler but suffer from lower resolution.The 525 MHz resolution applied in [30] is insufficient for accurately identifying the operating frequency of the RF source.Moreover, the power consumption in these designs remains constant regardless of external frequency changes, leading to increased overall power usage in the rectenna system.Therefore, there is an urgent need to research low-power, high-resolution frequency detection systems.
In this paper, we introduce a structurally simple, dynamically efficient in power consumption, and high-resolution frequency measurement system, as depicted in Fig. 1.The proposed system comprises a frequency reconfigurable antenna, a rectifier, a Microcontroller Unit (MCU), and a stretching device.By manipulating the antenna's tensile ratio using a stretching device controlled by the MCU, the antenna's operating frequency can be precisely adjusted.This adjustment is based on a well-defined one-to-one relationship between the antenna's operating frequency and its tensile ratio.In this arrangement, when the antenna's operating frequency aligns with the incoming frequency, the antenna achieves its maximum output power.Essentially, identifying the stretch ratio that corresponds to this peak output power allows for the determination of the external frequency.For efficient detection and comparison of the antenna's output power to ascertain the optimal tensile ratio, a broadband rectifier is utilized.This rectifier converts the RF power emitted by the antenna into DC power, facilitating the comparison of the antenna's output power.The MCU, by monitoring the output DC voltage during the antenna's stretching process, can detect this optimal power point.Once the ideal tensile ratio is found, the MCU instructs the stretching device to adjust the antenna's length, accordingly, ensuring the antenna's operating frequency remains in sync with the external frequency.
Should there be a variation in the external frequency, the antenna's output power drops due to the misalignment of its operating frequency with the external frequency.This decrease leads to a lower DC output voltage from the rectifier.The MCU, upon detecting this decline, initiates a new frequency detection cycle to accurately determine the new external frequency.

II. ANTENNA DESIGN
Firstly, a frequency continuously tunable stretchable antenna is proposed in this section to establish the one-to-one relationship between operation frequency and tensile ratio.The proposed antenna is fed by a microstrip line and radiated by a dipole radiator as shown in Fig. 2(a).The liquid metal is adopted as the conductive material of dipole radiator due to its good mobility at room temperature, which allows the electrical length of the dipole radiator to be changed by stretching dipole radiator, thus achieving the goal of adjusting the antenna's operating frequency.The coupling structure in the bottom layer consists of two symmetrical radial stubs, and the current on the radial stubs can be coupled to the dipole radiator in the top layer.The radial stubs are directly connected to coplanar strip-line, which is the conventional feeder port of a dipole antenna.To connect the proposed antenna to the subsequent rectifier, the feeder port of coplanar strip-line should be converted as microwave line.Therefore, the right line of the coplanar strip-line is directly connected to the upper metal line of the microstrip line, and left line of the coplanar strip-line is connected to the metal ground of the microstrip line through a metal hole, as shown in Fig. 2(b).The dimensional parameters of the final antenna structure are shown in Figs.2(a-c).
The evolution process of the feeder structure is shown in Fig. 3(a).Firstly, the dipole arm with coplanar strip-line feeder structure (Feed-1 in Fig. 3(a)) is designed, which can provide the upper radiator with the coupled current.However, the poor impedance of this structure is not favorable to match the input impedance to standard 50 , as shown in Figs.3(b-d).Therefore, two radial stubs are utilized instead of the dipole arm, which improves the input impedance due to its increased coupling area to the upper radiator.As can be seen in the Figs.3(b-c), the resistance of the input impedance is improved from 15.5 to 27.8 and the reactance is improved from -43.2 to -18 , which contributes to the reduction of S 11 from −3 dB to −8.7 dB, demonstrating the contribution of the radial stubs to the optimization of the impedance.Eventually, the coplanar strip-line feeder port is converted to microstrip line feeder port.In this process, the real part of the input impedance is further improved and the imaginary part is converted from -18 to 16.1 .In addition, the reflection coefficient is also reduced from -8.7 dB to −16 dB, demonstrating the good impedance matching performance of the antenna.
To study the balance of surface currents on radial stubs during the conversion of coplanar strip-line into a microstrip line, the surface current distribution of the Feed-2 and Feed-3 structures are shown in Figs.4(a-b).It is obvious that the surface current of the radio stub in the Feed-3 structure is almost the same as the that in Feed-2 after the coplanar stripline feeder port being transferred to microstrip line feeder port, indicating that the upper dipole radiator can form the surface current of the conventional dipole antenna.To further study the surface current distribution of the upper radiator, the surface current distributions of the upper radiator with Feed-2 and Feed-3 structures are shown in Figs.4(c-d).It can be seen from Figs. 4(c-d) that the surface currents are oriented in one direction and have a high current density in the middle and a low current density at the ends, which characterizes the surface current distribution of the half-wave dipole antenna.
As the design of the antenna in original state has been completed, the S 11 of the antenna at different tensile ratios are studied, as shown in Fig. 5(a), in which the definition of the tensile ratio is also shown.It can be seen that the frequency corresponding to the lowest reflection coefficient of the antenna shifts to a lower frequency as the tensile ratio increases.This is due to the fact that the operating frequency of the half-wave dipole antenna is related to the antenna size.Thus, when the antenna is stretched, the length of the radiator is increased, which leads to a shift of the operating frequency towards lower frequencies.To evaluate the performance of the proposed antenna, an antenna is fabricated, as shown in Fig. 5(b).Then, the antenna was measured in a chamber, during the measurement, a vector network analyzer (VNA, Agilent E5072A) was adopted to transmit and receive the RF signal.To fulfill the far-field condition, the LM-based antenna was placed 5 meters away from the receiving antenna when we conducted the gain measurement.The measured S 11 as a function of frequency at different tensile ratio is shown in Fig. 5(c).To compare the consistent of between measured and simulated results, the optimum operating frequency as a function of tensile ratios, is shown in Fig. 5(d).It is evident that although there are some differences between the measured and simulated results, the overall trend is consistent, both with the increasing of the tensile ratio, the operating frequency decreases, showing the effectiveness of the designed antenna.In addition, we have converted the reflection coefficient to reflected power ratio at each optimum operation frequency, as shown in Fig. 5(d).It can be seen that the reflected power ratio at the corresponding frequencies is less than 5% at different tensile ratios, indicating that the proposed antenna has outstanding impedance matching performance at large tensile ratio.Finally, to illustrate the robustness, the radiation performance of the proposed LM-based antenna has been measured after 5, 10, 15, 20, 25, and 30 tensile cycles.During this process, the strain force applied to our antenna repeatedly varies from 0 to 100%.The measured operation frequencies (Fig. 5(e)) and the corresponding S 11 (Fig. 5(f)) of the stretchable antenna applied with 0%, 50%, and 100% strain maintain stability even the tensile cycles reach 30, reflecting the excellent durability and robust stability of our design.
In fact, the S 11 varies with tensile ratio, resulting in power acceptance ability (realized gain) of the antenna changing with tensile ratios at a special frequency, which is basis for the frequency detection by using this frequency reconfigurable antenna.The receiving power of the antenna can be calculated by the following equation: where P t is the transmitting power of the transmitting antenna in dBm, P r is the receiving RF power of the proposed antenna in dBm, and G r and G t are the realized gains of the proposed antenna and transmitting antenna, respectively.d is the distance between the transmitting antenna and the proposed antenna, and λ is the operating wavelength.Based on Eq. ( 1), it's evident that the receiving power is related to the realized gain of the proposed antenna as the frequency and power of the incident signal is constant.When an electromagnetic signal at a certain frequency is irradiated to the antenna, by stretching the antenna, there exists a tensile ratio state which maximizes the real gain of the antenna, resulting in the existence of a maximum received power, and thus the frequency can be detected by identifying the tensile ratio corresponding to maximum received power.Based on this, the real gains of the proposed antenna at different tensile ratio for two the radiation direction (+z, and -z) are shown in Figs.6(ab).It can be clearly found that at six frequencies, there exists a tensile ratio that maximizes the realized gain of the antenna at the corresponding frequency.From Figs. 6(a-b), it is also found that the maximum realized gain at different frequencies may correspond to the same tensile ratio, due to the large interval for the tensile ratios.This phenomenon will disappear when the interval between the tensile ratios is reduced.As shown in Table 1, when the interval of the tensile ratio is reduced to 5%, at each frequency there exists a tensile ratio corresponding to the maximum realized gain, thus the one-to-one relationship between the antenna's operating frequency and tensile ratio can be established.
From the above description we can find that the received power of the antenna needs to be compared when detecting the frequency.This will complicate the whole system if a power meter is utilized to detect the power.Therefore, we propose to use a rectifier to convert the RF energy received by the antenna into DC energy and the receiving power of the antenna can be compared by comparing the DC output voltage of the rectifier.

III. RECTIFIER DESIGN
In this section, a broadband rectifier is designed to convert the RF energy received by antenna to DC energy.The designed rectifier comprises various elements, including an impedance matching circuit, two rectifying elements (diode) for RF-DC conversion, a DC-pass filter to smoothen the current output, and a load resistor.In our specific rectifier design, we aimed to enhance the operating bandwidth, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.and thus, we employed two rectifying networks for signal rectification.Rectifying network 1 operates within the frequency range of 1.8 GHz to 2.2 GHz, while rectifying network 2 operates between 2.2 GHz to 2.6 GHz, as shown in Fig. 7(a).Besides, a corresponding DC-pass filters (green part in Fig. 7(a)) are implemented to smooth the output current.Following the design of the rectifying networks, the next step involved designing two matching networks to match the impedance of the rectifying network to the characteristic impedance of the coaxial cable, which is 50 .These matching networks were designed to operate within the frequency bands corresponding to the two rectifying networks, i.e., 1.8 to 2.2 GHz and 2.2 to 2.6 GHz.To examine the operating bands of the two rectifying networks, two power probes (termed as P 1 and P 2 ) are added to the front of the diodes, as shown in Fig. 7(a).When the input RF power was set to 100 uW, the power detected by the two probes was recorded in Fig. 7(b).The result shows that the RF power at the 1.8 GHz to 2.2 GHz is primarily detected by power P 1 , while the RF power at the 2.2 GHz to 2.6 GHz is mainly detected by P 2 , which aligns with the design objective.Additionally, both power probes detect more than 80 uW within the 1.8 GHz to 2.6 GHz band, indicating the effectiveness of the designed matching network.However, it should be noted that the low power detected around 2.2 GHz is attributed to the power being split into two paths flowing into two rectifying networks.
After the rectifier has been designed, to study the impedance matching performance, simulated S 11 as a function of frequency at different input power levels is shown in Fig. 7(c).It is obvious that the S 11 is lower than −10 dB at 1.8 GHz ∼ 2.6 GHz at -15 dBm, -10 dBm, -5 dBm, and 0 dBm, showing the excellent matching performance.In addition, the simulated output voltage as a function of frequency at four input power levels is presented in Fig. 7(d), from which we can find the output voltage reach 0.75 V at the input power of 0 dBm.Besides, the 90-mV output voltage can be achieved at the low input power level of -15 dBm, indicating the good sensitivity of the proposed rectifier.Furthermore, the RF-DC conversion efficiency as a function of frequency is shown in Fig. 7(e).It can be seen from Fig. 7(e) that the proposed rectifier achieves high RF-DC efficiency at 1.8 GHz ∼ 2.6 GHz at different input power levels.Since the non-linear characteristic of the rectifying diode, the performance of the rectifier varies with input power.Therefore, it is essential to study the effect of the input power on the performance of the designed rectifier including S 11 , output voltage, and RF-DC efficiency.The simulated S 11 as a function of input power at 1.8 GHz, 2.1 GHz, 2.4 GHz, and 2.6 GHz is shown in Fig. 7(f).It is clear that the S 11 is lower than −6 dB at four operation frequencies, showcasing the proposed rectifier can work well at wide range of input power.Besides, Fig. 7(g) presents the output voltage varies input power at same four frequencies.We can find from Fig. 7(g) that the output voltage increases as the input power increases.When the power exceeds 1.5 dBm, even though the input power continues to increase, the rise trend of output voltage decreases abruptly due to voltage saturation of the diode.Similar to the output voltage with power, the RF-DC efficiency also increases with increasing input power as the input power does not exceed 1.5 dBm, as shown in Fig. 7(h).Once the input power exceeds 1.5 dBm, the RF-DC efficiency decreases sharply due to the stabilized output voltage resulting in little variation in DC output power.
Subsequently, to verify our design, a prototype is printed on a low-cost F4B substrate with a relative permittivity of 2.2, a loss tangent of 0.001, and a thickness of 0.762 mm, as shown in Fig. 8(a).First, the return loss of the rectifier is measured at different input power levels, and the measured result is shown in Fig. 8(b).It is clearly that the frequency range corresponding to measured S 11 below −10 dB is 1.8 GHz ∼ 2.55 GHz, which agrees well with the simulated one (Fig. 7(c)).Following, the output voltage of the rectifier needs to be measured to evaluate the performance.Throughout the experimentation process, a direct connection is established between an RF signal generator and the rectifier, facilitating the supply of RF energy characterized by varying frequencies and power levels to the rectifier.Simultaneously, a multimeter is utilized to accurately assess the output voltage of the rectifier.The RF-DC conversion efficiency can be obtained by using the following equation: where R is the optimal load resistance of the rectifier (910 ), P in is the input power provided by the signal generators, and V out is the voltage across the load resistance.The measured output voltage as a function of frequency is presented in Fig. 8(c).While the measured voltage exhibits a slight decrease compared to the simulated one (Fig. 7(d)), the rectifier still maintains high output voltage within the frequency range of 1.8 GHz to 2.6 GHz.Moreover, within this frequency band, it is observed from Fig. 8(d) that lower input power levels result in decreased efficiency, likely due to the inherent non-linearity of the diode.Ultimately, Figs.8(e-f) illustrates the output voltage and RF-DC efficiency as a function of input power, to assess the effect of the input power on output voltage and RF-DC efficiency.Notably, the conversion efficiency of the rectifier demonstrates an increasing trend with higher input power.However, after surpassing a certain threshold value of input power, the efficiency begins to decline, attributed to reverse breakdown of diodes, which is consistent with the trend in simulation (Fig. 7(h)).Nevertheless, it is worth noting that the output voltage in measurement, contrary to the simulation results in Fig. 7(g), continues to rise even after the diode has reached its breakdown voltage.This observation can be attributed to the nonlinear current-voltage (I-V) characteristics of the rectifying diode.Unlike a constant linear relationship, the reverse voltage exhibits a slight increment as the reverse current becomes indefinite.In addition, the sensitivity of the proposed frequency measurement system is related to the output voltage of the rectifier at low input power level.It can be seen from Fig. 8(e) that our rectifier can output 2-mV DC voltage at a low input power level of -30 dBm, thus the sensitivity of the proposed system can be determined as -30 dBm (approximately 20 dB signal-to-noise ratio if the noise floor is around -50 dBm) simultaneously considering the detection accuracy of the voltage detection modules (0.805 mV [31]).
A comparison between the proposed rectifier with other related designs is presented in Table 2.It is evident that our design achieves maximum operation band than all others listed in Table 2 while maintains high RF-DC conversion efficiency.This wide operating band is crucial for the realization of frequency measurement system that can cover multiple key communication bands effectively.

IV. OVERALL SYSTEM AND MEASUREMENT
Once the antenna and rectifier have been designed, a frequency measurement system as shown in Fig. 9(a) can be implemented through integrating a MCU and a tensile system (including a tensile fixture, a lead rail, a step motor and its driver) with the abovementioned rectifier.The MCU is equipped with the power to detect the dynamic DC voltage generated by the rectifier and simultaneously output the displacement signal for controlling the step motor and adjusting the strain loading onto the proposed antenna.With the help of the deliberately designed detection and feedback system (MCU and tensile system), the frequency measurement system can identify the input frequency according to one-to-one relationship like that in Table 1.
Before measuring the performance of the total system, the control code is embedded into the MCU to give the MCU the ability to detect the voltage and control the rotation of the motor.The control logic in the MCU is shown in Fig. 9(b).The whole control logic is divided into three parts, voltage detection, voltage comparison and dynamic adjustment.Firstly, the MCU controls the stretching system to gradually stretch antenna from the original length to tensile ratio of 100% at 5% intervals.While the antenna is being stretched, the antenna transmits the received RF energy to the rectifier and the rectifier converts the RF energy to DC energy.Then, the MCU can detect and save the output voltage of the rectifier in each tensile state.After a stretching cycle, the MCU searches for the maximum detected voltage (V max ) by comparing the detected voltages, and controls the motor rotation to restore the antenna under the tensile ratio corresponding to the V max .Up to now, as the tensile ratio has been obtained, the input frequency can be identified by the one-to-one relationship between the tensile ratio and frequency.Finally, when the frequency changes, the energy received by the antenna changes, causing the output voltage of the rectifier to increase or decrease.Here, we set the MCU to control the antenna to revert to the original state as the voltage detected by the MCU is outside the range of 0.95V max to 1.05V max .And then the MCU controls the antenna again to stretch from 0 to 100% tensile ratio to find the next tensile ratio corresponding to the V max .
To quantitatively analyze the tensile state of the antenna in the proposed system with respect to the external frequency, a horn antenna connected to a RF signal generator serves as the transmitting antenna to provide the required frequency, as shown in Fig. 10(a).The transmitting frequency of the horn antenna is set one after another in the frequency band range of 1.8 GHz ∼ 2.5 GHz.In the measurement process, the proposed system automatically changes its operating frequency by stretching the liquid metal antenna to search the V max and keep the antenna at the length corresponding to the V max .At the same time, the length of the antenna is recorded and the tensile ratio of the antenna is calculated according to the equation in Fig. 2(b), as shown in Fig. 10(b).By observing the relationship between the tensile ratio of the antenna and the frequency, it can be found that the tensile ratio gradually increases as the frequency decreases, which is consistent with the theoretical trend of our design (shown in Table 1).In addition, three demos for 2.5 GHz, 2.2 GHz and 1.8 GHz have been provided in Figs.10(c-e), and their dynamic frequency measurement process can be found in Supplementary Video for showcasing the frequency detection capability of the proposed system.From the Supplementary Video, as well as the three demos, it can be found that the MCU drives the stretching device to detect the new frequency only when the external frequency changes, otherwise the MCU only needs low energy to detect as well as compare the voltages, which showcases our unique and innovative design compared to traditionally frequency measurement system.In addition, to validate the reliability of the system across a wide range of environmental conditions, we have tested our system from the aspect of input RF power to supplement the original experiment results concerning the incident frequency shift.As shown in Fig. 11, as the input RF power varies from -30 dBm to 10 dBm at different frequencies, the corresponding length of antenna always maintains stable, reflecting the robust reliability of our total system.Although the measured results validate the feasibility of the proposed strategy, there is still some room for improvements from the aspect of real-life applications and power consumption.Considering the urgent demands for miniaturization and wearability, new deformation strategy should be adopted to replace the bulky stepper just for illustrating the basic functionality.As a feasible alternative, shape memory alloys [35] and ionic polymer metal composites [36] will be desirable candidates to replace the LM, of which the shape can be directly tuned by applying external DC Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.current or voltage field, making our system more convenient to integrate with other platforms.In addition, the power consumption of the entire system can be further optimized by alternative low-power motors [37], [38] and MCUs [39], [40], providing the possibility to realize a frequency detection system without externally powered in the future.
Finally, a comprehensive comparison between our design and other frequency measurement systems is presented in Table 3.It is evident that the configuration of our design is much simpler than that of other traditional solutions consisted of numerous control and RF devices, directly resulting in our system with lower power consumption.In addition, our frequency detection system demonstrates remarkable advantage in terms of resolution and can adapt to abundant application scenarios covering the space wave measurement and RF circuit test.The resolution of our system is comparable to that of low-cost systems requiring ADC and filters.Thus, we believe the proposed frequency sensor presents the state-of-the-art performance.

V. CONCLUSION
In this study, we introduce an innovative frequency detection system that employs a frequency reconfigurable antenna in conjunction with a broadband rectifier.This novel system is capable of continuously detecting external frequencies in the range of 1.8 GHz to 2.5 GHz.It operates by applying mechanical strain to the frequency reconfigurable antenna, which alters its resonant frequency to align with the external signal.The broadband rectifier is used to convert the received RF energy into DC power.Additionally, we have incorporated customized control logic into the MCU.This logic enables the system to automatically adjust and identify the frequency when the maximum voltage output is detected.Our experimental validation confirms the system's adaptability and robust performance across a variety of operating conditions.

FIGURE 1 .
FIGURE 1. Schematic of the frequency measurement system.

FIGURE 2 .
FIGURE 2. Structure of frequency continuously tunable stretchable antenna.(a) The top view.(b) The bottom view.(c) Structure of dipole radiator.(d) The side view.

FIGURE 3 .
FIGURE 3. (a) The evolution process of the feeder structure.The resistance (b), reactance (c) and S11 (d) of the antenna with different feeder structure.

FIGURE 4 .
FIGURE 4. The surface current distribution of the Feed-2 (a) and Feed-3 (b).The surface current distributions of the upper radiator with Feed-2 (c) and Feed-3 (d) structures.

FIGURE 5 .
FIGURE 5. (a) Simulated S11 curves of the stretchable antenna under a tensile ratio varying from 0 to 100%.(b) Photograph of the proposed antenna.(c) Measured S11 curves of the stretchable antenna under a tensile ratio varying from 0 to 100%.(d) Simulated and measured operation frequency and corresponding reflected power ratio of the stretchable antenna as a function of tensile ratio.Measured operation frequency (e) and the corresponding S11 (f) of the stretchable antenna loaded strain of 0, 50%, and 100%.

FIGURE 6 .
FIGURE 6.The realized gains of the proposed antenna at different tensile ratio for two radiation direction.(a) +z.(b) −z.

FIGURE 7 .
FIGURE 7. (a) Topology of the proposed broadband rectifier.(b) Detected power distribution by two power probes (P1 and P2) as the input power is set to 100 µW.Simulated S11 (c), output voltage (d) and RF-DC conversion efficiency (e) vs. frequency.Simulated S11 (f), output voltage (g) and RF-DC conversion efficiency (h) vs. input power.

FIGURE 8 .
FIGURE 8. (a) Photograph of the proposed broadband rectifier.Measured S11 (b), output voltage (c) and RF-DC conversion efficiency (d) vs. frequency.Measured output voltage (e) and RF-DC conversion efficiency (f) vs. input power.

FIGURE 9 .
FIGURE 9. (a) Illustration of the proposed frequency detection device.(b) Flow chart of the proposed frequency detection device.

FIGURE 10 .
FIGURE 10.(a) Measurement photograph for the proposed frequency detection device.(b) Measured tensile ratio and length of the antenna as a function of operation frequency.(c), (d) and (e) Measured stretched state and length of the antenna corresponding to each frequency.

FIGURE 11 .
FIGURE 11.Measured length of the antenna as a function of input power for different frequencies.