Resonantly enhanced dielectric sensing exhibits superior sensitivity and accuracy based on the signals measured from relative resonance shifts that are immune to signal fluctuations [1]. A wide variety of such resonant sensors exists; surface plasmons (SPs) [2], [3], [4] and microcavities [5], [6], [7], [8] working in optical frequencies may be the most well-known. Radiofrequency identification (RFID) tags [9], [10] and printed resonators embedded in circuits [11], [12] operating at microwave frequencies fall into this category. The sensing signal originates from the permittivity change (the imaginary part of the complex impedance) of the transducer materials. It has been validated that dielectric sensing can improve the linearity, dynamic range, stability, and accuracy compared with resistive sensing, which measures the real part of the impedance change of the same transducer material [13]. Resonantly enhanced dielectric sensing has broad applications and has been used for real-time monitoring of biomedical targets [5], [7], [14], [15], gases [13], strains [9], [10], humidity [16], and temperature [17].

The flourishing Internet of Things (IoT) has increased the requirements for sensor robustness, low cost, and compactness [18]. In this context, low frequencies, such as microwaves and radio frequencies are preferred in non-laboratory field applications because optical and terahertz sensing usually require bulky instruments and an optical table. For millimeter waves, the costs are high and the debugging of active devices is complex. However, microwave sensing is limited by its low sensitivity and large resonator size, owing to its long wavelength. Thus, multiple compressions of the effective wavelength at low frequencies may be an effective strategy. Spoof SPs (SSPs) that mimic the physical properties of optical SPs based on artificial metal structures [19], [20], [21], [22], [23], [24], [25], [26] enable deep-wavelength compression and high sensitivity, providing a promising avenue for microwave resonant sensing [11]. The SSP concept was proposed in 2004 and was experimentally realized in ultrathin metal patterns in planar circuits in 2013 [19], [21], including traveling and localized modes. Localized SSPs combine standing-wave enhancement and plasmonic enhancement of sensitivity [11]. The compatibility of SSPs with printed circuit boards (PCBs) and integrated circuits (ICs) makes them integrable with subsequent analog and digital circuits, making them suitable for IoT sensors [21], [24], [27], [28], [29], [30], [31], [32]. Additionally, the strong modal confinement of SSPs leads to low coupling with free-space electromagnetic (EM) fields. Thus, good EM compatibility (EMC), which is critical for increasingly complicated EM environments and crowded EM spectra, is expected. As a new field, microwave SSP sensing has grown rapidly with attempts in chemical sensing [33], monitoring of engineering structures [34], and dielectric measurements [35], [36].

Integrated sensors have become a popular trend in the IoT, merging sensors with signal detection, processing, and communication systems, and providing immediate accessibility to sensing data with compact equipment [9], [37], [38]. However, accurate detection of resonance-frequency shifts in compact circuits remains a challenge. Amplitude or intensity measurements at a single frequency have been performed using integrated resonant sensors [9], [10], [13], although they are susceptible to signal fluctuations. Other attempts include scanning the frequency back and forth over the resonance range to determine the dip or peak position, the same as in an on-bench measurement using vector network analyzers (VNAs). Integrated microwave resonant sensors were conceptually proposed some time ago using a microcontroller unit (MCU) to tune the frequency of a voltage-controlled oscillator (VCO) [39]. However, the scanning process is time-consuming and requires numerous spectral resources. Recently, significant efforts have been made toward resonance tracking using phase-locked loops (PLLs) [40], [41], [42]. However, the circuit must be designed elaborately from the basic transistors for each specific case; the settings are fixed during the design and lack versatility in different sensing scenarios. In addition, the circuit size is large for state-of-the-art prototypes.

In this study, we report an ultracompact and accurate integrated microwave SSP sensing system. A microwave SSP resonator (SSPR) was designed to simultaneously enhance sensitivity and resonance intensity. A software-defined resonance-tracking scheme with automatically determined control parameters was developed and executed in an MCU, which minimized the circuit volume and made the detection intelligently adaptable to the target resonance. The sensing system communicated and interacted with a smartphone via Bluetooth. The total size of the system is 1.8 cm × 1.2 cm. A signal-to-noise ratio (SNR) of 69 dB, data rate of approximately 2272 measuring points per second, and good EMC performance were achieved. The sensing function was validated using acetone vapor sensing. This study provides an ultracompact, accurate, and intelligent wireless solution for integrated resonant sensors and envisions the broad prospects of SSPRs in IoT sensors.

A diagram of the integrated microwave SSP sensing system is shown in Fig. 1(a). All hardware devices, including periphery circuits, were covered by a multilayer PCB with a size of 1.8 cm × 1.2 cm, except for a button cell, as shown in Figs. 1(b) and (c). The total thickness of the PCB including the device height was approximately 4.94 mm (see Section S1 in Appendix A for details). The sensing system transferred data to and received instructions from a smartphone. The sensing signal was measured using the resonance frequency of the SSPR. Similar to all resonance sensors, the function of the SSP sensing system is versatile and depends on the transducer material attached to the resonator surface (Section S2 in Appendix A). Sensing specificity originates from the specific reactions of the transducer materials with the sensing targets. In this study, the sensing function was validated by acetone vapor sensing using a polydimethylsiloxane (PDMS) film. The PDMS film swelled after absorbing acetone vapor, and its effective permittivity increased [43], [44], [45], [46], [47], [48]. Thus, the resonance frequency decreased with increasing acetone vapor concentration.

The signal detection and processing circuit, which converts the resonance shift of the SSPR to a voltage signal, is a minimal circuit including a VCO, a detector diode, and an MCU, as shown in Fig. 1(d). The resonance-tracking loop was primarily realized using an algorithm in the MCU. Instructed by the smartphone, the sensing system works in both the frequency scanning mode, which sweeps over each frequency point and presents the resonance curve, and the resonance tracking mode, which locks the VCO frequency to the instant resonance frequency of the SSPR and outputs the VCO controlling voltage as the sensing signal. The working frequency of the VCO was controlled by the digital-to-analog converter (DAC) voltage from the MCU. The transmitted power of the SSPR was detected by a detector diode and sent to the analog-to-digital converter (ADC) of the MCU. In the following discussion, the horizontal and vertical coordinates of the measured SSPR transmittance spectrum represent the DAC and ADC voltages.

The working frequency of the integrated sensing system was approximately 4.9 GHz; the system can be conveniently redesigned for other frequencies based on specific EM environments or other considerations. The working frequency was close to the resonance frequency of the SSPR and could be tuned by varying the size and pattern of the SSPR. The VCO and detector were selected to cover the working band. Transducer materials usually operate in a relatively broad spectrum compared to SSPR and other devices.

An SSPR in a sandwich excitation structure was designed for simultaneous enhancement of the resonance intensity and sensitivity, as shown in Figs. 2(a) and (b). A standalone SSPR metallic pattern with a thickness of 0.1 mm (made of stamped stainless steel and plated by copper, see Appendix A for details) was located above the PCB, with an intermediate PDMS film of 50 μm thickness inserted between the SSPR and PCB (see Sections S1 and S3 in Appendix A for the detailed layout). The microstrip pattern printed on the PCB top layer was widened from the 50 Ω microstrip line to provide efficient excitation. The field distributions of the SSPR modes are shown in Fig. 2(c). The simulated and on-PCB measured transmittance spectra of the proposed SSPR are presented in Fig. 2(d) (for details on the EM simulation, see Section S3). The upper and lower x-axes were calibrated using the frequency-tuning curve of the VCO. The SSPR resonated at approximately 4.92 GHz, indicating that the resonance was confined to a diameter of 1/14.2 wavelength. Based on the spoof plasmonic confinement of the spoke-like resonator, the resonance mode was further folded by the slit, breaking the spatial symmetry and inducing a circling current (see Section S3 for a detailed mode analysis) [26]. Deep-subwavelength confinement involves multiple effective wavelength compressions and results in high sensitivity at the same working wavelength. Intuitively, the proposed SSPR was quantitatively compared with a common microstrip ring resonator (MRR) operating in the same band (see Section S4 in Appendix A for details on the MRR). The same SSPR pattern printed on the top layer was chosen as a contrast to demonstrate the effects of the sandwich structure.

The resonance intensity δT, defined as the difference between the top and bottom of the transmittance resonance curve (Fig. 2(d)), was significantly enhanced by the sandwiching structure. The resonance intensity is a key issue in on-PCB measurements; it requires full use of the specific ADC resolution and affects the overall noise level (Section S5 in Appendix A). Feeding a deep-subwavelength resonator is challenging; capacitive coupling is commonly used to enhance resonance intensity [26], [49]. However, capacitive coupling significantly decreases sensitivity because the EM resonance fields are partly attracted to the inert capacitance, lowering the effective interactions of the modes with the dielectric. In this study, the proposed sandwiching structure simultaneously enhanced sensitivity and resonance intensity. As shown in Fig. 2(d), the simulated δT is −5.8 dB, which is greatly enhanced from −1.1 dB when the same SSPR is printed on the PCB top layer (Section S4).

As shown in Figs. 2(e) and (f), the resonance shift sensitivity of the proposed SSPR was clearly enhanced compared with that of the contrast MRR. The enhanced sensitivity can be attributed to several factors. From the EM resonance point of view, the maximum electric field enhancement of the SSPR was 2.7 times that of the contrast MRR, assuming that the same power was fed into the resonators (as shown in Fig. 2(c) and Section S4), which theoretically indicates a larger sensitivity according to the perturbation theory of resonators [50]. This enhancement is attributed to deep-subwavelength confinement and spoof plasmonic enhancement. From a structural perspective, sandwiching the PDMS film between the SSPR and top microstrip pattern of the PCB causes the EM fields to concentrate in the PDMS film. Because the resonance fields can interact adequately with the PDMS film in the sandwiching structure, the sensitivity is further enhanced to 9.7 times that of the same SSPR geometry printed on the microstrip layer (top metal layer) with the transducer materials on the top of the resonator. The contrast mode also possesses spoof plasmonic enhancements but its EM fields are mainly concentrated inside the PCB substrate. To highlight the effect of deep-subwavelength confinement and quantize the overall enhancement, we define the local sensitivity (S_L) as

where f_r is the resonance frequency, ε is the relative permittivity of the PDMS film, and S is the resonator area. S_L evaluates the sensing response within a unit size and indicates the distinguishing capabilities of small permittivity perturbations. The details of S_L calculations can be found in Section S4. The local sensitivity of the proposed SSPR was 108 times that of the MRR resonating in the same band.

Comparing the two transmittance curves in Fig. 2(d), there is a clear degradation in the Q-factor measured on the PCB. In addition to fabrication imperfections, other factors also contributed to distortion of the on-PCB measured transmittance resonance spectra, including the broadened linewidth of the VCO, varied VCO output powers depending on the tuning voltage, nonlinearity in the VCO output frequency tunability, nonlinear response of the detector to the input power, and frequency-dependent response of the detector. For a detailed analysis, please refer to Section S6 in Appendix A. By calibrating the DAC/ADC voltages to the VCO frequency and transmittance power, the on-PCB measured Q-factor was determined to be 18.5. Although this Q-factor degrades significantly, it is sufficient based on the proposed resonance-tracking scheme. Higher Q factors resulted in negligible SNR improvements (Section S7 in Appendix A). To improve the on-PCB measured Q-factor, the SNR, VCOs, and detectors with better linearity and lower dispersion can be used. However, such devices require elaborately designed compensatory circuits. Use of filters and balancers can also improve consistency. However, the main concern is the balance between SNR and circuit size. The proposed resonance-tracking scheme can effectively suppress noise, even with such broadened peaks. Thus, no further improvements were made and the total size remained compact.

It is difficult to couple spatial waves into deep-subwavelength resonators; high immunity to EM interference (EMI) can be expected. The EMI immunity test was performed with a continuous-wave (CW) radiation of 25 dBm from horn antennas located 100 mm apart (for details, see Section S8 in Appendix A). We noticed that the strong CW radiations caused only slight interferences to the transmittance curves, even at the resonance frequency (measured as 4.94 GHz, slightly deviating from the simulated value of 4.92 GHz), as shown in Fig. 2(g). The offsets of the ADC voltage at resonance measured by fixing the VCO output frequency (the DAC voltage) and collecting the detector response (the ADC voltage (V_ADC)) with CW-interfering radiations at 4.94 GHz are shown in Fig. 2(h). Larger offsets are generated by z-polarized interference because they are the main polarizations of the resonance mode and are coupled more with the SSPR. The standard deviation is 0.0067 V in Fig. 2(h) for the z-polarized interference, which corresponds to an SNR of 46 dB, referring to an average V_ADC of 1.33 V (defined as the ratio of the signal power to the noise power and presented on the dB scale in this study) [6]. In addition to frequency-scanning mode, the sensor was measured in resonance-tracking mode. The total SNR of the resonance-tracking measurement (V_out in Fig. 2(i) is the voltage signal output of the resonance-tracking scheme, defined and discussed in detail in the following section) degraded from 69 to 55 dB (Fig. 2(i)) with an interfering radiation of 25 dBm in the z-polarization at 4.94 GHz. From the emission perspective, the radiative efficiency of the proposed SSPR was as low as −17 dB. The sensing resonator generated little radiation; the radiation to the entire sensing system originated primarily from the Bluetooth module. The SSPR and the software-defined resonance-tracking scheme contributed to good EMC performance. From a hardware point of view, the software-defined scheme minimizes the hardware circuit and allows an ultracompact PCB board (1.8 cm × 1.2 cm with an incident wavelength of 6.07 cm). The interfering power coupled from the circuit board is considerably reduced compared to that of a larger circuit board and more complex wiring. From a software perspective, the noise level in V_out (SNR of 55 dB) is further suppressed from that in V_ADC (SNR of 46 dB) owing to the real-time locking algorithm, as demonstrated in Figs. 2(h) and (i) and will be discussed in detail in the next section.

We developed a Pound-Drever-Hall (PDH) locking scheme to detect the resonance shift of the SSPR using an error signal proportional to the resonance shift. It also locks the VCO output frequency at the instant resonance frequency of the SSPR. PDH locking was originally proposed for laser frequency stabilization via a feedback control loop [51], [52], and has been developed for other applications owing to its outstanding accuracy and time resolution in optical microcavity sensing [6], [7], [8], interferometric gravitational-wave detectors [53], and high-fidelity quantum control [54]. However, manipulation of such a precise locking loop and determination of control parameters are often difficult [55], [56]. In this study, we developed a PDH locking scheme and operated it discretely using a self-programmed MCU algorithm that minimized circuit size and achieved high accuracy. The control parameters were adaptively determined from the target resonance.

A block diagram of the proposed scheme is shown in Fig. 3(a); the conceptual basis is shown in Fig. 3(b). The output frequency of the VCO was instantly locked to the resonance frequency of the SSPR using the loop shown in Fig. 3(a); its instant control voltage was output as the resonance-tracking signal V_out. Thus, V_out was positively correlated to the resonance frequency and shifted with respect to the target signal. A square-wave modulation signal was used to tune the V_DAC, implemented by hopping the resonance up and down, equivalent to only two sampling points per period for a sinusoidal modulation signal. Thus, a square-wave signal leads to a higher data rate than any other modulation function using the same MCU clock configuration. The resonance-tracking effects were the same as those with sinusoidal modulation, except for the constant coefficient in the error signal formula, as presented in the mathematical derivations and Simulink simulations in Sections S9 and S10 in Appendix A. With the discrete operations in our MCU algorithm, the data rate was determined considering both the rising time of the modulation voltage and the time delay in the operation loop (Sections S11 and S12 in Appendix A). A stable data rate of 2272 measurement points per second was achieved based on an 8 MHz, 12 bit MCU and a baud rate of 921 600 bits per second (bps). The proposed resonance-tracking scheme produced output data in a few calculation steps in a short time, leading to a higher data rate than the common frequency scanning scheme based on the same time cycle, determined by the MCU oscillators and the baud rate.

The PDH locking parameters were calculated automatically according to the transmittance spectrum, which was recorded in frequency scanning mode (Fig. 3(b)). T in Fig. 3(b) represents the transmittance; Tʹ is its derivative. Both T and Tʹ curves shifted during the sensing process. For clarity, only one Tʹ curve is shown in Fig. 3(b). The starting value of V_DAC (V₀) in Fig. 3(a) (equivalent to f₀ in Fig. 3(b)) was determined from the resonance dip. The amplitude of the modulation signal (A_m) should generally be proportional to the resonance bandwidth; otherwise, the response transmittance differential generated in one modulation process may be overwhelmed by noise. As shown in Fig. 3(b), Tʹ was calculated from the T spectrum and A_m was determined to be 1/8 of the width between the maximum and minimum values of Tʹ. The value of A_m was calculated at the beginning of the resonance tracking process. The coefficient of 1/8 is experiential; we tested the resonances of different Q-factors and found that a value of 1/8 produced a good SNR in most cases. Calculating from the on-PCB measured transmittance spectrum in Fig. 2(d) and calibrating the horizontal coordinate to the frequency, A_m is determined to be 6 MHz. During resonance tracking, the instant working bandwidth was 12 MHz at a working frequency of 4.9 GHz. The consumed spectrum resources were significantly suppressed compared to the frequency scanning method.

The three control parameters K_p, K_i, and K_d of the proportional-integral-derivative (PID) controller are crucial for stable operation and accurate detection of the PDH locking loop. Determination of these parameters is typically empirical and difficult, although there are tuning guides such as the Ziegler-Nichols method [57]. The PID controller produces feedback voltage to V_DAC based on the error signal (taken as Tʹ in the MCU algorithm). In our discrete implementation, the integral term (K_i) evolves into a superposition of every feedback step, and K_p and K_d are set to zero. As interpreted from the modulation triangle in Fig. 3(b), the feedback signal in one step is proportional to Tʹ and is given by

where Δf is the frequency shift.

For convenience, a parameter K is defined as the reciprocal of the slope of Tʹ:

where T'' is the second derivative of T.

The value of K_i was determined based on K. When K_i = K, the feedback is equal to the frequency shift (the shift from the green curve to the blue curve in Fig. 3(b)). Thus, the VCO frequency can be shifted to the new instantaneous resonance position in a single step by taking a linear approximation of Tʹ. T″ was calculated using a linear least-squares regression of Tʹ in the [−3A_m, 3A_m] interval. By reducing K_i from K, the response gradually approached the target signal in several aggregations, and can be interpreted using Eq. (3). For our sensor, the data rate was sufficiently high compared to the target signal varying rate; smaller K_i values are preferred for lower noise levels because a large K_i can lead to overshoots and oscillations in the PID control. The effects of K_i on PDH resonance tracking were analyzed via Simulink simulations for cases with and without thermal noise, as shown in Sections S10 and S13 in Appendix A. The measured SNRs were 48, 53, 60, and 62 dB for K_i = K, 0.5K, 0.2K, and 0.1K, respectively, as shown in Fig. 3(c). However, if an excessively small K_i value is used (such as K_i = 0.001K), the response V_out signal may lag the target signal. Automatic determination of the PID control parameters can potentially be applied to any resonance case using PDH locking. For example, resonance-sensing cases are based on EM resonances ranging from microwaves to optical frequencies, mechanical resonances, and acoustic resonances. Automatic determination can be extended to laser frequency stabilization and atomic force microscopy (AFM) probe tracking. The automatic determination process was designed for a single resonance peak as there was only one resonance within the VCO band in this study. For multiple-resonance cases, the PID parameters should be determined for each resonance.

The power spectrum density (PSD) describes the power distribution over frequency and is defined as the Fourier transform of the V_out(t) noise level [6], [7]. Fig. 3(d) presents the PSD calculated from the K_i = 0.1K curve in Fig. 2(c). Histograms of the K_i = 0.1K signal with the fitted Gaussian distribution functions are shown in Fig. 3(e) [6], [7]. The noise was Gaussian but not white as the noise level was higher at lower frequencies. The thermal noise of the hardware circuit was measured at V_ADC as 67 dB (see Section S13 for details). The noise characteristics were consistent with those reported for PDH locking of optical resonators [6], [7]. In the software-defined PDH scheme, the noise level can be conveniently processed using a median filter. The raw and processed data using a median filter with a window size of 300 are shown in Fig. 3(f). The median filter sets each point as the average of all surrounding points within the window. The SNR was further improved from 62 to 69 dB using a median filter (K_i = 0.1K). Larger window sizes can further improve the SNR but may blur some detailed information. The window size should be based on the data rate and target signal trend.

As a proof-of-concept, the integrated system was validated by acetone vapor sensing using PDMS films as transducer materials. A correspondence between the acetone concentration and effective permittivity of PDMS has been reported, laying the foundation for acetone sensing [43], [44], [45], [46], [47], [48]. The coordinates and units were chosen to be consistent with those shown in Fig. 3, using V_out directly as the sensing signal. The operational flow of the sensing system is shown in Fig. 4(a); Video S1 in Appendix A and Figs. 4(a-ii) and (a-iii) show the screens for the frequency-scanning and resonance-tracking processes. The curves are dynamically displayed in both frequency-scanning and resonance-tracking modes. PDH locking starts with the automatically calculated A_m and K_i = K. The PID parameters can be manually set on the PID setting page, with automatically calculated values displayed on the smartphone for reference. Resonance-tracking data were processed using a median filter with a window size of 300. Using the “smooth” function, the displayed data are filtered by a median filter with a window size of 3000. The “relock” function on the resonance tracking page is designed to restart the resonance tracking process with automatically calculated control parameters. This was designed to address a common issue in PDH locking, in which locking fails when the target signal changes abruptly or the PID parameters are not suitable. The data collection methods between the integrated sensor and the smartphone or computer are described in Appendix A Section S14.

Fig. 4(b) shows a photograph of the sensing system operating on a smartphone. In addition to the PCB, only a button cell was required for operation. For acetone vapor sensing, a dynamic gas-mixing system was constructed to control the acetone vapor concentration, as shown in Appendix A Section S15. The interflow rate was fixed at 1 L·min⁻¹ to reduce possible temperature jitter caused by the flow. A median filter with a window size of 3000 was used. The response voltage V_out of the sensing system with increasing concentrations of acetone vapor is shown in Fig. 4(c). V_out decreased with increasing acetone vapor concentration. Air flowed after 12 min and V_out increased as the PDMS film released the absorbed acetone. V_out changed at approximately 0.04 V when the acetone vapor concentration increased from 0 to 10 000 ppm (1 ppm ≈ 2.4 mg·m⁻³ for acetone vapor). Assuming a linear response of V_out to the acetone vapor concentration and a confidence factor of 3.2 [58], [59], the detection limit was calculated as follows:

where the standard deviation is 5.3 × 10⁻⁴ V according to the SNR of 69 dB, and the baseline is approximately 1.5 V. The detection limit was only 1/58 of the lower explosive limit of acetone [60]. The responses to sequential acetone and air pulses are shown in Fig. 4(d). The responses were reproducible, and the acetone absorption was reversible. Comparing the signals at 10 000 ppm in Figs. 4(c) and (d), a slight hysteresis was observed, which is common for gas sensing [61] (for details, see Section S16 in Appendix A). The qualitative monitoring of acetone evaporation is shown in Appendix A Video S2.

The detection limit and dynamic range depend on both the sensing system and transducer materials. This study emphasizes physical and electrical investigations that present outstanding sensitivity and SNR and envision promising detection limits. The acetone vapor detection limit can be improved by replacing PDMS with transducer materials that produce larger permittivity changes when the target gas is absorbed [55], [56].

We reported an ultracompact, sensitive, accurate, and intelligent wirelessly integrated microwave SSP sensing system, and demonstrated its application in acetone vapor sensing. The proposed SSPR addresses the sensitivity and EMI issues of microwave resonant sensors. The software-defined resonance-tracking scheme minimizes the hardware circuit and consumed spectrum resources, and makes resonance-shift detection intelligently adaptive to the target resonance. It can be used for printed resonators embedded in circuits and for wirelessly excited RFID tags based on either rigid or flexible circuit boards. Broadly, ultracompact and intelligent PDH locking can be extended to mechanical and acoustic resonant sensors based on on-PCB integrated tunable sources and detectors. The ultrahigh compactness and accuracy of the proposed sensing system promote its application in smart homes and the IoT.

This work was supported by the National Natural Science Foundation of China (62288101, 61701108, and 61631007), the National Key Research and Development Program of China (2017YFA0700201, 2017YFA0700202, and 2017YFA0700203), the Major Project of Natural Science Foundation of Jiangsu Province (BK20212002), and the 111 Project (111-2-05).

Xuanru Zhang, Jia Wen Zhu, and Tie Jun Cui declare that they have no conflict of interest or financial conflicts to disclose.

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2023.05.013.