Inductor-Based Biosensors for Real-Time Monitoring in the Liquid Phase

Abstract

Current liquid-phase resonant biosensors, such as Quartz Crystal Microbalance, Surface Acoustic Wave, or Surface Plasmon Resonance, typically rely on specialized piezoelectric substrates or complex optical setups. These requirements often necessitate cleanroom fabrication, thereby limiting cost-effective scalability. This study presents a high-integration sensing platform based on standard Printed Circuit Board (PCB) technology, incorporating an embedded inductor within a fluidic system for real-time monitoring. This design leverages industrial manufacturing standards to achieve a compact, low-cost, and scalable architecture. Detection is governed by shifts in the resonance frequency of an LC tank circuit; specifically, increases in bulk ionic strength induce a frequency decrease, whereas biomolecular adsorption at the sensor surface leads to a frequency increase. This phenomenon can be explained by the modulation of the inter-turn capacitance, which is modeled as a combination of capacitive elements accounting for contributions from the bulk electrolyte and the surface-bound dielectric layer. Such divergent responses provide an intrinsic self-discriminating capability, allowing for the analytical differentiation between surface interactions and bulk effects. To the best of our knowledge, this is the first demonstration of an inductor-based resonant sensor fully embedded in a PCB fluidic architecture for continuous liquid-phase analyte monitoring. Validated through a protein-antibody model (Bovine Serum Albumin-anti-Bovine Serum Albumin), the sensor demonstrated a limit of detection of 1.7 ppm (0.026 mM) and a linear dynamic range of 31–211 ppm (0.47–3.2 mM). These performance metrics, combined with a reproducibility of 4 ± 3%, indicate that the platform meets the requirements for robust analytical applications. Its inherent simplicity and potential for miniaturization position this technology as a viable candidate for point-of-care diagnostics in diverse environments.

1. Introduction

Chemical sensors have become crucial tools across healthcare, industry, environmental monitoring, and agriculture, converting chemical information into analytically useful signals [1]. Their development has historically focused on enabling point-of-care diagnostics for biomolecular markers, with the goal of bringing clinical testing out of specialized laboratories and into more accessible settings. This shift began in 1962, when Leland Clark Jr. introduced the first enzyme-based amperometric glucose biosensor [2]. Since then, there has been significant advances in sensitivity and specificity for detecting disease-related biomolecules, but the widespread adoption of these sensors has been limited by challenges in system integration and miniaturization for portable applications.

Among the various sensing platforms available, resonant sensors use the principles of resonance to detect and quantify biomolecular interactions with remarkable precision. They operate by perceiving shifts in resonant frequency: when target molecules interact with the sensor surface, they modify the system, producing a measurable change in the resonant frequency of the sensor. This feature provides resonant sensors with exceptional stability, resolution, and accuracy while generating a frequency-based signal that remains unaffected by electrical current fluctuations [3], making them highly compatible with digital systems, a crucial feature for their effective use as measurement devices.

Resonant systems are open platforms that enable moderately skilled researchers to construct experimental devices using modular components. Historically, and as the understanding of resonant sensors in liquids advanced, the number of applications that have been generated has expanded significantly [4,5]. These sensors are currently considered powerful transducers for the rapid detection of a wide range of biological and chemical targets [6], revolutionizing fields such as diagnostics [7], environmental monitoring [8], and drug development [9].

Among resonant circuits, tank circuits stand out for their simplicity and enduring relevance [10]. Since the early 19th century, they have played a foundational role in the development of electromagnetism [11] and have evolved into key building blocks of modern wireless electronics [12]. They operate by exchanging energy between a parallel inductor (L) and capacitor (C), storing electrical energy through magnetic resonance. The key parameters of the inductor include inductance, resistance, and inter-turn capacitance, while the capacitor is defined by its capacitance and resistance. Resonance occurs when the inductive reactance equals the capacitive reactance, at which point the circuit reaches its resonant frequency. At this frequency, the circuit exhibits maximum impedance and minimal current draw, allowing a straightforward and precise measurement of the resonance frequency [13].

Tank circuits are versatile sensing platforms, capable of monitoring a wide range of environmental parameters, such as temperature, pressure, and humidity [14,15]. Traditionally, however, the intrinsic sensitivity of inductors to environmental fluctuations has limited their direct use in sensing, leading researchers to rely primarily on the capacitive component to ensure accurate measurements. While this focus on capacitors has enabled the development of passive wireless sensors for gases and humidity [14,16,17], it has largely overlooked the untapped potential of the inductor as a primary recognition element.

Addressing this limitation, the present work explores the inductor itself as the primary transduction element for biosensing. Specifically, a PCB-integrated planar inductor is implemented to monitor bioanalytes in the liquid phase by exploiting its intrinsic inter-turn capacitance. This strategy enables a label-free and inherently miniaturizable platform capable of real-time operation under continuous-flow conditions. By relying on standard PCB fabrication processes, the proposed approach offers a low-cost, robust, and scalable solution, thus extending high-precision biosensing beyond specialized laboratory environments toward automated and large-scale industrial monitoring.

2. Materials and Methods

2.1. Chemicals

All chemicals used in this work were of analytical grade. The surface modification of the PCB-integrated inductor was performed using 3-mercaptopropionic acid (3-MPA, ≥99%) and N-hydroxysuccinimide (NHS) from Sigma-Aldrich (St. Louis, MO, USA), while N-ethyl-N′-(3-dimethylaminopropyl)carbodiimide (EDC) was sourced from Merck (Darmstadt, Germany). Residual active groups were blocked using ethanolamine (ACS grade) from Panreac Química S.L.U. (Barcelona, Spain).

The biological model for specific sensing included Bovine Serum Albumin (BSA), Horseradish Peroxidase (HRP), and anti-BSA antibodies (rabbit polyclonal), all purchased from Sigma-Aldrich. Protein surface concentrations were quantified using a bicinchoninic acid (BCA) assay kit (Thermo Fisher Scientific, Madrid, Spain).

Buffer solutions and cleaning agents, including sodium dodecyl sulfate (SDS), Na₂HPO₄, KH₂PO₄, KCl, Na₂CO₃, NaHCO₃, and NaCl, were purchased from Sigma-Aldrich. All aqueous solutions were prepared daily using ultrapure water (18.2 MΩ·cm at 25 °C) from a Smart2Pure3 water purification system (Thermo Electron LED GmbH, Langenselbold, Germany).

Phosphate-buffered saline (PBS) at pH 7.4 with an ionic strength (I) of 200 mM was prepared using 8 mM Na₂HPO₄, 1 mM KH₂PO₄, 3 mM KCl, and 137 mM NaCl. A 10× concentrated PBS (I = 2 M) was prepared with ten times the amount of salts of the PBS formulation. Additionally, phosphate buffer (PB) at pH 7.4 with an I of 26 mM was prepared with 8 mM Na₂HPO₄ and 2 mM NaH₂PO₄. These buffer systems were selected to evaluate the sensor’s performance under varying ionic strengths and to ensure stable pH conditions during the bio-recognition assays.

2.2. Sensor Structure

The tank circuit is implemented on a printed circuit board (PCB, Eurocircuits N.V., Mechelen, Belgium) and incorporates a surface-mount technology (SMT) capacitor with a fixed value of 100 pF 1% as a key component. A planar copper coil with 36 turns is designed on the top layer of the PCB. This custom-made coil features a track width and inter-turn spacing of 100 µm, and a groove (track thickness) of 35 µm. It is important to note that this custom-made coil is the only component of the circuit in contact with the sensing solution, while the other circuit components remain isolated. To prevent chemical reactions, the coil surface is coated with epoxy resin, providing thermal stability and chemical resistance.

The resonant frequency of the tank circuit is measured using a resonance frequency measurement circuit (RFMC), connected to an AZDelivery ESP-WROOM-32 NodeMCU 2.4 GHz Dual Core development board, which integrates the high-performance ESP-WROOM-32 module (Espressif Systems, Shanghai, China). The microcontroller retrieves data from the RFMC at 100 ms intervals. After collecting 10 readings, it calculates their average and transmits the result to MATLAB R2023a (MathWorks, Carlsbad, CA, USA). Consequently, MATLAB receives one resonance frequency value per second, corresponding to the averaged data from 10 samples.

The MATLAB application interfaces with the electronic measurement system through the PC’s USB port. A converter module with galvanic isolation is used to convert the USB connection into a UART bus, which connects to the microcontroller. The electronic measurement system is powered by a battery, which, in combination with the galvanic isolation, isolates the system from both the power grid and the PC, thereby minimizing conducted noise interference.

Although the electronic configuration remains the same, the custom-made inductor sensor of the tank circuit was developed in two different setups: one optimized for a dipstick-like configuration and the other for a flow-based configuration, as shown in Figure 1 and detailed below.

2.3. Surface Functionalization

Surface activation was carried out at room temperature under an inert atmosphere and in the dark by immersing surfaces 24 h in freshly prepared 600 mM 3-MPA solutions. Following activation, surfaces were incubated for 1 h with gentle stirring, still in the dark, in a solution containing 600 mM EDC and NHS. The surfaces were then functionalized by incubation for 1 h at room temperature with a 40 µg/mL anti-bovine albumin antibody solution prepared in 100 mM carbonate-bicarbonate buffer (pH 9.6). Unreacted carboxyl groups were then blocked by incubating the surface with 0.1 M ethanolamine in borate buffer (pH 8.75) for 1 h. Covalent protein immobilization on the resin surface was confirmed by ATR-FTIR using a Bruker Tensor-27 spectrometer (Bruker Optik GmbH, Ettlingen, Germany) with a diamond ATR crystal and further corroborated by a BCA assay (Thermo Fisher Scientific, Waltham, MA, USA).

2.4. Dipstick-like Configuration

The performance of the developed device was assessed through dipstick-like measurements, in which only the PCB-integrated inductor was immersed in BSA solutions ranging from 20 to 600 ppm (0.3 to 9.0 mM). The experimental setup is shown in Figure 1a to ensure that the tank circuit’s inductor was uniformly covered throughout all measurements, a constant volume of 35 mL was used. For each sample, data were recorded every 6 s over a 10 min period, and each sample was measured three times to ensure consistency.

2.5. Flow-Based Configuration

A key objective in sensor development is its integration into a flow system, see Figure 1b. To accomplish this, a flow cell was created using a bottomless sticky-Slide (Ibidi GmbH, Martinsried, Germany), which was positioned and adhered over the inductor of the tank circuit using (Figure 1c). The sticky-Slide incorporates an obround channel 45.0 mm long and 19.0 mm wide, with a height of 235 µm and a total volume of 160 µL. This configuration ensured that the flow cell covered one-third of the total surface area of the custom-made inductor of the tank circuit. Finally, to complete the assembly of the flow injection assay system, a peristaltic pump (Minipuls-3, Gilson, Villiers LeBel, France) was used, and tubes were connected to the sticky-Slide via the embedded female Luer adapters, ensuring a leak-free system.

Under this flow injection analysis setup, measurements were done both with solutions with varying ionic strengths and solution containing BSA at concentrations ranging from 0 to 600 ppm (0 to 9.0 mM). All measurements were performed in triplicate. The system was monitored continuously for 15 min at a flow rate of 55 µL/min to ensure it reached a steady state. In bioanalyte assays, the surface regeneration procedure involved two washes with 1% SDS (w/v) in 0.1 M HCl for 30 min to elute the adsorbed proteins, each followed by a 15 min rinse with water. To ensure complete removal of the surfactant, a final 30 min wash with water was done.

2.6. Inductor Sensor Characterization

To characterize the custom-made inductors, five PCB-integrated inductors were individually characterized using the BK Precision 895 LCR meter (B&K Precision Corporation, Yorba Linda, CA, USA), with the value of $C_S$ determined from Equation (1). The $L_S$ and R_S of the planar coils were measured at a frequency of 1.2 kHz. Subsequently, the surface profile and roughness of the custom-made inductor, coated with epoxy resin, were analyzed using a 3D optical profiler (Filmetrics, Inc., San Diego, CA, USA).

Next, the resonant tank assembly was characterized in response to small changes in the inter-turn capacitance by connecting a low-value variable capacitor (on the order of hundreds of femtofarads) in parallel with the tank circuit, see Supplementary Material.

2.7. Surface Characterization

The sensor surfaces were characterized using a High-Resolution Field Emission Scanning Electron Microscope (HR-FESEM). HR-FESEM imaging and Energy-Dispersive X-ray Spectrometry (EDX) analysis were performed with a GeminiSEM 500 microscope (Carl Zeiss Microscopy GmbH, Jena, Germany). Images were acquired using an SE2 detector under the following conditions: 1.5 kV accelerating voltage, 4.9 mm working distance, and a 30 µm standard aperture size.

Ultraviolet-visible (UV-Vis) spectroscopy was employed to determinate the functionalization of the surfaces. These measurements were performed using a JASCO V-630 Spectrophotometer (JASCO, Easton, MD, USA), providing detailed information on the functionalization process. To quantify the amount of BSA bound to the sensors, the BCA assay method was also applied, following the manufacturer’s protocol with slight modifications. Additionally, the sensing surfaces were characterized using ATR-FTIR spectroscopy.

2.8. Data Analysis

When necessary, data processing was conducted in OriginPro 2019b 64-bit (OriginLab, Northampton, MA, USA). Calibration curves were subsequently fitted using either a four-parameter logistic model or a three-parameter Hill equation within the same software, thus ensuring precise analysis and accurate representation of the experimental data.

3. Results and Discussion

3.1. Sensing Principle and Transduction Logic

The sensing mechanism of the proposed platform is determined by the electromagnetic response of a resonant LC tank circuit. The electrical model, shown in Figure 1d, consists of two primary elements: a custom-designed planar spiral inductor, serving as the sole sensing transducer, and a high-precision external capacitor (C_T = 100 pF 1%). Notably, and as noted previously, only the inductor is exposed to the sensing environment; the external capacitor is electrically coupled but physically isolated from the liquid phase, thus ensuring it does not contribute to the analytical signal.

The planar spiral inductor is characterized by its inductance ($L_S$), series resistance (R_S), and, critically, its inter-turn capacitance ($C_S$). This capacitance arises from electric field coupling between adjacent turns of the coil and is highly sensitive to variations in the local dielectric environment. Neglecting secondary losses and parasitic inductance associated with PCB vias, the resonance frequency of the system is expressed as indicated in Equation (1) [15]:

$$f_{resonance}={\displaystyle \frac{1}{2\pi \sqrt{L_S\left(C_T+C_S\right)}}}$$

(1)

Since biological interactions in aqueous media exhibit negligible magnetic susceptibility (μr ≈ 1), the $L_S$ remains effectively constant. Consequently, all observed resonance frequency shifts (Δf) arise exclusively from dielectric perturbations at the sensing interface. Signal transduction is governed by the inductor’s fringing electric field sensitivity to the local permittivity, which is effectively captured by the modulation of $C_S$ in the lumped-element equivalent circuit (Figure 1d). These variations directly translate into shifts of the resonance frequency, as described by Equation (1).

In analogy to Gouy-Chapman-Stern model in electrochemistry [18], the fringing electromagnetic field of the planar inductor can be approximated as passing sequentially through two distinct dielectric regions: the rigid adsorbed biomolecular layer at the sensor surface, followed by the surrounding bulk aqueous solution. To describe this interaction, $C_S$ can be conceptually modeled as two capacitors [19], representing the primary dielectric contributions: C_r, corresponding to the rigid adsorbed layer at the sensor interface, and C_d, accounting for the bulk solution effects. Depending on which contribution dominates, this framework explains the sensor’s self-discriminating capability, as it may produce opposite shifts in resonance frequency depending on whether the dielectric variation originates from bulk changes or surface binding, see Figure 2:

• Bulk Effects (Matrix Interference): Increases in the ionic strength of the medium enhance electrostatic screening in the bulk solution. This raises the effective dielectric constant of the medium and, consequently, the C_d, resulting in a downward shift of the resonance frequency.
• Surface Interactions (Specific Binding): Conversely, when biomolecules (such as BSA) adsorb onto the sensor surface to form a rigid adsorbed layer, water molecules (high permittivity, ε ≈ 80 [20]) are displaced and replaced by a biomolecular layer with a significantly lower effective permittivity (ε ≈ 2–4 [21]). This reduces the local dielectric constant at the interface, decreases C_r, and produces a corresponding increase in the resonance frequency.

This self-discriminating capability provides a solid physical basis for the sensor, demonstrating that surface-specific biomolecular binding can be resolved even in the presence of bulk dielectric fluctuations. On this basis, the following section discusses the experimental results that validate the proposed transduction mechanism and its biosensing performance.

3.2. Experimental Validation and Biosensing Performance

The experimental validation of the proposed transduction mechanism begins with a detailed structural characterization of the PCB-integrated inductor. The sensing element consists of a conductive copper spiral patterned on an FR-4 epoxy substrate. While copper provides excellent electrical conductivity, its susceptibility to corrosion in aqueous environments necessitates a carefully engineered passivation and functionalization strategy.

To address this, the circuit is coated with a screen-printed solder mask (epoxy layer), offering both chemical protection and electrical isolation. Optimization of this layer is critical: excessive coverage of the inter-turn gaps would prevent the sensing medium from accessing regions of maximum fringing-field intensity, thereby reducing the modulation of the $C_S$ and compromising sensor sensitivity.

To confirm that the inter-turn regions remain accessible to the electrolyte, a 3D optical profilometry analysis was conducted on the custom-made inductor (Figure 3). The topographic mapping indicates that the grooves preserve a depth of 8.5 ± 0.5 µm, ensuring adequate exposure of the inter-turn spacing to the surrounding solution. This structural verification validates that local dielectric variations can effectively modulate $C_S$, providing a solid foundation for subsequent biosensing experiments.

Thereafter, the electromagnetic characteristics of the custom-made inductor were quantified, as it serves as the sole transduction element in direct contact with the sample. Experimental measurements yielded an inductance ($L_S$) of 13.62 ± 0.07 µH, a series resistance (R_S) of 8.1 ± 0.6 Ω, and an inter-turn capacitance ($C_S$) of 24.8 ± 0.6 pF. To assess the sensitivity of the resonant frequency to dielectric perturbations, a variable capacitor was employed to emulate controlled variations in $C_S$ (see Supplementary Material).

This analysis revealed a rigorous linear relationship between incremental changes in the inter-turn capacitance and the resulting resonance frequency shifts, described by |Δf| = (8140 ± 50) × ΔC (Figure 4, R-Square = 1.00). This near-unity correlation demonstrates that even slight dielectric variations at the interface are faithfully converted into measurable signals, establishing the inductor not merely as a passive component, but as a high-resolution, highly predictable transducer for continuous solution monitoring.

This linear behavior highlights the potential of the PCB-integrated inductor as a sensitive transducer. To test its performance in a biological context, BSA was used to modulate the dielectric environment around the coil. At pH 7.4, BSA carries a significant net negative charge (~−18e) [22], making it an ideal model analyte for inducing measurable dielectric changes. The sensor was immersed in BSA solutions (phosphate buffer, 20–600 ppm, 0.3–9.0 mM) in a dipstick-like configuration, where the resonance frequency primarily reflects the dielectric properties of the surrounding bulk solution. As the BSA concentration increases, the resonance frequency decreases; the absolute value of this shift follows a sigmoidal trend, which is depicted in Figure 5. This downward shift is consistent with the transduction mechanism described in the previous section: higher solute concentrations increase the effective permittivity of the bulk medium (C_d), raising the total inter-turn capacitance ($C_S$) and lowering the resonant frequency. These results confirm that the inductor sensor can effectively monitor analyte concentration in a rapid, dipstick-style format, in line with conventional antigen detection approaches.

The resonance frequency shift observed in the dipstick-like configuration shows a clear sigmoidal decay with increasing BSA concentration (see Figure 5). The data are presented in absolute values to ease the sigmoidal regression analysis. This behavior was quantitatively captured using a four-parameter logistic (4PL) model. Fitting the experimental data yielded |Δf| = (4600 ± 200) + ((500 ± 200) − (4600 ± 200))/(1 + ([BSA, ppm]/(100 ± 10))^(1.8 ± 0.3)) (R² = 1.00, Figure 5), confirming that the 4PL model accurately represents the nonlinear saturation of the inductor’s sensing volume as protein concentration rises.

From this calibration, the limit of detection (LOD) was estimated at 17 ppm or 0.26 mM (680 Hz), defined as the blank signal plus three times the standard deviation (3σ), while the limit of quantification (LOQ) was 38 ppm or 0.57 mM (1100 Hz) based on the 10σ criterion. These metrics highlight the sensor’s exceptional sensitivity and its capability for rapid, low-ppm detection. Importantly, this performance is achieved without complex instrumentation, demonstrating the practicality of the PCB-integrated inductor as a direct-immersion probe for liquid-phase analytes. Together, these results establish a reliable baseline for dynamic measurements, setting the stage for the following experiments under continuous flow conditions.

Building on the promising results from the dipstick-like configuration, the platform was next evaluated in a dynamic, flow-based setup for real-time monitoring. A custom flow cell was assembled by sealing a bottomless Sticky Slide over the PCB inductor using Luer adapters. This design ensures that the inductor’s sensing region is directly exposed to the fluidic environment, while the solder mask provides passivation and all other circuit components remain hermetically isolated from the liquid channel.

To assess the sensor’s response to bulk dielectric variations under flow, a Flow Injection Analysis (FIA) system was employed to modulate the ionic strength of phosphate-buffered saline (PBS) solutions. The sensor exhibited a robust and reproducible response: increasing ionic strength consistently decreased the resonance frequency (Figure 6). For example, injection of a water blank induced a minimal shift of −20 ± 9 Hz, whereas a 2 M ionic strength solution produced a substantial shift of −658,000 ± 5000 Hz.

This pronounced frequency response is primarily driven by the spatial modulation of the inductor’s fringing electric field. As the concentration of mobile ions increases, electrostatic screening within the sensing volume is enhanced, effectively raising the complex permittivity of the surrounding medium. This increase directly elevates the inter-turn capacitance ($C_S$), producing the observed downward shift in the resonant frequency. Quantifying this relationship with ionic strength establishes a robust analytical baseline, enabling the separation of non-specific bulk dielectric effects from the surface-specific binding events analyzed in the subsequent protein absorption experiments.

To focus exclusively on surface interactions, 0.2 M PBS was used to buffer the ionic strength, minimizing the influence of bulk dielectric changes. Using this controlled environment, the sensor’s performance as a label-free biosensor was then evaluated by injecting a 600 ppm (9.0 mM) BSA solution.

Figure 7a shows the real-time evolution of the resonance frequency during BSA injection. In contrast to the downward shifts observed with increasing ionic strength, BSA binding produced a progressive upward frequency shift, reaching 2880 ± 130 Hz. This positive shift reflects surface physisorption: as proteins adsorb onto the passivated inductor surface, high-permittivity water molecules (ϵ ≈ 80) are displaced by a lower-permittivity biomolecular layer (ϵ ≈ 2–4), effectively reducing C_r and increasing the sensor’s resonance frequency in accordance with the capacitance model described in Section 3.1, Sensing Principle and Transduction Logic.

The magnitude of the BSA-induced shift is smaller than in the dipstick configuration, reflecting the reduced effective sensing area within the flow cell (≈one-third of the inductor surface). Nevertheless, the signal-to-noise ratio remains excellent, with the BSA-induced response (2880 ± 130 Hz) exceeding the baseline noise (13 ± 9 Hz) by more than two orders of magnitude. Statistical analysis using a two-tailed Student’s t-test confirmed the significance of the shift (p < 0.001). Upon reintroduction of PBS, the resonance frequency returned to baseline, demonstrating both the reversibility of the dielectric perturbation and the stability of the sensor. These results confirm that the platform can reliably distinguish subtle surface events from bulk dielectric effects, enabling high-resolution, real-time monitoring of biomolecular interactions under continuous flow.

The divergent responses of the sensor under different conditions validate our theoretical framework. While PBS injections primarily modulate the bulk dielectric environment, the observed increase in resonance frequency during protein injections is caused by the physisorption of BSA molecules at the sensing interface. This adsorption displaces high-permittivity water molecules with a lower-permittivity biomolecular layer, effectively reducing the local dielectric constant and the inter-turn capacitance ($C_S$). By modeling $C_S$ as two capacitors, the contribution of surface-bound biomolecules can be decoupled from bulk medium effects, providing a clear interpretation of the signal.

To assess analytical sensitivity under continuous flow, a calibration curve was constructed using BSA concentrations from 50 to 600 ppm (0.75 to 9.0 mM, Figure 7b). The sensor response exhibits a characteristic sigmoidal upward trend, with the frequency shift increasing progressively until surface saturation is reached. The data were fitted to a Hill function, which effectively describes adsorption phenomena. The regression yielded |Δf| = (4000 ± 1000)·[BSA, ppm]^(1.4 ± 0.4)/((210 ± 80)^(1.4 ± 0.4) + [BSA, ppm]^(1.4 ± 0.4)) (R² = 0.99), confirming an excellent fit to the theoretical adsorption model. All replicates showed a relative error below 10%, highlighting the reproducibility and robustness of the integrated fluidic platform.

From this dynamic characterization, the LoD was determined to be 9 ppm (0.14 mM), with a LoQ of 21 ppm (0.32 mM). The linear dynamic range, defined between 20% and 80% of the maximum response, spans 79–555 ppm (1.2 to 8.4 mM). These analytical figures of merit highlight the potential of the PCB-integrated inductor for high-precision, label-free monitoring of bioanalytes in the liquid phase.

To advance from label-free monitoring to selective biosensing, the epoxy-based solder mask of the PCB was functionalized to enable the specific recognition of BSA through immobilized anti-BSA antibodies. Although the solder mask is typically regarded as a purely protective layer, its surface chemistry was deliberately exploited here as an active platform for covalent bioreceptor attachment. To the best of our knowledge, this constitutes a novel use of intrinsic PCB materials for biofunctionalization. Within the proposed detection framework, the formation of a dense antibody layer and subsequent antigen binding alters the local charge distribution and dielectric environment at the sensing interface. This functionalization was implemented directly on the inductor surface using an MPA/EDC/NHS activation strategy (see Materials and Methods), yielding an integrated architecture capable of continuous, real-time, and highly selective biosensing.

The biosensing performance of the functionalized platform was assessed using the calibration curve shown in Figure 8. Covalent immobilization of anti-BSA antibodies produces a pronounced enhancement of the transducer response, nearly doubling the maximum resonance frequency shift from 2880 ± 130 Hz to 5650 ± 190 Hz at 600 ppm (9.0 mM), corresponding to a 96% signal increase relative to non-functionalized surfaces. This amplification arises from the higher capture efficiency and increased surface density of BSA at the sensing interface. As the bound biomolecular layer displaces water within the fringing-field region, the effective $C_S$ decreases, leading to a systematic increase in the resonance frequency in full agreement with the transduction model described in Section 3.1.

To confirm that the observed signals originate from specific biorecognition, orthogonal validation was carried out by ATR-FTIR spectroscopy. The spectra reveal clear signatures of BSA at the surface, including the Amide I band at ≈1650 cm⁻¹ (C=O stretching), the Amide II band at ≈1540 cm⁻¹ (C–N stretching and N–H bending), and a broad N–H/O–H stretching band around 3289 cm⁻¹. This spectroscopic evidence, together with the positive frequency shifts, unequivocally confirms that the platform transduces specific antibody–antigen interactions.

In addition to sensitivity, surface functionalization markedly improves measurement precision. The relative standard deviation decreases from 8 ± 5% under non-specific conditions to 4 ± 3% for selective detection. This twofold improvement reflects the transition from a largely stochastic, physisorption-driven response to a well-defined and reproducible antibody–antigen binding process.

The calibration data were fitted using a Hill model, |Δf| = (6000 ± 400)·[BSA, ppm]^(1.5 ± 0.4)/((81 ± 6)^(1.5 ± 0.4) + [BSA, ppm]^(1.5 ± 0.4)) yielding an excellent agreement with the experimental results (R² = 1.00). The Hill coefficient (n = 1.5 ± 0.4) indicates moderate positive cooperativity, while the half-maximal response concentration (EC₅₀ = 81 ± 6 ppm = 1.22 ± 0.09 mM) provides a quantitative measure of the effective binding affinity.

The benefits of functionalization are further reflected in the analytical figures of merit: the limit of detection is reduced to 1.7 ppm (0.026 mM) and the limit of quantification to 3.8 ppm (0.057 mM), with a refined linear range of 31–211 ppm (0.47–3.2 mM). These values represent approximately a fivefold improvement over the non-specific configuration, demonstrating that the engineered biorecognition layer not only confers selectivity but also acts as an effective signal-amplifying interface that optimizes the electromagnetic coupling between the analyte and the inductor’s fringing field.

To further confirm that the observed responses originate from specific biomolecular interactions rather than non-specific adsorption or bulk dielectric fluctuations, competitive interference experiments were performed using Horseradish Peroxidase (HRP, ≈44 kDa) as a non-binding control (Figure 9a). To rigorously assess the sensor’s selectivity, HRP was tested at the highest concentrations used in the BSA calibration, maximizing potential interference from bulk permittivity changes or non-specific protein adsorption. Even though BSA and HRP have comparable molecular weights, results show that HRP produced a response approximately 60% lower than that of BSA. Statistical analysis verified this difference as highly significant (t ≈ 24, df = 4, p < 0.0001), demonstrating that the functionalized inductor surface maintains high molecular specificity toward its target analyte.

The dynamic robustness of the platform was further evaluated through real-time step-response analysis (Figure 9b). With successive injections of increasing BSA concentrations, the sensor exhibited rapid, well-defined, and monotonic upward frequency shifts (Δf↑), accompanied by stable baselines and clear steady-state plateaus for each step. This systematic upward trend reflects the cumulative displacement of water molecules by the adsorbing protein layer, consistent with the $C_S$ modulation model. In contrast, as shown in Figure 6a, bulk ionic variations consistently generated downward frequency shifts (Δf↓). The coexistence of these opposing responses, upward for surface-specific binding and downward for bulk dielectric effects, demonstrates the intrinsic self-discriminating capability of the PCB-integrated inductor. This dual-polarity behavior confirms that the sensor can reliably distinguish target biomolecule interactions from environmental fluctuations, providing strong evidence of its suitability for label-free, high-resolution biosensing in complex analytical environments.

4. Conclusions

This work establishes a novel paradigm for real-time bioanalytics by demonstrating a compact, low-cost PCB-based inductive biosensor engineered for stable operation under continuous flow conditions. Unlike conventional resonant sensors, which are often limited to static measurements, our architecture leverages a dual-capacitance mechanism, conceptually represented by two capacitors, to intrinsically differentiate between bulk ionic strength, which lowers the resonance frequency, and surface molecular adsorption, which increases it. This effectively addresses a critical bottleneck in label-free sensing: the interference of the surrounding liquid environment on surface-specific signals.

Experimental validation with the BSA–antibody model demonstrated a limit of detection of 1.7 ppm (0.026 mM), positioning the platform competitively with commercial QCM and SAW biosensors (typical LoD: 0.1–10 ppm for proteins). Beyond sensitivity metrics, the near-unity correlation (R² ≈ 1.00) and the significantly reduced measurement variability (4 ± 3%) achieved through specific surface functionalization demonstrate that PCB-integrated inductors are not merely a cost-effective alternative, but a robust and reliable platform for precision biosensing. By mitigating parasitic effects and electromagnetic noise through integrated design, this approach enables scalable, wireless, and wearable sensing architectures, as well as automated in-line monitoring. By integrating fluidics with electromagnetic sensing on a standard PCB, a common electronic component is transformed into a sensitive analytical tool, offering a flexible platform for applications in environmental monitoring, industrial quality control, and biomedical analysis.