Broadside‐Coupled Split Ring Resonators as a Model Construct for Passive Wireless Sensing

Passive and wireless Radio‐Frequency (RF) sensors are a unique, enabling modality for emerging applications in environmental sensing. These sensors exhibit several key features that may unlock new functionalities in complex environments: sensors are composed of zero electronic components, are wirelessly interrogated even in opaque media, and structures are often inherently biocompatible. Such capabilities make it unique in the realm of sensing architectures. Here, the broadside‐coupled, split‐ring resonator is studied as a compact and versatile model structure for RF sensing (of potentially mechanical and biochemical environments). A new analytical model is derived to assess resonator behavior—these yield a rapid, first‐order approximation of the resonator resonant frequency or sensitivity. Finally, experimental investigations into how sensors may be optimally designed, sized, and interrogated to enhance sensitivity or spectral intensity are performed. These studies encompass a wide variety of potential dimensional and dielectric modifications that may be relevant to emerging sensors. Last, hydrogel polymeric sensors are synthesized and studied to assess how practical sensors may deviate in response from expectations. Such investigations lay the groundwork for how such sensing architectures may be adapted to fit application needs.


Introduction
[3][4] Briefly, conventional RF sensors are composed of a circuit composed of series DOI: 10.1002/adsr.202300006inductance (L, realized by a planar coil) and capacitance (C, composed of parallel plates).Either the inductance or capacitance of the circuit varies with the environmental signal, which can then by read out wirelessly through magnetic/inductive coupling.This often (but not always) occurs via a nearby, wirelessly coupled readout coil that itself is directly connected to a vector network analyzer (VNA).[19] Real-world application of such sensors typically derives from the unique capabilities of this modality: sensing architectures do not require any electronics as they can be exclusively composed of patterned metal films, they are natively wirelessly interrogated even in light-scattering environments and are often inherently biocompatible.As such, these sensors have a particularly established role in remote pressure sensing within the human body.Despite these powerful characteristics, these sensors are often limited in practice.Stable interrogation remains tricky-particularly in mechanically-unstable environments-and sensors have typically low sensitivity and can be prone to cross-coupling of unwanted signals.Such weaknesses are being addressed by emerging techniques that modify sensors and their accompanying readout strategy.For example, sensors may be integrated into more complex structural relay networks that either significantly improve spectral stability, [20,21] or augment readout by enabling long-distance interrogation. [22][25][26] Such strategies primarily modulate the readout of the sensor itself, and typically sensor design has not varied from basic inductorcapacitor series architectures.
[33][34] For sensors, these split rings are interceded by environmentally-responsive materials that amplify external signals-for example, a soft material can render the resonator pressure-sensitive, while an absorbent biopolymer may render the resonator chemically responsive.Such sensor architectures effectively fold in the inductance and capacitance into the same region.This not only makes a highly compact construct but facilitates straightforward fabrication because each split ring can be built in a single plane separately and subsequently fused with an interlayer material.Such structures are additionally relatively straightforward to synthesize at high density using microfabrication (wherein split rings and dielectric layers can be deposited and patterned in single layers), or low-cost roll-to-roll fabrication techniques (wherein split rings can be patterned using vinyl/metal cutters and layered with interlayer materials).When designed properly, electric fields in such resonators localize near exclusively to in between the split rings-this means that sensor sensitivity is maximized as the minimal signal is lost due to fringing electric fields.This also improves sensor specificity due to reduced parasitic signal from the surrounding environment (which would suppress signal from the desired active region/material in between the split rings).Split-ring resonators are most commonly studied in the planar format, where analytical models have been developed to track the resonant frequency of such architectures. [31,34]Less common are studies on the broadside-coupled structure utilized in our research, where resonators are typically simplified into relatively basic LC resonator circuit structures.In general, these models assume substrates with low dielectric constants (well below 10), whereas sensors can potentially possess significantly higher dielectric constants (in addition to significant loss components) due to the presence of water within biosensors (or chemical sensors).In practice, this results in large deviations of more basic analytical models from the experimental response.
In this publication, we perform modeling and studies on the performance of BC-SRR sensing architectures given a wide variety of changing conditions meant to simulate their utilization in diverse applications (in either mechanical or biological sensing).We first develop an improved analytical model of resonator behavior.This is then validated with extensive studies on resonator response given different conditions in resonator geometry, combined alongside controlled modulations of interceding layer complex permittivity (real components and loss tangent).We achieve large variations in such conditions first by using 3D-printing of fixtures to precisely control resonator structural properties. [35]ext large shifts in interceding layer permittivity are achieved using solvents, salts, water, and dissolved polymer-these materials allow permittivity to span nearly an order of magnitude, alongside controlled variances in loss tangent.The sensitivity and spectral intensity of this architecture and its readout is measured.Finally, working hydrogel mechanical and chemical sensors are synthesized and studied for their deviation from expected behavior.Importantly, we identify the role that device characteristics play in the performance of BC-SRR sensors, summarize optimal regimes where sensors may operate, and how sensors may potentially be biased to improve behavior.We anticipate that such studies will aide engineers in the design, development, and optimization of BC-SRR-based RF sensors for a variety of applications that may utilize passive wireless mechanical or chemical sensing.

Sensor Architecture and Sensing Methodology
The BC-SRR consists of two conductive plates and a dielectric substrate (that we often term as interlayer) in between the plates.Each of the plates has one split, and the plates are placed across the interlayer such that the splits are positioned in opposite directions to each other as shown in Figure 1a.The magnetic field applied externally excites the BC-SRR and is perpendicular to the plane of the conducting loop.Thus, the plates support a circulating current within a magnetic field.An electric field is built across the gap due to the charge stored across the split of the SRR plates.These stored magnetic and electric fields result in a resonant spectral response and form an electromagnetic resonator.In a fixed construct where the mechanical dimensions and interlayer permittivity are constant, the resonant frequency remains static with time.However, this resonator can readily be transformed into a sensor by introducing environmentally responsive interlayers.Such interlayers may undergo several possible transformations with stimuli, including deformations (changes in thickness) or modulation in permittivity (both real and imaginary components).
To first order, the resonant frequency of this structure is modeled by a simple resonator with a single lumped inductance and lumped capacitance, where inductance is given by L = 0.00508l(2.303log10 4l d − 2.451) H, [36] and per unit capacitance is given by , [37] when the shape of BC-SRR has a circular shape.This simple model can only grossly predict the first mode of the resonator and loses accuracy in more complex environments or geometries.We first sought to develop a more advanced analytical model for resonator performance.The equivalent circuit of the BC-SRR (i.e., the sensor) is shown in Figure 1b which has an equivalent impedance that can be given as Z sensor = R sensor + jX assuming symmetry in the circuit along the SRR splits for simplicity.R sensor presents the ohmic loss due to current conduction through the metallic plates and X = j(L eq + L X ) − j 1 C X is total equivalent reactance of the circuit where L T = L eq + L X and C T = C X represents total inductance and capacitance of each half of the circuit shown in (Figure 1b) and whose first-mode f res can be determined from the equations 1. Where, and capacitances C a , C b computed by reducing the circuit shown in Figure 1b where these parameters directly depend on L 1 , L 2 , C 1 , C 2 .L X and C X can be determined by the following sets of equations: L 1 , L 2 are the inductance of each plate of the sensor, where the plate side has the length l 1 = L − g 2 − w d and l 2 = L − w d respectively.The side length of the sensor, L = 10, 13, 16 (mm) and split of each plate, g = 3 (mm), conductive metal strip width, w d = 3 (mm).These inductances have been computed based on their geometrical shapes. [36]C 1 , C 2 are the distributed capacitance formed between the sensor interlayer across the lengths To compute capacitance, capacitance per unit length can be determined using the following formula by Equation (4) and Equation ( 5), where  eff ,  r , h are elective dielectric constant of the interlayer under test, the relative dielectric constant of the interlayer material, and the interlayer height of the sensor respectively. ) In addition to its base response, resonator behavior is typically monitored using a VNA that is directly connected to a readout coil (often a simple loop antenna, (Figure 1c)).The input impedance seen by the VNA can be formulated as below where R an , L an , C an are the serial resistance, inductance, capacitance of the circular loop antenna, and M is the mutual inductance between the antenna inductance L an and resonator/sensor total inductance L Tthis can be represented as where k is the coupling coefficient between the antenna and resonator/sensor.With a reasonably high value of coupling the sensorresponse can be read by the VNA in terms of the S 11 parameter (dB).This reflection coefficient S 11 can be calculated as , where Z in can be found by Equation ( 6) and Z 1 is defined as per Equation (7).Embedded within this S11 parameter is the energy transferred by the VNA to the sensor (or the power consumption of the sensor).Within each spectral sweep of the VNA, the sensor absorbs heavily at its resonance, which is typically 10% of this bandwidth.The total power absorbed by the sensor is additionally proportional to the output power of the VNA (typically set as 10-100 mW) as well as its sweep rate.The simplified electrical model of the whole system is shown in (Figure 1c).
The analytically obtained spectral characteristics of an SRR were compared with finite element simulations conducted in COM-SOL Multiphysics.The eigenfrequencies of the structure were used to tune the dimensions.For a sub-gigahertz range of resonance frequency, a rectangular SRR with 16 mm × 16 mm and a strip width of 3 mm was designed.The interlayer was designed to exceed the SRR size by 1 mm on each side to ensure nearby fringing electric fields pass through the material under test.For frequency-domain simulations, the SRR was excited through an axially aligned multi-turn loop antenna (distanced ≈5 mm from the SRR) to obtain the reflection coefficients versus various interlayer thicknesses and materials.The resonant frequencies were then extracted and shown in figure 1c (right figure).The analytically obtained resonant frequencies using Equation (1) for various interlayer materials (i.e.different dielectric constant Er) at interlayer thicknesses of 2, 2.5, 3, and 3.5 mm closely matches with COMSOL simulation results.Deviation from finite element models primarily occurs in 2 regimes, at lower interlayer permittivity and at increased interlayer to resonator size ratios.In such situations, the effective capacitance is slightly underestimated in analytical models due to not accounting for fringing electric fields.

Resonator Characterization
A repeatable, well-controlled experimental setup was developed to study the behavior of the resonator under large variances of structural and dielectric conditions.This also captures how the resonator would effectively behave as a sensor, as environmental conditions modulate the state of the resonator.We are interested in experimentally-testing points where resonator performance will vary from modeled response-this primarily occurs at large interlayer-to-size ratios.As such, spacers were designed to approach the size of the resonator itself.Split ring resonator fabrication details and spacer design (Figure S1, Supporting Information) details are given in supplemental information.In practice, sensors can exhibit device-to-device variability that manifests from the fabrication techniques used, user error, dielectric variability in interlayer materials (as well as thickness variability), and misalignment in the two split rings.As such, devices can either present minimal or significant variability depending on the irregularity of the above parameters.To address device-to-device variations, sensors should be characterized very carefully, and multiple sensors should be tested to characterize properties such as resonant frequency, sensitivity, etc.Should variability be unacceptable, it is likely that process parameters will need to be modified to achieve a more stable device-to-device response.
The dielectric constant was modulated with the intermixing of water and solvents/salts.This is a relatively simple way of studying a wide variance of interlayer conditions-liquids can readily reach large variances in permittivity (≈5× changes) that are not possible in solid interlayers.The dielectric loss of liquid mediums is readily modulated via the simple addition of salt into the solution.In contrast, solid substrates with high loss are not easily obtained due to the inherent complexities of developing material heterostructures.Resonant responses of the sensors were characterized with a Keysight E5063A network analyzer using an RF Explorer H-loop antenna attached to the coaxial input.
We first studied the behavior of the resonator with deionized water as the base MUT (Figure 2).This relatively low-loss interlayer dielectric serves to give a baseline for resonator behavior (relative permittivity ≈ 80). [38]Interlayer thickness and resonator size were modulated and studied for their effect on spectral response.As expected, increasing interlayer thickness and reducing resonator size both lead to increases in the resonant frequency of the sensor (Figure 2d).This is due to reducing capacitance and inductance.However, rates of increase begin deviating from analytical models as interlayer thickness approaches 20% of the lateral size of the structure due to increasing parasitic capacitance.The sensor response is shown in terms of peak magnitude S 11 and resonant frequency.Experimentally observed resonant frequencies for different sizes of SRRs with modulating interlayer thicknesses were compared with analytically obtained resonant frequencies shown as dashed lines in the same Figure 2d.The 10 mm-sized resonator exhibits the largest deviation from analytically modeled response due to the larger interlayer to lower lateral size to interlayer ratios of these constructs.Note that these findings are given for an interlayer of exceptionally high dielectric constant and given interlayers with more typical dielectric constants (≈3-10), the interlayer thickness should ideally be at least 2 orders of magnitude smaller than the resonator width to reduce parasitic effects.
We next sought to experimentally test the impact of large shifts on MUT permittivity ′ and dielectric loss ′′ on resonator response, where the complex permittivity of the MUT is  () = ′ () − j′′().This is achieved by the addition of NaCl salt (that will heavily impact the dielectric loss while weakly changing the permittivity), [39] or ethanol (that will heavily impact the permittivity). [38]An advantage of our approach is the rapid and facile dissolution of either of these modulators directly in water, allowing us to easily modulate permittivity in controlled ways.Relative permittivity for lossy materials can additionally be formulated in terms of a dielectric conductivity,  S m −1 .Modulation of either term in the MUT changes the capacitance of the resonator, and whose impact on resonator spectral response is probed with VNA.We first tested the impact of varying concentrations of NaCl from 0% to 0.4% in the MUT.As expected, increasing concentration causes a noticeable dip in the S 11 as the MUT becomes more conductive and lossy (Figure 3a,d).The 1 mm thickness sensor exhibited a minor increase at a very low salt concentration that is an artifact of impedance matching that occurs in this condition.Such matching effects are explored in more detail below, however in practice, these may be undesirable and can be suppressed by shifting the sensor (changing its coupling coefficient).We experimentally observe a minor reduction in resonance frequency due to high concentrations of salt.This results from the increases in the total magnitude of the MUT capacitance, which leads to a reduction in the resonant frequency of the resonator (Figure 3c).The dielectric constant of concentrations of NaCl is modeled from an existing [39] publication.As can be seen, our model closely captures the experimental resonant frequency of our resonators.
We next studied the impact of varying ethanol concentrations in water (Figure 4).This primarily modulates permittivity ′.In this experiment we additionally experimentally measured this response at two different coupling coefficients, k 1 = 0.7 and k 2 = 0.9, where k 2 > k 1 .Here we seek to illustrate how shifts in the impedance at the VNA input node can impact the measured magnitude from resonators. Figure 4b shows the impact of increasing ethanol concentration on the resonant frequency of the structure.As expected, the resonant frequency increases alongside increasing ethanol concentration-these results from the low capacitance of the resonator as a portion of water ( ′ = 80) is effectively being replaced with proportions of ethanol ( ′ = 24).The relative dielectric constants for various concentrations of Ethanol-DI mixture are used from existing literature, [38] for the purpose of analytical analysis.Resonator response deviates from expected behavior at higher concentrations of ethanol.This is expected as in such scenarios parasitic capacitances begin to influence the response of the sensor/resonator and drive the experimental results away from our analytical model.
We then compared the maximum S 11 response for the resonator at the previous ethanol mixtures for two coupling coefficients (Figure 4d).These two experiments illustrate the impact of impedance at the VNA input, and how impedance matching impacts the measured spectral response from resonators.Increasing ethanol effectively reduces the impedance of the resonator as the permittivity of the MUT reduces.For the lower coupling coefficient case, the thicker interlayer resonators (2 and 3 mm, possessing lower impedance) reduce in S 11 magnitude response as the ethanol increases.However, the higher impedance 1 mm interlayer resonator exhibits a maximum in S 11 as ethanol increases (because of impedance matching at the VNA input node).This effect is more pronounced in the higher coupling coefficient case.In this scenario, the input impedance at the VNA from all the resonators is higher due to increased coupling.All resonators exhibit a maximum in S 11 response as the ethanol concentration increases, appearing at increasing concentrations of ethanol (lower permittivity) for 3, followed by 2, and then 1 mm thick interlayers.Such experiments are indicative of the simple ways BC-SRR resonators/sensors may be modified to enhance measured magnitude during backscatter measurement, which may include a variation of the coupling, solvent, or thickness of the construct.
We next extracted the sensitivity of several resonator geometries at various set points/biases in the resonator geometry or dielectric constant (Figure 5).These effectively illustrate the sensitivity of key resonator metrics (resonant frequency or magnitude) to major perturbations in thickness, permittivity, and loss tangent.Frequency is primarily impacted by thickness and real permittivity (approximated as ethanol here), whereas the magnitude is primarily impacted by changes in the loss tangent (approximated as the salt solution here).Resonators with larger resonator length to interlayer thickness ratios exhibited increased resonant frequency sensitivity in comparison to those with smaller ratios, this was found irrespective of resonator parameters being varied (whether changing interlayer thickness or dielectric permittivity).Given fabrication limits, it is generally desirable to push to thinner interlayer thicknesses to improve sensor sensitivity.In our presented studies thinner thicknesses also led to higher sensitivity in the magnitude of the resonator due to changes in salt concentration (or loss tangent).We note that in practice achieving higher sensitivity in the sensor magnitude is dependent on maximizing the S 11 magnitude response of the resonator.This typically depends both on resonator geometry and its coupling coefficient the readout coil.For a subset of geometries, we studied in this publication, we identified dielectrics to achieve a maximum S 11 response for our given coupling coefficient (Figure S2, Supporting Information).Note that the actual optimal spectral response is heavily dependent on required sensor characteristics (such as sensitivity, resonant frequency, footprint, coupling coefficient, etc).Broad trends that have been identified here can be used to optimize sensor response given application constraints.
We finally constructed working BC-SRR sensors and studied how the response of practical sensing structures may deviate from expected behavior.In practice, sensor interlayers are often not simply open to the environment (such structures are difficult to construct/scale to small sizes) and are instead built from absorbent or deformable interlayer materials that interact mechanically or chemically with the environment. [28,29,40,41]Here we form mechanical and chemical sensors from polyacrylamide hydrogel interlayers, which are composed of acrylamide polymer crosslinked to form a hydrophilic matrix that stores water. [42]This structure no longer needs solid surrounding support and can be synthesized simply by gelling the polymer in between layers of metal. [40]e sought to directly compare the response of this gelled hydrogel sensor with the response of our fixed resonator construct when immersed in a near-equivalent ungelled chemical environment (Figure 6).To obtain similar thicknesses of resonators, we gelled thinner hydrogel sensors that subsequently swell to a similar interlayer thickness as our fixed resonator construct after equilibration in water.Next, we utilized a mixture of dissolved acrylamide monomer particles as our MUT (at the same weight concentration) in our fixed resonator.In this way, we attempt to create equivalent constructs where the only difference is the crosslinking/gelation of hydrogel to form a solid matrix.
Practical interlayers may be formed from various percent weights of polymers (with different accompanying porosities), and we sought to understand how different weight percentages of polymer would impact resonator sensing behavior (whether in gelled or ungelled form).We first studied the impact of changing acrylamide weight in our fixed construct, and as expected we found large increases in the weight of acrylamide would be accompanied by a small reduction in the resonant frequency of the resonator as the total magnitude of the dielectric constant increases (this is primarily due to the loss tangent of the monomer).More importantly, we tested how our gelled sensors differed in sensitivity from our fixed resonators.Fixed resonators exhibit no sensitivity to mechanical pressure (due to the 3D printing of the encompassing solid scaffold), however, gelled resonators exhibit pressure sensitivity in accordance with the stiffness of the polymer interlayer (with lower percent weight creating a softer material, Figure S3, Supporting Information).We next studied the sensitivity of our fixed and gelled sensors to increasing concentrations of salt or ethanol.Hydrogel sensors exhibit reduced sensitivity in comparison to fixed resonators, with the higher percent weight (20%) hydrogel sensors exhibiting lower sensitivity than the lower percent weight (10%)-this was true both for the salt and ethanol measurement.This is a result of the absorption properties of the matrix itself, where less porous, higher percent weight polymers suppress the absorption of molecules.One caveat for this hydrogel formulation is the swelling properties of the polyacrylamide hydrogel itself, where at high concentrations of solvent (>50%) the hydrogel exhibited an extra accompanying physical contraction that leads to a further increase in resonant frequency beyond expectation.
Combined, these results are indicative of the impact of interlayer properties on the resonator behavior, whereby structural and dielectric properties combine with mechanical and absorptive properties to modulate final characteristics.Practical chemical sensors will often exhibit reduced sensitivity, however, may have a larger working range.Practical sensors may also utilize unique mechanical properties of the interlayer material itself, whereby the material may additionally compress or swell in response to stimuli.

Conclusion
In this work, we have investigated broadside-coupled split ring resonators as a model sensing construct for passive wireless sensing.We developed an updated analytical model for the behavior of such resonators, in addition to performing extensive studies on the spectral response of such constructs under large variations in dimensional and dielectric properties.Such variations were achieved through the combination of fixed, 3D-printed resonators that were immersed in liquid solutions that allow the permittivity (both real and imaginary components) to span nearly an order of magnitude.Last, working hydrogel mechanical and chemical sensors are synthesized and studied for their deviation from expected behavior.We study how material properties may impact resonator characteristics, and how sensors may potentially be biased to improve behavior (through changes in the immersion solvent, coupling coefficient, or geometry).We anticipate that such studies will aid engineers in the design, development, and optimization of BC-SRR-based RF sensors for a variety of applications that may utilize passive wireless mechanical or chemical sensing.

Experimental Section
The experimental details are provided in the Supporting Information.Statistical Analysis: A Keysight E5063A vector network analyzer was used for testing and data collection.All sensors were studied in duplicate for each type of experimental condition.Data were processed using MATLAB R2019b, wherein the peak S 11 and resonant frequency were numerically extracted from the spectral response acquired by the VNA.These metrics were averaged, and standard deviations (STD) were calculated and presented in plots with vertical lines on the data points along the averaged curves.

Figure 1 .
Figure 1.BC-SRR as a model architecture for passive wireless sensing.a) Diagram of the experimental setup and physical structure of BC-SRR.Side length L, interlayer thickness h, and relative dielectric material constant ′ and dielectric loss ′′ are varied throughout our studied.b) Equivalent electrical circuit representation of the resonator.c.i) Simplified equivalent circuit diagram of the sensor wirelessly coupled to its reader antenna directly connected to a VNA.c.ii) Comparison of analytically-derived data with COMSOL simulation for various interlayer thicknesses (in mm) with different dielectric constants (solid -COMSOL, dotted -analytical).

Figure 2 .
Figure 2. Modulation of BC-SRR geometry and impact on sensor spectral response.a) Experimental setup of a sensor with deionized water as the interlayer MUT.b) Physical structure of the BC-SRR sensor where the size of the sensor with length L and interlayer thickness h are being varied.Here, the interlayer material under test is DI water.c) Peak S 11 magnitude response of various resonator geometries.N = 2. d) Experimental response (with solid lines) as compared to analytical model response (with dashed lines) of sensor resonant frequency for varying resonator geometries.N = 2.

Figure 3 .
Figure 3. Impact of interlayer dielectric loss on BC-SRR spectral behavior.a) Experimental setup where the sensor MUT is NaCl of varying concentrations -this weakly reduces the permittivity ′, while heavily increasing the dielectric loss ′′.b) Spectral response of a single sensor (h = 2 mm) for three different concentrations of NaCl.c) Comparison of the experiment (Solid lines) and analytical model (Dashed lines) of the resonator f res for various concentrations of salt solution for different interlayer thicknesses.N = 2. d) Experimental maximum S 11 response for various concentrations of salt solution with interlayer thickness also being varied.N = 2. L = 13 mm for all sensors.

Figure 4 .
Figure 4. Impact of interlayer dielectric permittivity on BC-SRR spectral behavior.a) Experimental setup where the MUT is changing concentrations of ethanol in water-this primarily modulates the permittivity ′.Two coupling coefficients are studied in this experiment, k 2 > k 1 .b) Comparison of the experiment (solid) and analytical model (dotted) of the resonator f res for various concentrations of ethanol for different interlayer thicknesses (k 1 = 0.7).c) Experimental maximum S 11 response for the varying concentration of ethanol while interlayer thickness is varied.d) Similar experimental maximum S 11 response for a sensor whose coupling coefficient is higher (k 2 = 0.9).L = 13 mm and N = 2 for all plots.

Figure 5 .
Figure 5. Sensitivity of BC-SRR spectral behavior.a) Percentage shift in resonator resonant frequency to local changes in thickness for different sizes of the resonator as the interlayer thickness is modulated from 1 to 10 mm (DI water interlayer).b) Percentage shift in resonator resonant frequency to local changes in ethanol concentration for various interlayer thicknesses when L = 13 mm.c) Change in the maximum magnitude of S 11 to local changes in salt concentration for various interlayer thicknesses when L = 13 mm.

Figure 6 .
Figure 6.Synthesis and study of practical BC-SRR biosensors.a.i) Fixed resonator construct with acrylamide (AAm) dissolved in water as the interlayer of the BC-SRR structure, a.ii.)Practical sensing construct with polyacrylamide hydrogel (PAAm) crosslinked with N, N′-Methylenebisacrylamide as the interlayer.b) Resonant frequency versus acrylamide weight for our fixed resonator construct, N = 1.c) Peak magnitude response S 11 of PAAm hydrogel sensors (Solid line) compared with AAm solution (Dashed lines) for increasing salt concentration.Resonator h = 1 mm and N = 2. d) Resonant frequency of PAAm hydrogel sensors (Solid line) compared with AAm solution (Dashed lines) for increasing ethanol concentration.Resonator h = 1 mm and N = 2. L = 13 mm for all resonators.