The design of meander sensor

The measurement principle of the cancellation-type sensor is that the signal is evenly divided into two signals with the same amplitude and phase after passing through the first Wilkinson power divider, one of which is 180° out of phase with the other after passing through an inverter, and the two signals with the same amplitude and opposite phase offset each other at the second Wilkinson power divider, which plays the role of power synthesis. The design schematic of the conventional cancellation-type sensor based on the microstrip line is shown in Fig. 1.

Figure 1. The schematic of straight sensor.

The measurement of straight sensor can be divided into three cases according to the analysis in [Reference Liu, Zou, Zhu, Lin and Wang30].

1. (1) When the same substances are added to the test and reference segments and the losses of the straight sensor are not considered, the transmission coefficient can be expressed as

   (1)\begin{equation}{S_{21}} = 0\end{equation}

2. (2) When different substances are added to the test and reference segments and the losses of the straight sensor are not considered, the transmission coefficient can be expressed as [Reference Liu31]

   (2)\begin{align} {S_{21}}& = {S_{21\_Ea}} \times \Delta {S_{21\_{\textrm{MUT}}}} \\& = {S_{21\_Ea}} \times \left( {{S_{21\_a}} - {S_{21\_b}}} \right) \\& = {S_{21\_Ea}} \times \left[ {{{2{Z_0}} \over {2{Z_0} + {Z_a}\left( \omega \right)}} - {{2{Z_0}} \over {2{Z_0} + {Z_b}\left( \omega \right)}}} \right] \\& = 2A{Z_0}{S_{21\_Ea}}j\omega {C_{\textrm{l}}} \times \left( {{\varepsilon _a} - {\varepsilon _b}} \right) \\& = B\left( {{\varepsilon _a} - {\varepsilon _b}} \right) \end{align}

   where ${\varepsilon _a}$ and ${\varepsilon _b}$ are the complex permittivity of microfluidics added to test branch and reference branch, C _l is the channel capacitance of the liquid, ${Z_0}$ is the characteristic impedance of the transmission line and the impedance of the upper branch ${Z_a} = 1/\left( {j\omega {C_p} + j\omega {C_l}{\varepsilon _a}} \right)$, ${S_{21\_Ea}}$ represents the transmission coefficients of the remaining signal lines after removing ${l_a}$ section, and ${S_{21\_a}}$ and ${S_{21\_b}}$ are the signal transmission coefficients of branch ${l_a}$ and ${l_b}$. The different transmission coefficient of the upper and lower branches is ${\Delta }{S_{21\_{\textrm{MUT}}}}$.

3. (3) When different substances are added to the test and reference segments and the losses of the straight sensor are considered, the transmission coefficient can be expressed as

   (3)\begin{align} {S_{21}} = & {S_{21\_Ea}} \times {\Delta} {S_{21\_{\textrm{MUT}}}} + {S_{21\_{\textrm{lad}}0}} \\ = & 2A{Z_0}{S_{21\_Ea}}j\omega {C_l} \times \left( {{\varepsilon _a} - {\varepsilon _b}} \right) + {S_{21\_Ea}}\left( {{\Delta}{C_{\textrm{l}}}{\varepsilon _a} + {\Delta}{C_{\textrm{p}}}} \right) \\ & + \left( {{S_{21\_Ea}}{S_{21\_b}} + {S_{21\_Eb}}{S_{21\_a}}} \right)\left( {{C_l}{\varepsilon _a} + {C_p}} \right) \\ = & M{\varepsilon _a} - N{\varepsilon _b} + P \end{align}

The parameters M, N, and P can be obtained by calibrating sensor based on two microfluidics with known dielectric properties. When a microfluid of the same known dielectric parameter is placed at both the test branch ${l_a}$ and the reference branch ${l_b}$ of the sensor for calibration, ${\varepsilon _a} = {\varepsilon _b}$. The non-ideality of the power divider and synthesizer and the difference between the two channels are set to $ {S_{21\_{\textrm{lad}}0}}$, where ${S_{21\_Ea}}\left( {{\Delta }{C_{\textrm{l}}}{\varepsilon _a} + {\Delta }{C_{\textrm{p}}}} \right)$ indicates the transmission effect due to the difference in the materials added to the two branches and the unsatisfactory design of the power splitter. $\left( {{S_{21\_Ea}}{S_{21\_b}} + {S_{21\_Eb}}{S_{21\_a}}} \right)\left( {{C_l}{\varepsilon _a} + {C_p}} \right)$ indicates the transmission effect due to the difference between the two branches.

Equation (3) can be rewritten to ${({S_{21}})_b} = M{\varepsilon _b} - N{\varepsilon _b} + P$. The material at the reference branch ${l_b}$ remains unchanged, and the material at the test branch ${l_a}$ is changed, ${\varepsilon _a} \ne {\varepsilon _b}$. Then ${({S_{21}})_a} = M{\varepsilon _a} - N{\varepsilon _b} + P$. The parameters from Equation (3) can be approximated as constants when the dielectric properties of the microfluidics are varied in small ranges. Then ${({S_{21}})_a} - {({S_{21}})_b} = M\left( {{\varepsilon _a} - {\varepsilon _b}} \right)$, that is,

(4)\begin{equation}{\Delta }{S_{21}} = M{\Delta }\varepsilon \end{equation}

According to Equation (4), the dielectric parameter of the microfluidics at the test branch can be acquired by measuring the variation of the transmission parameters of the sensor. As can be seen in Fig. 1, the straight sensor is designed to achieve a 180° phase difference by extending the ${\lambda \mathord{\left/ {\vphantom {\lambda 4}} \right. } 4}$ path on each side of the test side. Now, this part is replaced by meander line, and the schematic of the meander sensor is shown in Fig. 2, where ${l_a} - {l_b} = 3\lambda /2$.

Figure 2. The schematic of the meander sensor.

The derivation process of the meander sensor is like that of the straight sensor, which gives the relationship between the transmission parameters of the meander sensor and the microfluidics dielectric properties. The difference between two sensors comes from case 3. The introduction of meander line reduces impedance at the meander section and at the same time the length of the meander section is close to three times that of the straight section, which can be approximated by microwave theory as ${G_a}\left( \omega \right) = 1/{Z_a} \approx {\left( {j\omega {C_p} + j\omega {C_l}{\varepsilon _a}} \right)^3}$. The materials added to the test branch and reference branch are not the same, as well as losses are considered. The non-ideality of the power dividers and the subtle differences of the two channels are set to ${S_{21\_{\textrm{lad}}}}$. According to Equation (3), the transmission coefficient can be expressed as

(5)\begin{align} {S_{21}} &= {S_{21\_Ea}} \times {\Delta} {S_{21\_{\rm{MUT}}}} + {S_{21\_{\rm{lad}}}} \\ &= {S_{21\_Ea}} \times \left( {{S_{21\_a}} - {S_{21\_b}}} \right) + {S_{21\_{\rm{lad}}}} \\ &= {S_{21\_Ea}} \times \left[ {{{2{Z_0}} \over {2{Z_0} + {Z_a}\left( {\omega} \right)}} - {{2{Z_0}} \over {2{Z_0} + {Z_b}\left( {\omega} \right)}}} \right] + {S_{21\_{\rm{lad}}}} \\ &\quad \approx \,U\,\varepsilon _a^3\, -\,V\,{\varepsilon _b}\, + \,W \end{align}

The introduction of meander line changes R, L, C, and G in the equivalent circuit, so that the impedance of the test branch decreases, which is about the third power of the reference branch after approximate analysis. After calibrating the sensor with two microfluidics of known dielectric parameters, there is

(6)\begin{equation}{\Delta }{S_{21}} = U{({\Delta }\varepsilon )^3}\end{equation}

When the dielectric parameters of materials in the test change in small ranges after calibration, the parameter U is regarded as a constant. However, when the dielectric parameters of materials in the test change far from the calibration value, the parameter U also gradually deviates from the constant value, leading to an increase in error. This is similar to the parameter M in the straight sensor. According to Equation (6), a larger variation of the transmission coefficient S ₂₁ is observed in Vector Network Analyzers after three amplifications. This proves that the meander sensor is easier for detecting small changes of the dielectric properties of microfluidics.

Figure 3. The simulation models of two different cancellation-type sensors: (a) straight sensor and (b) meander sensor.

Comparative simulation analysis

The simulation models are constructed in Ansoft-HFSS according to above straight and meander sensor schematics, as shown in Fig. 3. The operating frequency of the sensors is 10 GHz, the dielectric substrate is Rogers 6010 with a relative permittivity of 10.2, the substrate thickness is 0.635 mm, and the microstrip line is 18 μm thick. The dielectric substrate and size are chosen to suppress the high frequency waveform and to avoid the deterioration of the transmission line performance. The operating frequency of the sensor is set at 10 GHz in order to achieve a compact design and reduce the amount of material to be measured at the meander section. Since chemical reagents are often used as test solutions for validating sensors, the dielectric parameters of methanol–ethanol mixtures with different molar fractions in [Reference Mashimo, Umehara and Redlin16] are used as reference values in this paper. The methanol–ethanol mixture is added to the test branch in simulation to obtain the transmission coefficient S ₂₁ for the two sensors. The performance of the two sensors is compared based on the simulation results.

The cancellation-type sensor works by measuring the changes of the sensor transmission parameter S ₂₁ in response to the changes of the microfluidics dielectric properties. To measure the unknown dielectric parameters of microfluidics, two microfluidics with known dielectric parameters are required as calibration fluids to calibrate the two sensors and obtain the parameters M and U. Absolute methanol (0.4 μL) is placed at test and reference branch to calibrate. The straight sensor was calibrated to −108.72 dB at 10 GHz, and the meander sensor was calibrated to −105.78 dB at 9.95 GHz. Calibrating the two sensors to similar positions is to facilitate the comparative analysis later.

The material under reference branch is not changed, the material of test branch is replaced with the methanol–ethanol mixture with a molar fraction of 0.9 (${x_M} = 0.9$). The ${\Delta }{S_{21}}$ obtained after calibration is substituted into Equations (4) and (6) to obtain the parameters M and U. Changing the solution at the test branch to methanol–ethanol mixture with different molarity (${x_M} = 0.0 \sim 0.8$), the S ₂₁ values are obtained by simulation and then are compared with the calculated values through Equations (4) and (6) as shown in Fig. 4. The error between measured and calculated values is smaller for both the straight sensor and meander sensor, but the misclassification rate is higher for the straight sensor than that of the meander sensor. Since the meander sensor can widen the distance of transfer coefficient S ₂₁ between different molar fraction mixture, it makes the meander sensor more accurate in determining the molar fraction of the microfluidic mixture, and the meander sensor does not have the phenomenon that any subsequent determination will be wrong once there is a misjudgment.

Figure 4. The contrastive analysis of simulation and calculation results of two sensors.

Figure 5. Sensors without the adjustable cavity: (a) straight sensor and (b) meander sensor.

Figure 6. Sensors with the adjustable cavity. (a) Straight sensor with adjustable cavity but without shielding cover. (b) Meander sensor with adjustable cavity but without shielding cover. (c) Front view of the meander sensor with shield cover. (d) Side view of a meander sensor with shield cover.

Experiments

The design and implementation of sensors

The above simulation models are processed into two physical sensors, as shown in Fig. 5. In testing the sensor performance, chemical reagents are often used as test solutions for the sensor performance. The experiments are conducted with different molar fractions of the methanol–ethanol mixture as test solution to analyze the accuracy of the meander sensor in measuring the unknown microfluidics dielectric parameters. The dielectric parameters of methanol–ethanol mixtures with different molar fractions in [Reference Mashimo, Umehara and Redlin16] are used as reference values in this paper. This test is conducted in the room of 23°C, and the type of vector network analyzer is 3672C, and the sweep range is 9–11 GHz. Among the purchased absolute methanol (${\textrm{C}}{{\textrm{H}}_3}{\textrm{OH}}$) content $ \ge 99.5\% $, non-volatile is ≤ 0.001%. For absolute ethanol (${\textrm{C}}{{\textrm{H}}_3}{\textrm{C}}{{\textrm{H}}_2}{\textrm{OH}}$) mass fraction ≥99.7%, volatile residue mass fraction is 0.001%.

In order to fine-tune the electrical length, compensate for the losses and shield the interference from environment, and the adjustable cavity is designed in this paper to fine-tune the offset effect of the sensor. The sensor after adding the adjustable cavity is shown in Fig. 6. The offset effect of the sensor is adjusted by different positions, depths, and number of the screws, which is rotated into the thread holes on the cavity wall.

Figure 7. No-load test system of meander sensor.

The size of the meander sensor without the adjustable cavity is 30 mm × 25 mm × 0.635 mm, which is smaller than that of straight sensor. The size of the meander sensor and the straight sensor with an adjustable cavity are 38 mm × 31 mm × 36 mm and 38 mm × 33 mm × 36 mm, respectively.

No-load and calibration testing of sensors

The vector network analyzer after calibrating is used to test the no-load condition of both sensors without placing microfluidics at the test and reference branches. The sensors are fine-tuned with the tuning screws and tuned to a better offset effect. The no-load test system of sensor with an adjustable cavity is shown in Fig. 7. When no test materials are loaded on the sensors, the S ₂₁ parameter of straight sensor at 9.88 GHz is −86.64 dB, the S ₂₁ parameter of the meander sensor at 9.94 GHz is −84.86 dB. Both sensors achieve good cancellation effect after fine-tuning with an adjustable cavity.

An equal amount (0.4 μL) of absolute methanol solution is placed at the test and reference branch of the sensor using a micro-syringe, and the sensor is tuned to a better offset point with the help of an adjustable cavity. The test result of the meander sensor after calibration with absolute methanol solution is shown in Fig. 8. The offset effect of the meander sensor can reach −87.75 dB at 9.67 GHz and the offset effect of the straight sensor is −91.18 dB at 9.73 GHz.

Figure 8. S-parameters tested after calibration.

The simulation and test results of the meander and straight sensors after calibration with absolute methanol are shown in Fig. 9. It can be seen from the graph that the test values differ from the simulation values by nearly 20 dB due to processing errors, the effects of welding, and air disturbance. The frequency shift occurs under the fine adjustment of the cavity.

Figure 9. The simulation and test comparison chart of two sensors.

The no-load and calibration results of the meander sensor designed in this paper were compared with the experimental results obtained by previous scholars, as shown in Table 1. Under the fine-tuning of an adjustable cavity with a shield cover, the offset effect of this paper is improved by more than 9 dB.

Table 1. Comparison table of no-load and calibration test results for different sensors

The test of minimum measurement volume for meander sensor

The volume of measured solution is tested to explore the effect of different solution volumes on the transmission parameters of the sensor, thus facilitating the control of the solution volume in the subsequent experiments. The meander sensor is calibrated with absolute methanol solutions of 0.2 μL, 0.4 μL, 0.6 μL, and 0.8 μL, which laid flat on the measurement end to observe the variation of the transmission coefficient S ₂₁, and the test results are shown in Fig. 10. As can be seen from the graph, the offset effect becomes worse as the liquid increases. This is due to the fact that when the volume of microfluidics increases, the channel capacitance changes accordingly, and thus the meander branch senses the change in liquid volume better, resulting in a larger difference in transmission between the two branches and a poorer offset effect. When the solution volume is 0.2 μL, as well as 0.4 μL, it is observed that the sensors’ offset effect do not change significantly. However, the meander test branch is not completely covered by fluid if the solution volume is below 0.4 μL, so that the transmission coefficient S ₂₁ variation ${\Delta }{S_{21}}$ detected by the meander sensor is less than the true value. Therefore, the volume of microfluidics should be controlled in the subsequent experiment to reduce the error. The minimum volume of fluid that ensures that the microfluidics can spread over the meander test branch of the meander sensor is 0.4 μL (Table 2). In order to reduce the volume of the microfluidics measured, the design of reducing the meander line width can be further explored.

Table 2. Comparison table of minimum measurement volume for different sensors

Figure 10. Effect of microfluidics volume on meander sensor.

The reagent test of two sensors

After calibrating both sensors with 0.4 μL absolute methanol solution (${x_M} = 1.0$), the ${({S_{21}})_{{x_M} = 1.0}}$ values of both sensors are obtained. The material under reference branch remains unchanged, and the material under test branch is replaced with methanol–ethanol mixture with a molar fraction of 0.9 to obtain the test values ${({S_{21}})_{{x_M} = 0.9}}$ of the two sensors. The parameters M and U are found by substituting ${({S_{21}})_{{x_M} = 1.0}}$ and ${({S_{21}})_{{x_M} = 0.9}}$ into Equations (4) and (6), respectively, where ${\varepsilon _{{x_M} = 0.9}}$ and ${\varepsilon _{{x_M} = 1.0}}$ are obtained by calculation in the literature [Reference Mashimo, Umehara and Redlin16]. The methanol–ethanol mixture with different molar fractions (${x_M} = 0.0 \sim 0.8$) is changed at the test branch. The complex permittivity ${\varepsilon _{{x_M}}}$ (${\varepsilon _{{x_M}}} = \varepsilon {^{\prime}} - j\varepsilon {^{\prime \prime}}$) of the methanol–ethanol mixture at different molar fractions is obtained by substituting the measured ${\Delta }{S_{21}}$ into Equations (4) and (6). The complex permittivity measured by the two sensors is compared with the reference values to obtain Fig. 11.

Figure 11. The complex permittivity of mixture from test and reference. (a) The test results of straight sensor. (b) The test results of meander sensor. (c) Comparison of the relative error measured by two sensors.

As shown in Fig. 11, the complex permittivity measured by the two sensors after calibration with mixture solution in literature is close to the reference value. Except the ${x_M} = 0.1$ group, the relative error of the meander sensor in measuring the complex permittivity of the methanol–ethanol mixture is less than 1% for all groups, which is smaller than that of straight sensor (less than 3%). In the simulation analysis of the methanol–ethanol mixture with a molar fraction of 0.1, the relative error is also larger than that of the other groups. The characteristics of the mixture solution at this molar fraction (${x_M} = 0.1$) is different from other groups, or the error in the data from the reference compared in this group is larger than in the other groups. It can be seen from the experimental results that the meander sensor has a smaller test error and a higher test accuracy than straight sensor, which is more likely to detect the subtle changes of dielectric property from the precious and rare samples.