3. Multilayered substrate configurations

In a previous section, we presented how the real and imaginary parts of the dielectric constant of the conventional microstrip configuration can be determined using the phase-shift method based on the phase of the transmitted signal. The same method can be applied for nonhomogeneous substrate such as multilayered or heterogeneous substrate. In this section we will analyze different microstrip multilayered substrate configurations interesting for the realization of different sensor topologies. The phase-shift method will be used for the calculation of the effective dielectric constant and determination of the real part of dielectric constant of individual layers. Similarly, the imaginary part of the complex permittivity can be determined from real part using procedure described in Section 2.2.

If we assume that the microstrip transmission line is realized on a multilayered substrate consisting of N layers with different dielectric constants, the effective dielectric constant, εs, of the multilayer substrate with N layers can be calculated using [14, 23]

$$\varepsilon\_{\varepsilon} = \frac{\sum\_{i=1}^{N} |d\_i|}{\sum\_{i=1}^{N} \left| \frac{d\_i}{\kappa\_i} \right|},\tag{15}$$

where N is the number of the layers, ε<sup>i</sup> is the dielectric constant of the i-th layer, and di is a coefficient which can be calculated using the following equation:

$$d\_i = \frac{K(k\_i)}{K'(k\_i)} - \frac{K(k\_{i-1})}{K'(k\_{i-1})} \cdots - \frac{K(k\_1)}{K'(k\_1)},\tag{16}$$

where K and K<sup>0</sup> = K(ki) are the complete elliptical integrals of the first kind [24] and ki is

$$k\_i = \frac{1}{\cosh\left(\frac{\pi w}{4\sum\_{i=1}^{N} h\_i}\right)},\tag{17}$$

where w is the width of the microstrip line and hi is the thickness of the i-th layer. If all geometrical parameters are known as well as the dielectric constants of all layers except of one arbitrary layer, this unknown dielectric constant can be determined based on effective dielectric constant of the multilayered substrate. Previously, the effective dielectric constant has to be determined from the phase shift of the transmitted signal.

If the parameters of several layers are unknown, the unknown values of the dielectric constants can be found by solving system of equations. This procedure requires several measurements with different sets of geometrical parameters, typically the length of the microstrip line. In that case, the number of the essential measurements required for the determination of all parameter depends on the number of the unknown materials.

causality [21]. K-K relation describes a fundamental correlation between the real and imaginary part of the complex dielectric constant and allows us to retrieve imaginary part of the dielectric constant from the measured real part or vice versa. The imaginary part of the complex dielectric constant can be calculated as

Real part of the dielectric constant calculated using the phase-shift method compared with the predetermined

<sup>π</sup> <sup>℘</sup>

ð<sup>∞</sup> 0 ε0 ð Þ� Ω 1

where ω is the angular frequency, ε<sup>0</sup> is the frequency-dependent real part of the

The imaginary part of the complex dielectric constants retrieved using K-K relation from the real part of the dielectric constant (Figure 2) measured by phaseshift method is shown in Figure 3. The calculated imaginary part shows a good

Imaginary part of the complex dielectric constant retrieved by K-K relation from real part of the dielectric

<sup>Ω</sup><sup>2</sup> � <sup>ω</sup><sup>2</sup> <sup>d</sup>Ω, (14)

<sup>ε</sup>00ð Þ¼� <sup>ω</sup> <sup>2</sup><sup>ω</sup>

Figure 2.

Electromagnetic Materials and Devices

Figure 3.

74

constant measured by phase-shift method.

value.

dielectric constant, and ℘ is the Cauchy principal value [22].

Beside conventional microstrip line, next three examples present typical microstrip configurations commonly used in the sensor design. Therefore, the determination of the dielectric constant will be explained on bilayered, tri-layered, and the embedded substrate configurations. In the following section, the practical applications of the analyzed configurations will be demonstrated.

The simplest case is a microstrip line realized on a bilayer substrate, shown in Figure 4, when the property of one layer is known (εr1) and the other one is unknown (εr2). This presents a typical configuration of the microstrip sensor with thin sensitive film deposited on the dielectric substrate.

The effective dielectric constant of the substrate combination bellow microstrip line (εs) can be obtained using procedure explained in Section 2, while the unknown dielectric constant in the bilayered configuration can be expressed as

$$\varepsilon\_{r2} = d\_2 \left[ \pm \left( \frac{|d\_1| + |d\_2|}{\varepsilon\_{\varepsilon}} - \frac{|d\_1|}{|\varepsilon\_{r1}|} \right) \right]^{-1},\tag{18}$$

calculated dielectric constant is in a good agreement with the preset value in the

<sup>i</sup>¼<sup>1</sup> di j j εs

The example of the calculated unknown dielectric constant in tri-layered configuration is shown in Figure 7. The dielectric constants used for this configuration

� j j <sup>d</sup><sup>1</sup> <sup>þ</sup> j j <sup>d</sup><sup>3</sup> j j εr<sup>1</sup>

, (19)

" # ! �<sup>1</sup>

<sup>ε</sup>r<sup>2</sup> <sup>¼</sup> <sup>d</sup><sup>2</sup> � <sup>∑</sup><sup>3</sup>

where coefficients di can be determined using Eq. (16).

Calculated unknown dielectric constant in the tri-layered substrate configuration.

Another example presents tri-layered substrate where middle layer is the one with an unknown dielectric constant, Figure 6. The bottom and top layers have the same known dielectric contestants, while the middle one is with an unknown material and with known geometrical parameters. This geometrical configuration is typical for the realization of the sensor for the characterization of a fluid or gasses in which the reservoir is placed between two dielectrics bellow microstrip line [25, 26]. Using above-described procedure, the effective dielectric constant of the trilayer substrate (εs) can be obtained from the phase shift, while the unknown dielectric constant, εr2, can be calculated using the following equation:

Phase-Shift Transmission Line Method for Permittivity Measurement and Its Potential in Sensor…

calculated frequency range.

DOI: http://dx.doi.org/10.5772/intechopen.81790

Figure 6.

Figure 7.

77

Microstrip line on tri-layered substrate.

where coefficients di can be obtained using Eq. (16).

The example of the calculated unknown dielectric constant in the bilayered configuration is shown in Figure 5. The preset values for the dielectric constants were set to constant value of ε<sup>r</sup><sup>1</sup> = 3.6 and ε<sup>r</sup><sup>2</sup> = 2.4, while the geometrical parameters of the microstrip line were set to h<sup>1</sup> = 0.1 mm, h<sup>2</sup> = 0.2 mm, and w = 1.5 mm, and the length of the microstrip line was set to L = 10 mm. It can be seen that the

Figure 4. Microstrip line on bilayered substrate.

Figure 5. Calculated unknown dielectric constant in the bilayered substrate combination.

Phase-Shift Transmission Line Method for Permittivity Measurement and Its Potential in Sensor… DOI: http://dx.doi.org/10.5772/intechopen.81790

calculated dielectric constant is in a good agreement with the preset value in the calculated frequency range.

Another example presents tri-layered substrate where middle layer is the one with an unknown dielectric constant, Figure 6. The bottom and top layers have the same known dielectric contestants, while the middle one is with an unknown material and with known geometrical parameters. This geometrical configuration is typical for the realization of the sensor for the characterization of a fluid or gasses in which the reservoir is placed between two dielectrics bellow microstrip line [25, 26].

Using above-described procedure, the effective dielectric constant of the trilayer substrate (εs) can be obtained from the phase shift, while the unknown dielectric constant, εr2, can be calculated using the following equation:

$$\varepsilon\_{r2} = d\_2 \left[ \pm \left( \frac{\sum\_{i=1}^3 |d\_i|}{\varepsilon\_i} - \frac{|d\_1| + |d\_3|}{|\varepsilon\_{r1}|} \right) \right]^{-1},\tag{19}$$

where coefficients di can be determined using Eq. (16).

The example of the calculated unknown dielectric constant in tri-layered configuration is shown in Figure 7. The dielectric constants used for this configuration

Figure 6.

Beside conventional microstrip line, next three examples present typical microstrip configurations commonly used in the sensor design. Therefore, the determination of the dielectric constant will be explained on bilayered, tri-layered, and the embedded substrate configurations. In the following section, the practical

The simplest case is a microstrip line realized on a bilayer substrate, shown in

The effective dielectric constant of the substrate combination bellow microstrip line (εs) can be obtained using procedure explained in Section 2, while the unknown

�<sup>1</sup>

εs

The example of the calculated unknown dielectric constant in the bilayered configuration is shown in Figure 5. The preset values for the dielectric constants were set to constant value of ε<sup>r</sup><sup>1</sup> = 3.6 and ε<sup>r</sup><sup>2</sup> = 2.4, while the geometrical parameters of the microstrip line were set to h<sup>1</sup> = 0.1 mm, h<sup>2</sup> = 0.2 mm, and w = 1.5 mm, and the length of the microstrip line was set to L = 10 mm. It can be seen that the

� j j <sup>d</sup><sup>1</sup> j j ε<sup>r</sup><sup>1</sup>

, (18)

Figure 4, when the property of one layer is known (εr1) and the other one is unknown (εr2). This presents a typical configuration of the microstrip sensor with

applications of the analyzed configurations will be demonstrated.

dielectric constant in the bilayered configuration can be expressed as

<sup>ε</sup><sup>r</sup><sup>2</sup> <sup>¼</sup> <sup>d</sup><sup>2</sup> � j j <sup>d</sup><sup>1</sup> <sup>þ</sup> j j <sup>d</sup><sup>2</sup>

thin sensitive film deposited on the dielectric substrate.

Electromagnetic Materials and Devices

where coefficients di can be obtained using Eq. (16).

Calculated unknown dielectric constant in the bilayered substrate combination.

Figure 4.

Figure 5.

76

Microstrip line on bilayered substrate.

Microstrip line on tri-layered substrate.

Figure 7. Calculated unknown dielectric constant in the tri-layered substrate configuration.

were set to constant values of εr<sup>1</sup> = 3.6 and εr<sup>2</sup> = 2.4, while the geometrical parameters of the microstrip line were set to h<sup>1</sup> = 0.1 mm, h2= 0.2 mm, w = 1.5 mm, and L = 10 mm. Good agreement is obtained with the maximal relative error of 10% in the observed frequency range.

The third configuration in which the substrate with an unknown dielectric constant is embedded into the substrate with known properties and dimensions is shown in Figure 8. This configuration is particularly interesting for the microfluidic applications, for the characterization of the fluid inside the channel [21].

This configuration of the substrate can be observed as a tri-layered substrate in which the middle layer is composed of two materials with different dielectric constants, εr<sup>1</sup> and εr2. The first and third layers are with known dielectric constant, εr1. If we assume that all geometrical parameters are known, the calculation of the effective dielectric constants of the middle layer (εr1eff ) can be calculated using Eq. (19). This formula does not determine the unknown dielectric constant, just the effective dielectric constant of the middle layer. Therefore, the unknown dielectric constant ε<sup>r</sup><sup>2</sup> can be calculated using Bruggeman formalism [27]:

$$
\varepsilon\_{r2\varepsilon} = V \varepsilon\_{r2} + (1 - V)\varepsilon\_{r1} \tag{20}
$$

determined using the procedure for the extraction of the effective dielectric constant of the tri-layered substrate from the phase shift combined with Eqs. (19) and (20). The example of the calculated unknown dielectric constant in the embedded substrate configuration is shown in Figure 9. The preset values in this case were set to constant values of εr<sup>1</sup> = 3.6 and εr<sup>2</sup> = 2.35, while the geometrical parameters of the microstrip line were set to h<sup>1</sup> = 0.1 mm, h<sup>2</sup> = 0.2 mm, w = 1.5 mm, and L = 10 mm. The good agreement between the calculated dielectric constant and the preset value

Phase-Shift Transmission Line Method for Permittivity Measurement and Its Potential in Sensor…

From the previous examples, it can be seen that the phase-shift method has a potential for the characterization of the unknown dielectric materials in different configurations with a good accuracy, and therefore it presents good choice for the

This section summarized various innovative techniques that can be used for improvement of the sensitivity of phase-shift measurement in the microstrip archi-

Soil moisture sensor based on Hilbert fractal curve: (a) layout of the sensor, (b) fabricated sensor,

The first technique is based on increasing the effective length of the transmission line, that is, increasing the inductance and capacitance of the microstrip line. However, this technique results in increased length and reduction in the compactness of the structure. To preserve compactness and satisfy the requirements for good performances, different shapes of the microstrip line have been recently used [28–31]. Since the space-filling property of a fractal offers high potentials for miniaturization of microwave circuits [28–31], the application of the fractal curves theoretically allows the design of infinite-length lines on finite substrate area. In that manner compact transmission line with improved phase response can be obtained using fractal curves. Based on that principle, we have designed a compact soil moisture sensor [28] that consists of two parallel fractal line segments, where each segment comprises two Hilbert fractal curves of the fourth order connected in serial, Figure 10a. The additional analyses confirm that the increase of the iteration of the Hilbert fractal curve

is obtained with the relative error lower than 8.5%.

DOI: http://dx.doi.org/10.5772/intechopen.81790

4. Techniques for increasing the phase shift

tecture and their advantages over conventional design.

rapid characterization of material.

Figure 10.

79

(c) phase-shift response, and (d) insertion loss [28].

where V is the volumetric fraction of the microfluidic channel in the surrounding substrate. The dielectric constant of the unknown embedded material can be

Figure 8.

Microstrip line on the substrate with embedded rectangular channel.

Figure 9. Calculated unknown dielectric constant in substrate configuration with embedded channel.

Phase-Shift Transmission Line Method for Permittivity Measurement and Its Potential in Sensor… DOI: http://dx.doi.org/10.5772/intechopen.81790

determined using the procedure for the extraction of the effective dielectric constant of the tri-layered substrate from the phase shift combined with Eqs. (19) and (20).

The example of the calculated unknown dielectric constant in the embedded substrate configuration is shown in Figure 9. The preset values in this case were set to constant values of εr<sup>1</sup> = 3.6 and εr<sup>2</sup> = 2.35, while the geometrical parameters of the microstrip line were set to h<sup>1</sup> = 0.1 mm, h<sup>2</sup> = 0.2 mm, w = 1.5 mm, and L = 10 mm. The good agreement between the calculated dielectric constant and the preset value is obtained with the relative error lower than 8.5%.

From the previous examples, it can be seen that the phase-shift method has a potential for the characterization of the unknown dielectric materials in different configurations with a good accuracy, and therefore it presents good choice for the rapid characterization of material.

## 4. Techniques for increasing the phase shift

This section summarized various innovative techniques that can be used for improvement of the sensitivity of phase-shift measurement in the microstrip architecture and their advantages over conventional design.

The first technique is based on increasing the effective length of the transmission line, that is, increasing the inductance and capacitance of the microstrip line. However, this technique results in increased length and reduction in the compactness of the structure. To preserve compactness and satisfy the requirements for good performances, different shapes of the microstrip line have been recently used [28–31]. Since the space-filling property of a fractal offers high potentials for miniaturization of microwave circuits [28–31], the application of the fractal curves theoretically allows the design of infinite-length lines on finite substrate area. In that manner compact transmission line with improved phase response can be obtained using fractal curves. Based on that principle, we have designed a compact soil moisture sensor [28] that consists of two parallel fractal line segments, where each segment comprises two Hilbert fractal curves of the fourth order connected in serial, Figure 10a. The additional analyses confirm that the increase of the iteration of the Hilbert fractal curve

#### Figure 10.

Soil moisture sensor based on Hilbert fractal curve: (a) layout of the sensor, (b) fabricated sensor, (c) phase-shift response, and (d) insertion loss [28].

were set to constant values of εr<sup>1</sup> = 3.6 and εr<sup>2</sup> = 2.4, while the geometrical parameters of the microstrip line were set to h<sup>1</sup> = 0.1 mm, h2= 0.2 mm, w = 1.5 mm, and L = 10 mm. Good agreement is obtained with the maximal relative error of 10% in

The third configuration in which the substrate with an unknown dielectric constant is embedded into the substrate with known properties and dimensions is shown in Figure 8. This configuration is particularly interesting for the microfluidic

This configuration of the substrate can be observed as a tri-layered substrate in

where V is the volumetric fraction of the microfluidic channel in the surrounding

substrate. The dielectric constant of the unknown embedded material can be

ε<sup>r</sup>2<sup>e</sup> ¼ Vε<sup>r</sup><sup>2</sup> þ ð Þ 1 � V ε<sup>r</sup>1, (20)

applications, for the characterization of the fluid inside the channel [21].

constant ε<sup>r</sup><sup>2</sup> can be calculated using Bruggeman formalism [27]:

Microstrip line on the substrate with embedded rectangular channel.

Calculated unknown dielectric constant in substrate configuration with embedded channel.

which the middle layer is composed of two materials with different dielectric constants, εr<sup>1</sup> and εr2. The first and third layers are with known dielectric constant, εr1. If we assume that all geometrical parameters are known, the calculation of the effective dielectric constants of the middle layer (εr1eff ) can be calculated using Eq. (19). This formula does not determine the unknown dielectric constant, just the effective dielectric constant of the middle layer. Therefore, the unknown dielectric

the observed frequency range.

Electromagnetic Materials and Devices

Figure 8.

Figure 9.

78

increases the range of phase shift [32], but accordingly the insertion loss too. Therefore, in the proposed configuration, two transmission lines are connected in parallel to reduce insertion losses. When Hilbert fractal curves are connected in parallel, the range of the phase shift is approximately the same, but insertion losses are reduced. The Hilbert curve itself is realized with the line width and the spacing between the lines of 100 μm. The results of the proposed sensor placed in the medium with different values of the dielectric constants are shown in Figure 10. The range of the phase shift for this configuration at the frequency of 1.2 GHz is 66.64°, while the insertion loss in the worst case is 2.98 dB. The consequence of the line modification is 0.4 dB greater insertion loss comparing to the conventional microstrip line. Although the insertion loss in this case is larger, it is still within acceptable range of 3 dB. However, for the same line length, the range of the phase shift is increased for more than three times. Stated results show that the usage of Hilbert fractal curve leads to more compact sensor characterized by higher sensitivity.

simplified to Eq. (5). In (Figure 12), fitted calibration curves (volumetric water content in the function of the phase shift) for the measurement performed at 500 and 2500 MHz are presented. A significant difference between the calibration curves is obtained at 500 MHz from differently treated samples. However, if the operating frequency is 2500 MHz, the phase shifts obtained from all three samples are almost identical. These results indicate that the Hilbert sensor with the aperture in the ground plane can be successfully used to measure soil moisture indepen-

Phase-Shift Transmission Line Method for Permittivity Measurement and Its Potential in Sensor…

Third technique to improve sensitivity is based on a defected electromagnetic bandgap (EBG) structure, periodical structure realized as a pattern in the microstrip ground plane. A concept to improve microstrip sensor sensitivity based on the EBG structure was firstly proposed in [35], where it is demonstrated that the sensor sensitivity can be increased by reducing the wave group velocity of the propagating signal. Illustration of this technique is shown in Figure 13 in the realization of the 3D-printed microfluidic sensor for the determination of the characteristics of different fluids in the microfluidic channel [14]. The bottom layer of the sensor, shown in Figure 13c, represents the ground plane realized using defected EBG structure, periodical structure that consists of etched holes. The introduction of the uniform EBG structure in the ground plane forms a frequency region where propagation is forbidden, that is, bandgap in the transmission characteristic [36], while the defect in the EBG results in a resonance in the bandgap, which frequency is determined by the size of the defect. Introduction of the defected EBG structure improves phase shift of the microstrip line in comparison to the conventional microstrip line. Moreover, in comparison with a conventional microstrip line, the intensity of the electric field is stronger in the vicinity of the defect in the EBG [14]. Therefore, the changes of the dielectric constant of the liquid that flows in the channel will have the highest impact to the phase response. In the proposed configuration, the EBG structure is designed to provide bandgap between 5 and 9 GHz, while the defect in the EBG causes the resonance at 6 GHz. By introducing defected EBG structure, the phase change significantly increases, especially at the frequencies that are close to the bandgap edges and at the resonance in the bandgap, due to decrease in the wave phase velocity. From the transmission characteristic, Figure 14, it can be seen that the resonant frequency of the defect in the bandgap slightly shifts due to the change of the dielectric constant of the fluid in microchannel. The effect of the EBG structure is predominant at the frequency of 6 GHz where the wave phase velocity is minimal. The results show that the change of the fluid permittivity from 1 (air) to

Volumetric water content for 500 MHz (dashed lines, upper abscissa) and 2500 MHz (full lines, lower

dently of the soil type (Figure 12).

DOI: http://dx.doi.org/10.5772/intechopen.81790

Figure 12.

81

abscissa) [33, 34].

Another technique to increase the phase shift is based on an aperture in the ground plane, where the part of the ground plane, positioned under Hilbert curves of the sensor, shown in Figure 11, was removed. In this manner a certain passage for the lines of the electric field is made, so they can pass through it into the soil under the sensor and end up at the bottom side of the ground plane, Figure 11. In this manner, soil moisture has larger effect on the sensor characteristics. The results for the sensor with the aperture in the ground plane are presented in Figure 11. It can be seen that the range of the phase shift for the sensor with the aperture in the ground plane is 70.76° at the frequency of 1.2 GHz, and the insertion loss is 2.98 dB. Modification in ground plane improved the range of the phase shift for additional 6%, while insertion loss did not change. Quartz sand was used to validate the sensor performances, and the phase-shift measurements were performed for different moisture levels, at operating frequencies in the range of 500–2500 MHz [33, 34]. To investigate the influence of the conductivity, that is, of the soil type, on the calibration curves, the measurement procedure was repeated for the sand moisturized with water with two different salinities (conductivities): 29 and 70‰. If the operating frequency is sufficiently high, Eq. (4) will be satisfied. Therefore, the electrical conductivity can be neglected, and the expression for the phase velocity can be

#### Figure 11.

Soil moisture sensor with the aperture in the ground plane: (a) cross section, (b) phase-shift response, and (c) insertion loss [28].

#### Phase-Shift Transmission Line Method for Permittivity Measurement and Its Potential in Sensor… DOI: http://dx.doi.org/10.5772/intechopen.81790

simplified to Eq. (5). In (Figure 12), fitted calibration curves (volumetric water content in the function of the phase shift) for the measurement performed at 500 and 2500 MHz are presented. A significant difference between the calibration curves is obtained at 500 MHz from differently treated samples. However, if the operating frequency is 2500 MHz, the phase shifts obtained from all three samples are almost identical. These results indicate that the Hilbert sensor with the aperture in the ground plane can be successfully used to measure soil moisture independently of the soil type (Figure 12).

Third technique to improve sensitivity is based on a defected electromagnetic bandgap (EBG) structure, periodical structure realized as a pattern in the microstrip ground plane. A concept to improve microstrip sensor sensitivity based on the EBG structure was firstly proposed in [35], where it is demonstrated that the sensor sensitivity can be increased by reducing the wave group velocity of the propagating signal. Illustration of this technique is shown in Figure 13 in the realization of the 3D-printed microfluidic sensor for the determination of the characteristics of different fluids in the microfluidic channel [14]. The bottom layer of the sensor, shown in Figure 13c, represents the ground plane realized using defected EBG structure, periodical structure that consists of etched holes. The introduction of the uniform EBG structure in the ground plane forms a frequency region where propagation is forbidden, that is, bandgap in the transmission characteristic [36], while the defect in the EBG results in a resonance in the bandgap, which frequency is determined by the size of the defect. Introduction of the defected EBG structure improves phase shift of the microstrip line in comparison to the conventional microstrip line. Moreover, in comparison with a conventional microstrip line, the intensity of the electric field is stronger in the vicinity of the defect in the EBG [14]. Therefore, the changes of the dielectric constant of the liquid that flows in the channel will have the highest impact to the phase response. In the proposed configuration, the EBG structure is designed to provide bandgap between 5 and 9 GHz, while the defect in the EBG causes the resonance at 6 GHz. By introducing defected EBG structure, the phase change significantly increases, especially at the frequencies that are close to the bandgap edges and at the resonance in the bandgap, due to decrease in the wave phase velocity. From the transmission characteristic, Figure 14, it can be seen that the resonant frequency of the defect in the bandgap slightly shifts due to the change of the dielectric constant of the fluid in microchannel. The effect of the EBG structure is predominant at the frequency of 6 GHz where the wave phase velocity is minimal. The results show that the change of the fluid permittivity from 1 (air) to

Figure 12. Volumetric water content for 500 MHz (dashed lines, upper abscissa) and 2500 MHz (full lines, lower abscissa) [33, 34].

increases the range of phase shift [32], but accordingly the insertion loss too. Therefore, in the proposed configuration, two transmission lines are connected in parallel to reduce insertion losses. When Hilbert fractal curves are connected in parallel, the range of the phase shift is approximately the same, but insertion losses are reduced. The Hilbert curve itself is realized with the line width and the spacing between the lines of 100 μm. The results of the proposed sensor placed in the medium with different values of the dielectric constants are shown in Figure 10. The range of the phase shift for this configuration at the frequency of 1.2 GHz is 66.64°, while the insertion loss in the worst case is 2.98 dB. The consequence of the line modification is 0.4 dB greater insertion loss comparing to the conventional microstrip line. Although the insertion loss in this case is larger, it is still within acceptable range of 3 dB. However, for the same line length, the range of the phase shift is increased for more than three times. Stated results show that the usage of Hilbert fractal curve leads to

Another technique to increase the phase shift is based on an aperture in the ground plane, where the part of the ground plane, positioned under Hilbert curves of the sensor, shown in Figure 11, was removed. In this manner a certain passage for the lines of the electric field is made, so they can pass through it into the soil under the sensor and end up at the bottom side of the ground plane, Figure 11. In this manner, soil moisture has larger effect on the sensor characteristics. The results for the sensor with the aperture in the ground plane are presented in Figure 11. It can be seen that the range of the phase shift for the sensor with the aperture in the ground plane is 70.76° at the frequency of 1.2 GHz, and the insertion loss is 2.98 dB. Modification in ground plane improved the range of the phase shift for additional 6%, while insertion loss did not change. Quartz sand was used to validate the sensor performances, and the phase-shift measurements were performed for different moisture levels, at operating frequencies in the range of 500–2500 MHz [33, 34]. To investigate the influence of the conductivity, that is, of the soil type, on the calibration curves, the measurement procedure was repeated for the sand moisturized with water with two different salinities (conductivities): 29 and 70‰. If the operating frequency is sufficiently high, Eq. (4) will be satisfied. Therefore, the electrical conductivity can be neglected, and the expression for the phase velocity can be

Soil moisture sensor with the aperture in the ground plane: (a) cross section, (b) phase-shift response, and

more compact sensor characterized by higher sensitivity.

Electromagnetic Materials and Devices

Figure 11.

80

(c) insertion loss [28].

Microfluidic EBG sensor: (a) top layer, (b) substrate with embedded channel, (c) bottom layer with defected EBG, (d) 3D view, (e) cross section, and (f) top and bottom side of the fabricated sensor [14].

permeability, more commonly referred to as LH materials, have a propagation constant equal to zero at non-zero frequency [37]. Therefore, they can support electromagnetic waves with a group and phase velocities that are antiparallel, known as backward waves [39]. Consequently, energy will travel away from the source, while wave fronts travel backward toward the source. However, the ideal LH structure does not exist in the nature and can be formed as a combination of the LH section and conventional transmission line (RH). This structure known as a composite left-/right-handed (CLRH) transmission line can be formed using a capacitance in series with shunted inductance. In the case of CLRH due to the backward wave propagation, the phase "advance" occurs in the LH frequency range, while phase delay occurs in the RH frequency range [38]. This concept was used in the design of microfluidic sensor for the measurement of the characteristic of the fluid that flows in the microfluidic reservoir placed under CLRH transmission line. The conventional microstrip line in phase comparator was replaced with CRLH transmission line, Figure 16. Since the proposed line consists of one CRLH unit cell, it provides passband response at frequency of 1.9 GHz that is characterized with narrowband LH behavior. Therefore, the phase advance at Output 2 is obtained comparing to the signal that propagates true the conventional RH line (Output 1), Figure 17b. By changing the properties of the fluid that flows in the microfluidic channel, the central resonance of the LH band slightly shifts to the lower frequency, Figure 17a, while the slope of the phase characteristics intensely changes, Figure 17b. It can be mentioned that the level between two signals is lower than 8 dB in the worst case at 1.9 GHz; therefore the standard phase detector can be used for the phase-shift measurement. In the proposed configuration, the conventional RH line was used as a referent one, and therefore it was bent in the meander shape to provide maximal measurement phase-shift range at 1.9 GHz. The proposed sensor is characterized with maximal achievable sensitivity, good linearity, and design flexibility, since the maximum extent of the phase can be obtained for the arbitrary range of the dielectric constants by simple modifica-

Measurement of the toluene concentration in toluene-methanol mixture: sensor measured response (dots) and

Phase-Shift Transmission Line Method for Permittivity Measurement and Its Potential in Sensor…

tion of the CLRH transmission line.

83

Figure 15.

the corresponding fitting curves (lines) [14].

DOI: http://dx.doi.org/10.5772/intechopen.81790

81 (water) causes the phase-shift difference of 84°, Figure 14. Compared to the phase shift of the conventional microstrip line without EBG which is only 10.2° at 6 GHz, the proposed design shows eight times higher phase shift. Furthermore, the proposed sensor shows relatively high and almost linear dependence for the fluid materials with permittivity lower than 30. Therefore, the proposed sensor is characterized by relatively high sensitivity and linearity, which makes it a suitable candidate for monitoring small concentrations of a specific fluid in different mixtures. The potential application has been demonstrated in the realization of the microfluidic sensor for detection of toluene concentration in toluene-methanol mixture [14], Figure 15.

The fourth technique is based on metamaterials and a left-handed (LH) transmission line approach [37, 38]. Metamaterials are artificial structures that can be designed to exhibit specific electromagnetic properties not commonly found in nature. Metamaterials with simultaneously negative permittivity and

Figure 14.

Measured results of the microfluidic EBG sensor with different fluids inside the microfluidic channel: (a) transmission characteristic and (b) phase characteristic [14].

Phase-Shift Transmission Line Method for Permittivity Measurement and Its Potential in Sensor… DOI: http://dx.doi.org/10.5772/intechopen.81790

#### Figure 15.

81 (water) causes the phase-shift difference of 84°, Figure 14. Compared to the phase shift of the conventional microstrip line without EBG which is only 10.2° at 6 GHz, the proposed design shows eight times higher phase shift. Furthermore, the proposed sensor shows relatively high and almost linear dependence for the fluid materials with permittivity lower than 30. Therefore, the proposed sensor is characterized by relatively high sensitivity and linearity, which makes it a suitable candidate for monitoring small concentrations of a specific fluid in different mixtures. The potential application has been demonstrated in the realization of the microfluidic sensor for detection of toluene concentration in toluene-methanol

EBG, (d) 3D view, (e) cross section, and (f) top and bottom side of the fabricated sensor [14].

Microfluidic EBG sensor: (a) top layer, (b) substrate with embedded channel, (c) bottom layer with defected

The fourth technique is based on metamaterials and a left-handed (LH) transmission line approach [37, 38]. Metamaterials are artificial structures that can be designed to exhibit specific electromagnetic properties not commonly found in nature. Metamaterials with simultaneously negative permittivity and

Measured results of the microfluidic EBG sensor with different fluids inside the microfluidic channel:

(a) transmission characteristic and (b) phase characteristic [14].

mixture [14], Figure 15.

Electromagnetic Materials and Devices

Figure 13.

Figure 14.

82

Measurement of the toluene concentration in toluene-methanol mixture: sensor measured response (dots) and the corresponding fitting curves (lines) [14].

permeability, more commonly referred to as LH materials, have a propagation constant equal to zero at non-zero frequency [37]. Therefore, they can support electromagnetic waves with a group and phase velocities that are antiparallel, known as backward waves [39]. Consequently, energy will travel away from the source, while wave fronts travel backward toward the source. However, the ideal LH structure does not exist in the nature and can be formed as a combination of the LH section and conventional transmission line (RH). This structure known as a composite left-/right-handed (CLRH) transmission line can be formed using a capacitance in series with shunted inductance. In the case of CLRH due to the backward wave propagation, the phase "advance" occurs in the LH frequency range, while phase delay occurs in the RH frequency range [38]. This concept was used in the design of microfluidic sensor for the measurement of the characteristic of the fluid that flows in the microfluidic reservoir placed under CLRH transmission line. The conventional microstrip line in phase comparator was replaced with CRLH transmission line, Figure 16. Since the proposed line consists of one CRLH unit cell, it provides passband response at frequency of 1.9 GHz that is characterized with narrowband LH behavior. Therefore, the phase advance at Output 2 is obtained comparing to the signal that propagates true the conventional RH line (Output 1), Figure 17b. By changing the properties of the fluid that flows in the microfluidic channel, the central resonance of the LH band slightly shifts to the lower frequency, Figure 17a, while the slope of the phase characteristics intensely changes, Figure 17b. It can be mentioned that the level between two signals is lower than 8 dB in the worst case at 1.9 GHz; therefore the standard phase detector can be used for the phase-shift measurement. In the proposed configuration, the conventional RH line was used as a referent one, and therefore it was bent in the meander shape to provide maximal measurement phase-shift range at 1.9 GHz. The proposed sensor is characterized with maximal achievable sensitivity, good linearity, and design flexibility, since the maximum extent of the phase can be obtained for the arbitrary range of the dielectric constants by simple modification of the CLRH transmission line.

Figure 16.

Blok diagram and layout of the CRLH sensor.

Figure 17. Response of the CLRH sensor: (a) transmission characteristic and (b) phase characteristic.
