## Abstract

This chapter offers a detailed insight into a dielectric characterization of the materials based on the phase-shift measurements of the transmission signal. The chapter will provide in-depth theoretical background of the phase-shift transmission line measurement in the microstrip architecture and determination of dielectric permittivity of design under test for several measurement configurations. Potential of the phase-shift method will be demonstrated through applications in the characterization of an unknown dielectric constant in multilayered structure, realization of the soil moisture sensor, and sensor for determination of the dielectric constant of a fluid in microfluidic channel. Moreover, specific techniques for increasing the phase shift based on the electromagnetic bandgap structure, the aperture in the ground plane and the left-handed effect will be presented. In the end, the realization of simple in-field detection device for determination of permittivity based on the phase-shift measurement will be demonstrated.

### Keywords

- phase-shift method
- transmission line
- microstrip
- permittivity
- sensors

## 1. Introduction

The measurement of dielectric properties of the materials found application in different fields, such as material science, absorber development, biomedical research, tissue engineering, wood industry, food quality control, etc. [1, 2, 3, 4, 5]. A number of methods have been developed over a time for characterization of the dielectric properties of the materials such as time domain method [6, 7], capacitive method [3, 8], transmission line (TL) methods [3, 9, 10], resonant method [3, 9], etc. The selection of the appropriate method depends on the measured frequency range, expected values of permittivity, measurement accuracy, form of material (solid, powder, and liquid), sample shape and size, temperature, etc. [8, 11]. Moreover, depending on some important aspects, the measurement methods can be divided into contact or noncontact methods (depends on whether the sample is touched or not), destructive or nondestructive (depends on whether sample can be destroyed or not), narrowband and wideband (depends on frequency range), etc. Since each method has its own advantages and limitations, the selection of the appropriate one depends on a particular application, required accuracy, sample, and other factors. There are a number of commercially available holders, kits, and probes that operate on different principles and allow measurement of the dielectric constant of the material in different forms on different temperatures and frequency ranges [8, 11]. However, the most of them are designed to be connected with expensive instruments such as network analyzers, LCR meters, or impedance analyzers.

One of the commonly used methods suitable for the material characterization in a wide frequency range, from around 10 MHz to 75 GHz, is the TL method. The TL method includes both measurements of the reflection and/or transmission characteristic [3, 4, 5, 6, 7, 8, 9, 10]. This method can be used for characterization of permittivity as well as permeability of hard solid materials with medium losses. High-loss materials can be also characterized using this method, if the sample is kept relatively thin. The TL holders are usually made of a coaxial, a waveguide, or a microstrip line section. However, the specific design of the holder or specific multilayered configurations can be used for characterization of powders, liquid, or gases. Usually, the method requires initial sample preparation to fit into the section of the TL, typically the waveguide or the coaxial line. For accurate permittivity measurement, the sample has to be exposed to the maximal electric field, and therefore the position of the sample is very important. A typical measurement configuration of this method consists of the TL section with a sample placed inside, a vector network analyzer (VNA) used to measure the two ports complex scattering parameters (S-parameters), and a software that converts the measured S-parameters to the complex permittivity or permeability. In addition, the TL method requires initial calibration with various terminations before the measurement.

The measurement of the phase shift of the transmitted signal represents relatively fast and simple method for determination of the dielectric properties of the material. It is characterized by fast time response, and in comparison with other methods, it is less sensitive to the noise [10, 12]. Furthermore, this method allows characterization at a single frequency which simplifies the development of a supporting electronic, allows easy integration with sensor element, and allows realization of low-cost in-field sensing devices. Therefore, it found application in the realization of different types of sensors such as soil moisture sensors [13], microfluidic sensor for detention fluid mixture concentration [14], etc.

In this chapter, the phase-shift method will be explained on the example of a microstrip line configuration, and the permittivity of the materials will be determined by measuring the phase shift of the transmitted signal. Theoretical background of the phase-shift method and mathematical equations for determination of real and imaginary part of complex permittivity based on the phase of the transmitted signal will be presented in Section 2. The unknown permittivity of material will be determined for several measurement configurations in Section 3. Potential of the phase-shift method will be demonstrated through several applications in the characterization of an unknown dielectric constant in multilayered structure, a soil moisture sensor, and sensor for determination of fluid properties in microfluidic channel. Advance techniques for increasing the sensitivity of the phase-shift measurement will be presented in Section 4, while the simple in-field detection device for determination of the permittivity based on the phase measurement will be presented in Section 5. The conclusions are given in Section 6.

## 2. Phase-shift method

### 2.1. Determination of real part of the dielectric constant

Phase-shift method is based on the measurement of the phase shift of a sinusoidal signal that propagates along a transmission line.

Phase shift *Δφ* is defined by velocity and frequency of the propagating signal as well as physical properties of the transmission line:

where ω is the angular frequency,

In order to determine a phase velocity of electromagnetic wave, we will start with the expression for imaginary part of the complex propagation constant for lossy medium [15]:

where *μ*, *ε*, and *σ* are the real parts of the permeability, permittivity, and electrical conductivity of the medium through which the signal is propagating, respectively. If the imaginary part of the complex propagation constant is known, the phase velocity can be determined as

Based on Eq. (3), it can be seen that phase velocity is dominantly influenced by permittivity, permeability and signal frequency, and then electrical conductivity.

The main advantage of the phase-shift method lies on the fact that on the frequencies high enough, the influence of conductivity can be neglected:

therefore, expression for velocity on high frequencies can be reduced to

where phase velocity is determined by permeability and permittivity only. This is especially important for soil moisture sensor which will be discussed later since most of the materials in the soil are diamagnetic or paramagnetic. If we assume that electromagnetic wave propagates through a nonmagnetic medium, that is, the magnetic permeability is equal to

where

Unlike the coaxial line or the waveguide, the microstrip structure is particularly interesting for a simple and low-cost fabrication of compact sensors based on dielectric permittivity change which can be easily integrated with supporting electronics. In this way, standard printed circuit board technology used for microstrip manufacturing offers fabrication of a complete solution of the sensor in a single substrate. Therefore, the concept of the phase-shift measurement will be explained on the example of microstrip line. In the microstrip, the influence of the change in permittivity is reflected in effective permittivity which is determined by permittivity of a medium above the microstrip line and permittivity of the dielectric substrate, Figure 1.

Effective permittivity of the microstrip line shown in Figure 1 can be expressed as

where

It can be seen that a variation in the permittivity of the medium causes a variation in effective permittivity that results in the change of the phase velocity. The change in the phase velocity changes the phase shift of the signal. It is evident that phase shift is determined by the value of the permittivity of the medium above the microstrip line. Therefore, the real part of dielectric constant of unknown medium can be detected with simple measurement of the phase shift of the transmitted signal.

The range of the phase shift *ΔΦ*, is determined by the upper and lower values of the measured permittivity:

This parameter needs to be adjusted to the supporting electronics that measure the phase shift. From Eq. (8) it can be seen that with appropriate choice of the operating frequency and the proper optimization of the geometrical parameters (mostly the length of the transmission line), the range of the phase shift can be optimized to the maximal measurable value.

As stated above, the phase shift depends on the properties of the transmission line. Since the microstrip line can be characterized by inductance per unit length,

Combining Eqs. (1) and (9), phase shift of the signal propagating along microstrip line with length

The capacitance can be written in the form of the vacuum capacitance

In addition, if we assume that the electromagnetic wave propagates through a nonmagnetic medium, the inductivity of the transmission line does not depend on the sample under test (

Based on Eq. (13), it can be concluded that the phase-shift range can be increased by performing the measurements on higher frequencies or by increasing the total microstrip line inductance or capacitance. Therefore, the phase-shift range can be optimized to the capabilities of the supporting electronics for measurement of the phase shift.

To validate the proposed method for the characterization of the material properties in wider frequency range, we compare the results of the dielectric constant calculated using proposed method with a predetermined value of dielectric constant, Figure 2. For the comparison, the microstrip transmission line was used where the unknown medium was placed above the microstrip line and dielectric substrate, as shown in Figure 1. The calculated dielectric constant was extracted from the phase shift of the transited signal using described procedure. The proposed result reveals that the phase-shift detection method provides high accuracy with the relative errors lower than 0.5% for the real parts of the dielectric constant in the measured frequency range.

### 2.2. Determination of the imaginary part of the dielectric constant

From the previous analysis, we demonstrate how the real part of the complex permittivity can be determined from the phase shift of the transmitted signal. However, the imaginary part of the complex permittivity cannot be directly calculated from the phase shift. It can be estimated using Kramers-Kronig (K-K) relation [18, 19, 20, 21, 22].

The real and imaginary part of the complex dielectric constant is correlated with K-K relation [18, 19, 20]. This relation is a direct consequence of the principle of 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

where *ω* is the angular frequency, *ε′* is the frequency-dependent real part of the dielectric constant, and ℘ is the Cauchy principal value [22].

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 phase-shift method is shown in Figure 3. The calculated imaginary part shows a good agreement with the predetermined value of imaginary parts. However, the relative error is about 9% since the accuracy of Eq. (14) depends on the measured frequency range. It can be noted that the range from 0 to ∞ in the integral in Eq. (14) is not achievable in practice. Therefore, the limited range of frequencies affects the accuracy of the results and causes the error that can be observed in Figure 3.

## 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]

where *N* is the number of the layers, *i*-th layer, and

where *K* and *K′ = K(ki)* are the complete elliptical integrals of the first kind [24] and

where *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.

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 (

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

where coefficients

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

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 tri-layer substrate (

where coefficients

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

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, *.* The first and third layers are with known dielectric constant,

where

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 *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, 29, 30, 31]. Since the space-filling property of a fractal offers high potentials for miniaturization of microwave circuits [28, 29, 30, 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 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.

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 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 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 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.

## 5. Simple in-field detection circuit

The phase-shift method, as it was stated above, is the simple method that can be used for the determination of the complex permittivity. Therefore, the expensive instrument for the determination of permittivity can be replaced with a simple detection circuit. The block diagram, and detailed electrical scheme for measurement of the phase shift at single operating frequency, is presented in Figure 18 together with the fabricated prototype realized in LTCC (low-temperature cofired ceramics) technology.

Detection circuit consists of a microwave oscillator, a quadrature hybrid, a sensor element, and a phase detector functional blocks. The operating principle can be described in the following way: sinusoidal signal generated by source, that is, microwave oscillator, is divided by quadrature hybrid on measurement and referent signal. The measurement signal propagates along sensor element where phase shift occurs according to the dielectric properties of the surrounding medium. The signal from the sensor element is fed into the input of the phase detector which compares the phase of the measurement and the referent signal. The output of the phase detector is the voltage proportional to the phase shift of the input signals which can be related to the measured dielectric constant. Referent signal propagates through the phase-shifter module which has a purpose to provide the calibration of the sensor and to overcome deviations of the nominal properties of the materials and components used for sensor fabrication. In this way the repeatability of measurement of the different sensors will be secured.

The phase-shift measurement electrical circuit is detailly presented in Figure 18c, indicating abovementioned functional blocks of the circuit, Figure 18a. The oscillator is realized by the voltage-controlled oscillator MAX2751 (8), which is adjusted by the referent voltage (9) and the voltage divider (10) to operating frequency of 2.2 GHz. The signal from the oscillator is divided into measurement and referent signals using commercially available quadrature coupler circuit HY22-73 (2). The phase-shifter module allows control of the phase shift and enables fine-tuning of the difference in the phase between the measurement and referent signals. The phase shift can be achieved by varying the control voltage (11) that affects the capacitance of the varactor diodes (12 and 13). The change in capacitance affects the signals (14) and (15) which superimpose with the input referent signal (3) through the quadrature coupler (16) and in this way changes the phase of the resultant signal at the output of the module (17). The measurement of the phase shift between the measurement and referent signal is done using a phase detector module implemented with the integrated circuit AD8302 Analogue Devices (18). The phase detector circuit is set to the phase difference measurement mode according to the manufacturer’s recommendation. Integrated circuit AD8302 on its output (21) gives a voltage signal that is proportional to the phase difference of the signal on its inputs (19) and (20).

The accuracy of the designed phase-shift measurement device was experimentally verified by comparing the results of the measurement of the phase shift of the signal, induced by phase-shift circuit (functional block (7), Figure 18c), in the range from 0 to 90° with the results of the measurement obtained using vector network analyzer (VNA). The results of the comparison are shown in Figure 19. It can be seen that the results agree well and the relative error in respect of the full-scale output is 5.56% which confirms performance of the designed phase-shift circuit.

Additional module for different sensor topologies can be designed to provide a conversion of the measured voltage to the corresponding value of the dielectric constant.

## 6. Conclusions

In this chapter dielectric characterization technique based on the phase-shift method has been presented. It has been shown that both the real and imaginary part of a complex permittivity can be calculated solely by using the phase shift of the transmitted signal. The exact formulas for the calculation of the unknown dielectric properties in the microstrip and multilayered substrate configurations such as bilayered, tri-layered, and embedded configurations were presented.

To enhance sensitivity of sensors that operate on phase-shift principle, various techniques for increasing the phase-shift range have been presented. The first technique uses space-filling property of Hilbert fractal curve to increase the phase-shift range and yet preserve the compactness of the structure. The technique that increases sensitivity of the sensor by introducing an aperture in the ground layer has been presented on the example of the soil moisture sensor. The third technique based on EBG effect has been illustrated on the example of 3D-printed microfluidic sensor for detection of toluene concentration in toluene-methanol mixture. Metamaterial and CRLH transmission line approach is used as the technique in the realization of microfluidic sensor with a maximum extent of the phase-shift range.

In the end a simple in-field detection circuit for determination of permittivity based on the phase-shift measurement on single operating frequency has been described. With the help of described concepts, a complete set of tools has been introduced which enables the design and optimization of the phase-shift-based sensors.

## Acknowledgments

This result is part of a project that has received funding from the European Union’s Horizon 2020 research and innovation programme under the grant agreement No. 664387.