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. [1–5]. 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.

2. Phase-shift method

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

of transmission line.

lossy medium [15]:

phase velocity can be determined as

2.1 Determination of real part of the dielectric constant

dal signal that propagates along a transmission line.

well as physical properties of the transmission line:

Phase-shift method is based on the measurement of the phase shift of a sinusoi-

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

Phase shift Δφ is defined by velocity and frequency of the propagating signal as

, (1)

, (2)

<sup>Δ</sup><sup>φ</sup> <sup>¼</sup> <sup>ω</sup>LTL vp

where ω is the angular frequency, vp is the phase velocity, and LTL is the length

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> <sup>σ</sup><sup>2</sup> ω2ε<sup>2</sup>

<sup>r</sup> <sup>q</sup> : (3)

<sup>ω</sup><sup>2</sup> <sup>ε</sup><sup>2</sup> <sup>≪</sup> <sup>1</sup>; (4)

<sup>μ</sup><sup>ε</sup> <sup>p</sup> , (5)

c0

ffiffiffiffi εr

p , (6)

1 þ

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

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> <sup>σ</sup><sup>2</sup> ω<sup>2</sup>ε<sup>2</sup>

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

1 þ

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

> ffiffi 2 p ffiffiffiffiffi με p

frequencies high enough, the influence of conductivity can be neglected:

σ2

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

vp <sup>¼</sup> <sup>1</sup>

ffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffi μ0ε0ε<sup>r</sup> <sup>p</sup> <sup>¼</sup> <sup>ω</sup>LTL

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 <sup>μ</sup><sup>0</sup> <sup>¼</sup> <sup>4</sup><sup>π</sup> <sup>∙</sup> <sup>10</sup>�<sup>7</sup> H/m, the phase velocity and the

s r

<sup>β</sup> <sup>¼</sup> <sup>ω</sup> ffiffiffiffiffi με p ffiffi 2 p

vp <sup>¼</sup> <sup>ω</sup> β ¼

phase shift are dependent on dielectric permittivity only:

ffiffiffiffiffiffiffi <sup>μ</sup>0<sup>ε</sup> <sup>p</sup> <sup>¼</sup> <sup>ω</sup>LTL

Δφ ¼ ωLTL

71

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 [3–10]. 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.

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