# A modified complex permittivity measurement technique at microwave frequency.

1 INTRODUCTIONMany well-established frequency domain [1]-[94] and time-domain [95]-[103] techniques are available for microwave measurement of the materials complex permittivity. Microwave techniques using one-port method were described in [56], [59], [65], [72], [79], [82], [84]-[86], [89], [90], [91], [98], [99], while microwave techniques using two-port techniques were described in [1]-[55], [57], [58], [60]-[64], [66]-[71], [73]-[78], [80], [81], [83], [95]-[97], [100]-[103]. Some of these methods are suitable for solid materials [1]-[24], [27]-[29], [31]-[37], [39]-[45], [47]-[57], [59]-[62], [64]-[83], [85], [91], [103], while other methods are suitable for liquid or other amorphous materials [20], [25], [26], [30], [38], [43], [46], [58], [63], [84], [41], [42], [44], [47], [49], [54], [59], [81], [87], [91], [95], [98] [100]. Some of the microwave measurement techniques are simple and inexpensive [25]-[84], [89], [91], [98] while others are complex and expensive, and need for complex measurement apparatus, such as network analyzer or optical devices [31], [41], [47], [55], [83], [85], [95], [100].

Complex permittivity measurement at microwave frequencies with transmission and reflection coefficients was adopted widely using guided wave geometries, where the material sample is put inside precisely to fill the space with a certain width [24], [53], [82], [85], [96]. In [100] a microwave technique was used to measure materials complex permittivity using transmission and reflection coefficients at free space with a material filling a container placed between a pair of antennae for measurement. This technique is accurate but the measurement has not a unique solution and it is expensive because of using the Network Analyzer (N/A). In this paper A modification to the measurement system setup presented in [100] was achieved to make this technique inexpensive by using X-Band circulator and dual channel digital power meter instead of the coupler and N/A, respectively, while a MathCAD[TM] platform is used to solve the transmission/reflection power measurement equations numerically to find a unique solution.

2 DEFINITION OF COMPLEX PERMITTIVITY

The properties of a material may be specified by two complex constants called complex permittivity ([epsilon]) or dielectric constant and complex permeability ([mu]). The real and imaginary parts of these constants are indicated in the equations

[epsilon] = [epsilon]' + j[epsilon]" (1)

[mu] = [mu]' + j[mu]" (2)[right arrow]

Where [epsilon]' is the dielectric constant and [epsilon]" is the loss factor. Since the materials[right arrow] are considered to be nonmetallic, thus a measure of the energy lost in the form of heat is called the loss tangent (tan[delta]). It is the ratio of the power dissipated to the power stored per cycle;

tan[delta] = [epsilon]"/[epsilon]' (3)

The dielectric properties may be determined at microwave frequencies by measuring the propagation characteristics of the electromagnetic[right arrow] wave through the medium. There is a great variety of experimental techniques by which dielectric measurements can be made. The technique used for a particular measurement depends upon the frequency, the dielectric properties of the material, and the amount and form of the available material.

3 APPLICATIONS OF COMPLEX PERMITTIVITY MEASUREMENT

Measurement of materials complex permittivity has many applications in different fields.

3.1 Industrial Applications

Application of materials in microwave and communication industries requires the exact knowledge of material parameters such as permittivity. For examples, the dielectric materials used for manufacturing microstrip antenna substrates and the plastics & rubbers which are used in manufacturing of antenna sleeves, of particular concern are those which are used on the band sets of personal communication systems [85], [86].

Another application of complex permittivity measurement is for evaluation of material deterioration. This microwave measurement technique was used for evaluation of both combustion engine oil-fill and electrical transformer oil deterioration [91].

3.2 Biological Applications

Since 1970s, the measurement of biological substances complex permittivity took a big concern to evaluate the effect of microwave devices radiation, such as microwave ovens, on human body. Nowadays, measurement of biological substances complex permittivity takes a lot of attention to mitigate the mobile telephone radiation hazard [14], [20], [42].

3.3 Agricultural Applications

The agricultural applications of complex permittivity measurement includes

1. Controlling the seeds conditions and humidity rate in feed storage (silos) [83].

2. Microwave moisture content determination in dried green tea applied for control of a drying process [101].

3. Microwave moisture measurement of grains [83], [102].

4. Permittivity of fresh fruits and vegetables at microwave frequencies [103].

4 AMPLITUDES OF TRANSMISSION/REFLECTION METHOD

A microwave method for dynamic measurement of permittivity is required in many industrial processes (i.e., in order to observe the quality or moisture of the material which is moving on a belt conveyer, the permittivity of the material needs to be measured dynamically) [100]. The essence of the dynamic measurement is that the instantaneous and noncontacting measurement of the permittivity can be realized. The microwave free-space technique can be expected for the dynamic measurement because the microwave parameters can be measured instantaneously and without contacting the material. The purpose of this method is to be used for the dynamic measurement of the permittivity by using the microwave free-space technique.

In the studies performed thus far, the attenuation and phase shift were used to determine the permittivity of material [103]. The instantaneous and noncontacting measurements of these two parameters can be realized. However, the measured value of the phase shift may differ by an integral multiple of from the actual value caused by the material. To obtain the actual value of the phase shift, it is necessary to do the measurement at least twice using different thicknesses.

Furthermore, it is difficult in the dynamic measurement to prepare the samples with the same permittivity and different thicknesses because the sample under measure changes instantly. Therefore, the actual value of the phase shift and then the permittivity cannot, in fact, be measured instantaneously.

The general consideration of this paper is to use only the amplitudes of the transmission and reflection coefficients to determine the permittivity because the instantaneous and no contacting measurements of these two parameters can be realized. According to the analysis, the permittivity of the sample can be determined uniquely from the measurement values of the amplitudes in the case that the sample has large enough attenuation that the multiple reflections (MR's) between the two surfaces of the sample can be neglected. Thus, this method can be used for the dynamic measurement of permittivity.

4.1 Principle

A typical situation in the measurement of the permittivity of material using the free-space technique is shown in Figure 1. The material filling a container is placed between a pair of antennas for measurement.

[FIGURE 1 OMITTED]

The wave travels from the radiating antenna to the receiving antenna through the three media of the air, container, and material. Reflection occurs at the interfaces of the air-container I and IV and the container-material II and III, and MR's occur between each of the two adjacent interfaces. The reflection coefficients are denoted by at I, at IV, at II, and at III, respectively. Using the signal-flow graph technique, the transmission coefficient and reflection coefficient can be obtained as in [100]. We can be sure that amplitudes of the transmission (T) and reflection (R) coefficients in decibel are functions of the permittivity ([[epsilon].sub.rs]) of the sample because the permittivity ([[epsilon].sub.rc]) and then the propagation constant [k.sub.c] of the container are constants;

T = T([[epsilon]'.sub.rs], [[epsilon]".sub.rs]) (4)

R = R([[epsilon]'.sub.rs], [[epsilon]".sub.rs]) (5)

T = T([[epsilon]'.sub.rs], [[epsilon]".sub.rs]) and R = R([[epsilon]'.sub.rs], [[epsilon]".sub.rs]) are curved surfaces with respect to the permittivity ([[epsilon]'.sub.rs] and [[epsilon]".sub.rs]) of the sample.

For given Measurement values of the amplitudes of the transmission and reflection coefficients ([T.sub.meas] and [R.sub.meas]), we can obtain the constant value lines of the transmission and reflection coefficients expressed by CT and CR;

CT = CT([[epsilon]'.sub.rs], [[epsilon]".sub.rs]) (6)

CR = CR([[epsilon]'.sub.rs], [[epsilon]".sub.rs]) (7)

The lines CT and CR are different with the measured values [T.sub.meas] and [R.sub.meas].[right arrow] Using the numerical method with the assistant of MathCAD[TM], the lines CT and CR can be obtained from [100]. The necessary and sufficient condition for determining the permittivity ([[epsilon]'.sub.rs], and [[epsilon]".sub.rs]) from the measured values [T.sub.meas] and [R.sub.meas] is that there is just one cross point between the lines CT and CR.

The lines CT and CR with several different measured values of [T.sub.meas] and [R.sub.meas] are obtained using a numerical method.

To validate the proposed numerical method using MathCAD[TM] a calculation with frequency f = 9.4 GHz, permittivity of the container wall [[epsilon].sub.rc] = 2.55-j0.07, and its thickness [t.sub.c] =

3 mm given in [97] is used. It can be seen that the possibility of having more than one cross point exists between the lines CT and CR, and the permittivity cannot be determined uniquely. Especially for low-loss material (with small value of [[epsilon]".sub.rs]), the lines CT and CR are complicated and they have many cross points. If the sample has permittivity [[epsilon].sub.rs] = 20 - j1 and thickness [t.sub.s] = 30 mm, the measured values should be [T.sub.meas] = 8.375 dB and [R.sub.meas] = 5.036 dB. For these values, the lines CT and CR are shown together in Figure 2, It can be seen that there are many cross points between the lines CT and CR in addition to the actual point [[epsilon].sub.rs] = 20 - j1, as shown in Figure 2. Thus, the value [[epsilon].sub.rs] = 20 - j1 cannot be obtained uniquely from the lines CT and CR.

The lines CT and CR become complicated with the decrease of the loss factor ([[epsilon]".sub.rs]). This phenomenon implies that the complexity of the lines is due to the MR's between the two surfaces of the sample. When the attenuation caused by the sample is small, the MR cannot be neglected. Therefore, the transmitted and reflected waves ([E.sub.t] and [E.sub.r]) and then the lines CT and CR become complicated with the decrease of the attenuation caused by the sample. The influence of the MR can be reduced by preparing the sample with large attenuation. For example, if the sample with attenuation larger than 10 dB is prepared by making an appropriate thickness, the power reflected at interface III is 1/10 smaller than the power reflected at interface I. After propagating through the sample and container wall of the input side, it becomes 1/100 smaller than the power reflected at interface I. In this case, the MR can be neglected for the measurement of the reflection coefficient.

[FIGURE 2 OMITTED]

4.2 Measurements

The measurement system set up shown in Figure 3 is used in [100] to measure the amplitudes of the transmission and reflection coefficients. This setup was modified, as shown in Figure 4, by using a dual-channel power meter instead of the N/A and a circulator instead of the coupler, since the measurement is concerned on the amplitude, excluding the phase, of the transmitted and reflected power only. The adopted modified setup is more simple and inexpensive.

The wave power of 9.065 GHz from the oscillator is measured in advance. The reflected and transmitted waves are fed into the dual-channel power meter. The aperture of the horn antennas is 58.80 mm and the distance between them is 200 mm.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The permittivity of the glass container is approximately equal to (5 - j0.03) and the thickness of the wall of container 4-mm. In measurements, a combustion-engine oil-fill (SAE 20W/40) is used as the sample by putting it into the container. The section area (normal to the propagation direction) of the sample is 250 X 250 mm and its thickness is 50 mm.

The measurement results were:

--Incident power = 97 mW

--Transmitted power = 42.3 mW

--Reflected power = 36.8 mW

Using MathCAD[TM] (numerical solver) the roots that satisfied both transmission and reflection coefficient equations [100] can be calculated and drawn as shown in Figure 5.

The roots of the complex permittivity are:

2.35-j0.00185 and 2.27-j0.00185. The correct root is 2.35-j0.00185. This non unique solution is due to many reasons:

1. Multi-reflection, and it can be avoided by increasing the sample width which means increasing the container width.

2. Diffraction influence at the edges of the sample, and it can be reduced by attaching a plate of a microwave absorber around the sample (which is not available during the measurement process)

[FIGURE 5 OMITTED]

5 CONCLUSIONS

A simple, low-cost, and acceptable accuracy technique for measuring materials complex permittivity was achieved and examined in this paper. This technique is based on measuring the amplitude of transmission/reflection coefficients in presence of the material sample to do permittivity measurement after solving the measured data numerically. The numerical solution was achieved in this work with the assistance of MathCAD[TM]. The adopted technique is suitable for liquid materials, it is also suitable for solid materials if their dimensions chosen carefully. Good results can be achieved if the material sample width is greater than the container wall width by more than ten times to reduce the effect of the multi-reflections. The main advantage of this technique is no need for a guess or approximate value of the sample permittivity, as in the short-circuited line technique where infinite solutions are exist, which makes the solution a unique. The other advantage of this technique is that it can be used easily to measure the material permittivity dynamically, which is required in many industrial applications. More accuracy analysis for the adopted microwave measurement technique is recommended as a future work.

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Salah I. Yahya Al-Mously

School of Computer Engineering, Koya University Koya, Kurdistan Region, Iraq

E-mail: salah.ismaeel@koyauniversity.org

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Author: | Al-Mously, Salah I. Yahya |
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Publication: | International Journal of New Computer Architectures and Their Applications |

Article Type: | Report |

Date: | Apr 1, 2012 |

Words: | 5762 |

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