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RING RESONATOR AS A SENSOR TO DETERMINE DIELECTRIC PROPERTIES OF BIOLOGICAL MATERIALS Abstract— When materials are to be treated with microwaves for different purposes such as drying, online moisture measurements, disinfestations, and remote sensing, thorough knowledge of the material dielectric properties becomes extremely important. Unlike for other materials, measurement of dielectric properties for biological substances is very complicated due to the nature of the materials themselves. This paper presents study on dielectric properties of various biological materials like cucumber, paneer, etc using a ring resonator. The dielectric ring resonator is used as a model for both analysis and measurement.
I. INTRODUCTION The measurement of dielectric properties is not only important in scientific but also in industrial applications. The interest in microwave dielectric properties of biological materials has been high in recent years. Numerous measurement methods have been developed in recent years. Using the method described in this paper the dielectric properties of various biological materials like cucumber, paneer, etc. can be determined using a ring resonator. Moisture measurement is also done for all these samples since moisture is a major content in all biological samples. For this purpose ring resonators of 3 different frequencies were designed viz. 2GHz, 2.5GHz and 2.2GHz. Different substrates for these resonators are used like Glass Epoxy and RT Duroid. Basically, microwave resonators are the devices in which maximum energy transfer takes place at the resonant frequency at which they are designed. This resonant frequency changes with a change in effective permittivity of the material, which is in contact with the resonator. The use of ring resonators for the measurement gives more accurate results since the parasitic losses in ring are less. There are also no radiation losses since a ring resonator is a closed structure. Using the same principle, we have collected the database for biological samples mentioned above, with the help of Network Analyzer.
Initially, to fix the sample size for which there is maximum sensitivity, samples with different sizes were taken for measurement. Sample
Fig.1. The dielectric ring resonator
Finally with the decided sample size the measurements were done. The readings were taken by changing the moisture content of the sample. This was done by drying the sample in sun and taking readings after every 5 min. while simultaneously noting down the weights of the sample. These weights were then used to calculate the moisture content of the sample. The moisture content of material, M, expressed in percentage, wet basis, is defined as
(1) where, ww = mass of water wd = mass of dry sample
II. THEORY The configuration of dielectric ring resonator is shown in figure 1. It includes inner radius r1, outer radius r2 and side arms of length Ls and width w. The sample was kept as shown in the figure and the number of samples was increased horizontally as well as vertically, so that the range of sensitivity could be determined.
For plane wave propagation through low loss materials, the ratio of phase shift and attenuation, Ф/A, can be expressed in terms of permittivity as [1], [2] (2) The first term of right hand side of (2), (ε’-1)/ε” was considered earlier as a density-independent function in calibration equations for microwave measurement of moisture content of a number of particulate dielectrics [3], because the second term had a little significance for low loss materials. However, work by Kress-Rogers and Kent [2] on food powders revealed that this term could be too important to neglect. A newer density independent function of the permittivity for moisture calibration in microwave measurement was reported by Trabelsi [4]. This function was based on an observation of the complex plane plot of ε’/ρ vs ε”/ρ for a large set of measurements for several frequencies and moisture content. It was noted that, for permittivities determined from attenuation and phase measurements at a given frequency, all of the points fell along a straight line and that differences in moisture content amounted to translation along the same line (fig2). The lines for each frequency intersected the ε”/ρ = 0 axis at common point, ε’/ρ = k, which represents the value of ε’/ρ for 0% moisture content. Any change in the frequency amounted to a rotation of the straight line about that intersection point. Thus for a give frequency, the equation of the line is expressed as ε”/ρ = af (ε’/ρ - k)
(3)
where af is the slope at a given frequency. It
was determined that the slope varied linearly with frequency. Considering that tanδ = ε”,/ε’,
where δ is the loss angle of the dielectric and that tanδ various with bilk density. Solving (3) for ρ, we have (4) For a given frequency, af is constant and for a
given material k is constant. Thus the bulk density is provided by (4) in terms of permittivity alone, without regard to temperature or moisture content. Using this expression for ρ, we can write
(5) For a given frequency and particular kind of material, kaf is a constant and a new density
independent moisture calibration function can be defined as follows:
(6) The quadratic relationship between the calibration function and moisture content was determined empirically [4]. The new calibration function has been studied for a large set of measurements over practical range of moisture content, bulk density and temperature. Regression analysis provided the values for the constants a, b and c in the following equation: (7)
Fig 2. Complex plane plot of the dielectric constant and loss factor, normalized to bulk density of samples of various moisture content and bulk densities at indicated temperature for two frequencies, [4]
which defines a plane in three-dimensional space as shown in fig 3. The resulting equation for moisture content, M= (Ψ-aT-c) / b, is then given in terms of density independent calibration function Ψ, which at any given frequency depends only on sample permittivity as shown in (6) The dielectric constant and loss factor can be determined by any suitable microwave measurement.
Further research with this new densityindependent moisture calibration function has shown that very similar values of regression constants were obtained for different materials. These findings support the idea of a universal calibration, which would provide a significant advantage.
III. READINGS T min Initi al 10 20 30 40 50 60
Wt gms 1.75
BW Freq (MHz) (MHz) 47.60 2188.1
Q
Loss
45.9
-28.5
1.67 1.50 1.42 1.40 1.38 1.38
100.42 88.24 76.68 66.30 63.27 62.47
21.4 24.5 28.2 32.7 34.3 32.7
-35.4 -34.9 -33.4 -33.4 -32.9 -33.7
2153.6 2170.2 2164.5 2174.3 2172.8 2172.4
Weight (grams) 2.39 2.20 2.13 2.06 1.90
Time (min) Initial 10 20 30 40
Freq (MHz) 1829.15 1834.42 1836.98 1843.21 1839.43
Q 39.58 40.91 41.23 49.50 38.22
Table 4. Readings for cucumber on RT Duroid Substrate
IV. CONCLUSIONS
Table 1. Table for readings of Paneer on Glass Epoxy Substrate Ring Resonator
T min Initi al 10 20 30 40 50 60
Wt gms 1.75
BW (MHz) 114.72
Freq (MHz) 1863.0
Q
Loss
14.5
-42.1
1.67 1.50 1.42 1.40 1.38 1.38
35.47 74.91 21.47 19.73 19.58 20.65
1848.7 1869.0 1869.0 1870.2 1870.6 1869.0
52.1 24.9 87.0 94.7 95.5 90.0
-23.5 -20.0 -19.5 -19.1 -20.0 -18.2
Table 2. Table for readings of Paneer on RT Duroid Substrate Ring Resonator
Weight (grams) 2.20 2.13 2.06 2.00 1.90
Time (min) Initial 10 20 30 40
Freq (MHz) 2068.68 2075.09 2122.16 2144.08 2150.25
Q 15.43 15.70 23.77 19.03 18.97
Table 3. Readings for cucumber sample on Glass Epoxy Substrate Ring Resonator
Fig 3. Moisture and temperature dependence of density-independent function Ψ
REFERENCES [1] M. Kent and E. Kress-Rogers, 1986. “Microwave moisture and density measurements on particulate solids”, Trans. Inst. Meas. Control, vol. 8, no. 3, pp. 161-168, 1986. [2] M. Kent and E. Kress-Rogers, “Microwave measurement of powder moisture and density”, J. Food Eng., vol. 6, pp. 345-376, 1987. [3] W. Meyer and W. Schilz, “Feasibility study of density-independent moisture measurement with microwaves”, IEEE Trans. Microwave Theory Tech., vol. 29, no. 27, pp. 732-739, 1981. [4] S. Trabelsi, A. W. Kraszewski and S. O. Nelson, “New density-independent calibration function for microwave sensing of moisture content in particulate materials”, IEEE Trans. Inst. Meas. Vol. 47,no. 3, pp. 613-622, 1998.
I. INTRODUCTION The measurement of dielectric properties is not only important in scientific but also in industrial applications. The interest in microwave dielectric properties of biological materials has been high in recent years. Numerous measurement methods have been developed in recent years. Using the method described in this paper the dielectric properties of various biological materials like cucumber, paneer, etc. can be determined using a ring resonator. Moisture measurement is also done for all these samples since moisture is a major content in all biological samples. For this purpose ring resonators of 3 different frequencies were designed viz. 2GHz, 2.5GHz and 2.2GHz. Different substrates for these resonators are used like Glass Epoxy and RT Duroid. Basically, microwave resonators are the devices in which maximum energy transfer takes place at the resonant frequency at which they are designed. This resonant frequency changes with a change in effective permittivity of the material, which is in contact with the resonator. The use of ring resonators for the measurement gives more accurate results since the parasitic losses in ring are less. There are also no radiation losses since a ring resonator is a closed structure. Using the same principle, we have collected the database for biological samples mentioned above, with the help of Network Analyzer.
Initially, to fix the sample size for which there is maximum sensitivity, samples with different sizes were taken for measurement. Sample
Fig.1. The dielectric ring resonator
Finally with the decided sample size the measurements were done. The readings were taken by changing the moisture content of the sample. This was done by drying the sample in sun and taking readings after every 5 min. while simultaneously noting down the weights of the sample. These weights were then used to calculate the moisture content of the sample. The moisture content of material, M, expressed in percentage, wet basis, is defined as
(1) where, ww = mass of water wd = mass of dry sample
II. THEORY The configuration of dielectric ring resonator is shown in figure 1. It includes inner radius r1, outer radius r2 and side arms of length Ls and width w. The sample was kept as shown in the figure and the number of samples was increased horizontally as well as vertically, so that the range of sensitivity could be determined.
For plane wave propagation through low loss materials, the ratio of phase shift and attenuation, Ф/A, can be expressed in terms of permittivity as [1], [2] (2) The first term of right hand side of (2), (ε’-1)/ε” was considered earlier as a density-independent function in calibration equations for microwave measurement of moisture content of a number of particulate dielectrics [3], because the second term had a little significance for low loss materials. However, work by Kress-Rogers and Kent [2] on food powders revealed that this term could be too important to neglect. A newer density independent function of the permittivity for moisture calibration in microwave measurement was reported by Trabelsi [4]. This function was based on an observation of the complex plane plot of ε’/ρ vs ε”/ρ for a large set of measurements for several frequencies and moisture content. It was noted that, for permittivities determined from attenuation and phase measurements at a given frequency, all of the points fell along a straight line and that differences in moisture content amounted to translation along the same line (fig2). The lines for each frequency intersected the ε”/ρ = 0 axis at common point, ε’/ρ = k, which represents the value of ε’/ρ for 0% moisture content. Any change in the frequency amounted to a rotation of the straight line about that intersection point. Thus for a give frequency, the equation of the line is expressed as ε”/ρ = af (ε’/ρ - k)
(3)
where af is the slope at a given frequency. It
was determined that the slope varied linearly with frequency. Considering that tanδ = ε”,/ε’,
where δ is the loss angle of the dielectric and that tanδ various with bilk density. Solving (3) for ρ, we have (4) For a given frequency, af is constant and for a
given material k is constant. Thus the bulk density is provided by (4) in terms of permittivity alone, without regard to temperature or moisture content. Using this expression for ρ, we can write
(5) For a given frequency and particular kind of material, kaf is a constant and a new density
independent moisture calibration function can be defined as follows:
(6) The quadratic relationship between the calibration function and moisture content was determined empirically [4]. The new calibration function has been studied for a large set of measurements over practical range of moisture content, bulk density and temperature. Regression analysis provided the values for the constants a, b and c in the following equation: (7)
Fig 2. Complex plane plot of the dielectric constant and loss factor, normalized to bulk density of samples of various moisture content and bulk densities at indicated temperature for two frequencies, [4]
which defines a plane in three-dimensional space as shown in fig 3. The resulting equation for moisture content, M= (Ψ-aT-c) / b, is then given in terms of density independent calibration function Ψ, which at any given frequency depends only on sample permittivity as shown in (6) The dielectric constant and loss factor can be determined by any suitable microwave measurement.
Further research with this new densityindependent moisture calibration function has shown that very similar values of regression constants were obtained for different materials. These findings support the idea of a universal calibration, which would provide a significant advantage.
III. READINGS T min Initi al 10 20 30 40 50 60
Wt gms 1.75
BW Freq (MHz) (MHz) 47.60 2188.1
Q
Loss
45.9
-28.5
1.67 1.50 1.42 1.40 1.38 1.38
100.42 88.24 76.68 66.30 63.27 62.47
21.4 24.5 28.2 32.7 34.3 32.7
-35.4 -34.9 -33.4 -33.4 -32.9 -33.7
2153.6 2170.2 2164.5 2174.3 2172.8 2172.4
Weight (grams) 2.39 2.20 2.13 2.06 1.90
Time (min) Initial 10 20 30 40
Freq (MHz) 1829.15 1834.42 1836.98 1843.21 1839.43
Q 39.58 40.91 41.23 49.50 38.22
Table 4. Readings for cucumber on RT Duroid Substrate
IV. CONCLUSIONS
Table 1. Table for readings of Paneer on Glass Epoxy Substrate Ring Resonator
T min Initi al 10 20 30 40 50 60
Wt gms 1.75
BW (MHz) 114.72
Freq (MHz) 1863.0
Q
Loss
14.5
-42.1
1.67 1.50 1.42 1.40 1.38 1.38
35.47 74.91 21.47 19.73 19.58 20.65
1848.7 1869.0 1869.0 1870.2 1870.6 1869.0
52.1 24.9 87.0 94.7 95.5 90.0
-23.5 -20.0 -19.5 -19.1 -20.0 -18.2
Table 2. Table for readings of Paneer on RT Duroid Substrate Ring Resonator
Weight (grams) 2.20 2.13 2.06 2.00 1.90
Time (min) Initial 10 20 30 40
Freq (MHz) 2068.68 2075.09 2122.16 2144.08 2150.25
Q 15.43 15.70 23.77 19.03 18.97
Table 3. Readings for cucumber sample on Glass Epoxy Substrate Ring Resonator
Fig 3. Moisture and temperature dependence of density-independent function Ψ
REFERENCES [1] M. Kent and E. Kress-Rogers, 1986. “Microwave moisture and density measurements on particulate solids”, Trans. Inst. Meas. Control, vol. 8, no. 3, pp. 161-168, 1986. [2] M. Kent and E. Kress-Rogers, “Microwave measurement of powder moisture and density”, J. Food Eng., vol. 6, pp. 345-376, 1987. [3] W. Meyer and W. Schilz, “Feasibility study of density-independent moisture measurement with microwaves”, IEEE Trans. Microwave Theory Tech., vol. 29, no. 27, pp. 732-739, 1981. [4] S. Trabelsi, A. W. Kraszewski and S. O. Nelson, “New density-independent calibration function for microwave sensing of moisture content in particulate materials”, IEEE Trans. Inst. Meas. Vol. 47,no. 3, pp. 613-622, 1998.
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