Dielectric Measurements Using A Coaxial Resonator ... - IEEE Xplore

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 2, APRIL 1997

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Dielectric Measurements Using a Coaxial Resonator Opened to a Waveguide Below Cut-Off Bogdan A. Galwas, Jerzy K. Piotrowski, Member, IEEE, and Jerzy Skulski Abstract—A model of a quarter-wavelength coaxial resonator opened to a semi-infinite circular waveguide below cut-off is presented in the paper. A full-wave analysis of the transition between coaxial-line and circular waveguide was used. The analysis was based on a mode-matching formulation. The circular waveguide is filled with a dielectric material. As a consequence, the parameters of the resonator, resonant frequency, quality factor and resonant transmission, change in relation to the complex permittivity of the material. A fully automated L-band microwave system with resonator sensor was fabricated and used for measurements of the permittivity of low-loss and highloss powdered materials. Results obtained using the system are compared with those of other method. Index Terms— Automated measurement systems, coaxial resonators, dielectric measurements, electrodynamics, microwaves, sensors.

I. INTRODUCTION

M

ICROWAVES are widely used in sensors for dielectric materials characterization [1]-[4]. When the microwave resonator is used as a sensor, the material to be measured is introduced into contact with some part of the electromagnetic field of the resonator. The important advantages of these types of sensors are the high sensitivity and resolution [4]. The opened ended coaxial line resonator is well known as a useful tool for dielectric permittivity measurements [4]. The previously described solutions are based on coaxial line opened to the half-space. In such a case the effect of radiation from resonator to open space strongly influences on quality factor. The placing of dielectric sample inside a circular waveguide below cut-off removes the effect of radiation to open space and, in consequence, increases quality factors and measurement resolution. II. QUARTER-WAVELENGHT COAXIAL RESONATOR OPENED TO THE CIRCULAR WAVEGUIDE BELOW CUT-OFF

The quarter-wavelength coaxial resonator, opened to a semiinfinite circular waveguide, as shown in Fig. 1, is modeled in order to predict the relationship between the resonator parameters and the complex permittivity ( ) of any dielectric sample in the waveguide below cut-off. The coaxial line-circular waveguide transition, built in the resonator, is studied using a full-wave analysis. An expression for the unknown, normalized to the characteristic admittance of the coaxial line, input admittance (y ) of the TEM mode at the T plane is derived. After the y is accurately calculated,

Fig. 1. Geometry of a quarter-wavelength coaxial resonator opened to a semi-infinite circular waveguide below cut-off.

other parts of the resonator model, which are expected to be independent of the permittivity of the dielectric sample, are experimentally determined. A. Full-Wave Formulation for the Coaxial Line—Circular Waveguide Transition The geometry of the transition, which is a part of resonator shown in Fig. 1, is formed by a coaxial line and a semi-infinite circular waveguide which consists of two dielectric regions. The radii of the inner and the outer conductors of an air-filled ( , ) coaxial line are and , respectively. A dielectric spacer of the complex permittivity and thickness is placed in the circular waveguide of radius . The second region is filled by a dielectric sample of unknown complex permittivity . Both materials are linear, isotropic, homogeneous, and nonmagnetic. The analysis of the transition has been carried out with the simplifications that the conductivity of conductors is infinite and only the TEM mode with the amplitude is incident upon the T plane. For the electromagnetic field inside the coaxial line, because of rotational symmetry, only higher order TM modes may be found when a TEM mode is incident. As a consequence of this, only rotationally symmetrical TM modes are excited in the circular waveguide. Following the notation of Marcuvitz’s Waveguide Handbook [5], the total electric and magnetic field components transverse to the z direction at the T plane in the coaxial line are expressed as

Manuscript received June 20, 1996; revised October 1, 1996. The authors are with the Institute of Microelectronics and Optoelectronics, Warsaw University of Technology, 00-665 Warsaw, Poland Publisher Item Identifier S 0018-9456(97)01582-9. 0018–9456/97$10.00  1997 IEEE

(1a)

(1b)

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where is the unknown reflection coefficient of the TEM mode, is the amplitude of the TM modes, and are wave admittances of the TEM and the TM modes, respectively. is the propagation constant of the th TM mode. The coaxial line electric and magnetic field modal vecand , respectively. These orthonormal tors are and eigenvectors are expressed as for the TEM mode with , and with

and

for the TM modes, where and are Bessel functions and is the discrete eigenvalue associated with eigenfunction . Analogously, the total transverse EM field components at the T plane in the circular waveguide are

(a)

(2a) (2b) where is the reflection coefficient, is the unknown amplitude at the T plane, is wave admittance of the TM modes and is the propagation constant in and for spacer layer. The orthonormal eigenvectors with the circular waveguide are and , where eigenvalues are determined by the boundary condition The is related to the reflection coefficient of the th TM mode at the plane by the relation where , is the wave admittance of the th TM mode and is the propagation constant in the region of the dielectric sample. Matching the tangential EM field across the aperture at plane and using the orthogonality properties of the eigenvectors in relations (1) and (2) results in the following set of equations: (3a)

(3b)

(b) Fig. 2. The reflection coefficient 0" as a function of frequency for " = "o (a) and " = (4 0:5j )"o (b) with a = 20 mm, b = 5:5 mm,d = 0:8 mm, "s = (8:3 0:007j )"o , M = 3 and N = 6.

0 0

first N TM modes in the waveguide. With the assumption that the short-circuit cannot be placed at the T plane (3) has been normalized to the total amplitude of TEM mode at this plane. Next, the substitution of (3b) in (3c) leads to the following set of simultaneous linear equations

(4) and are the unknown normalized total amplitude and input wave admittance of the th TM mode at the T plane, respectively. The solution of (4) by a typical numerical subroutine determines these amplitudes. The normalization of (3a) yields a relation for the admittance as follows:

where

(3c) where as well as are coupling coefficients between the th TM mode in the waveguide and the TEM mode as well as the th TM mode in the coaxial line, respectively. The infinite series (3) may be truncated by taking into consideration the first M TM modes in the coaxial line and the

(5) The described solution may be applied for the multilayer structure in the waveguide region and only the expression for must be appropriately modified. Exemplary frequency characteristics of at the T plane are shown in Fig. 2.

GALWAS et al: DIELECTRIC MEASUREMENTS USING A COAXIAL RESONATOR

Fig. 3. Equivalent circuit model of the quarter-wavelength resonator opened to the circular waveguide.

B. Model of the Resonator The arrangement of the resonator under consideration has been presented in Fig. 1. At the input (plane T ) and the output (plane T ) of the cavity two 50 SMA connectors, which are schematically shown between planes T T and T T in Fig. 1, are combined with the coupling loops. The size of loops should be appropriately large to ensure strong magnetic coupling in order to obtain not too high transmission loss of the resonator at the resonant frequency when high-lossy dielectric material is placed in the circular waveguide. The equivalent circuit model of the resonator is shown in Fig. 3. In the cavity, the determination of power loss due to the nonperfectly conducting walls of the coaxial line is essential for calculation of the loaded quality factor . Thus, the propagation constant and the characteristic impedance of the coaxial line as well as the impedance of this line end wall are complex and described by classical relations given in [6]. The coaxial linecircular waveguide transition is represented by the admittance . The two coupling loops are modeled in Fig. 3 by transformer ratios susceptances and reactances . The transformer ratios are proportional to the coupling of the coaxial line to the SMA connectors. The connectors are represented by the coaxial lines of the length with the characteritic impedance and the phase constant . Since the resonator has been strongly coupled, the evanescent modes appearing in the surroundings of the loops should be taken into consideration. This effect is modeled by susceptances and reactances which may be determined from measurements. III. PRACTICAL SOLUTION OF MEASUREMENT SENSOR SYSTEM The measurement system with resonator sensor has been fabricated. The system should allow one to measure resonant frequency and quality factor of resonator very accurately, and from their small changes obtain information about the dielectric sample. The block diagram of the system is shown in the Fig. 4. The general parts of the system are: synthesized source of microwave signals, resonators, receiving unit, microprocessor control unit and external computer. The source of L-band microwave signals is coupled to the measurement resonator

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Fig. 4. Block diagram of system. MR (measurement resonator), RR (reference resonator), RP (reference power channel).

MR with dielectric sample, the reference resonator RR and to the reference power channel RP. The reference resonator RR is the same as the measurement resonator MR but without a dielectric sample. The transmitted power is measured by the receiving unit. Simultaneous measurements of power transmitted by the three channels makes measured changes of and independent of operation temperature. The action of the source is controlled by the microprocessor control unit. The control unit collects the digital data on power transmitted by the three channels. After finishing a measurement procedure the information is transmitted to a central computer. Extraction of resonator parameters ( , ) are obtained from measurements of power transmission by the resonator at many frequencies and by the proper calculation procedure. IV. EXAMPLE OF

THE

EXPERIMENTAL RESULTS

The measurement system was used with the coaxial resonator of dimensions mm, mm, and mm. First, a short-circuit was placed in the T plane creating a half-wavelength resonator in order to determine the conductivity of gold plated metallic walls and to estimate the parameters of the coupling system. The measurements have indicated that differences between loops are negligible, conductivity of walls is S/m and values of the parameters are 10.3, 45.4 , 0.024 S, respectively. The ceramic spacer 0.8-mm thick with permittivity was used. In order to reduce the resonant frequency detuning range and degradation of quality factor an additional 1-mm thick air-filled layer was formed between the coaxial line and spacer in both resonators of the system. The measured resonant frequency and the quality factor of the RR resonator are 1.165 GHz and 110.5, respectively. To validate the model of the resonator sensor, powdered silica as well as seven powdered silica–graphite mixtures, with concentration of graphite from 2% to 14%, have been measured. The MR resonator was positioned vertically and 30-mm thick layer (due to the fact that granular materials are very pressure sensitive) of the material under test was poured into the circular waveguide. Fig. 5 shows the measured coefficients of detuning and quality factor of the resonator. On degradation

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and measurement sensitivity. The developed system makes possible the industrial characterization of dielectric materials. The system may be used to measure moisture in granular materials (e.g., sand, concrete, grain), unburnt carbon content in ashes as well as biological tissues, chemical liquids, etc. Practically the system is able to measure on-line. It is possible to join several independent resonator sensors to a central computer and to create a proper measurement network.

REFERENCES

Fig. 5. Detuning (p) and quality factor degradation (q) coefficients of the MR resonator measured for powdered silica–graphite mixtures. Percentages indicate concentration of graphite.

[1] D. Misra, “A quasistatic analysis of open-ended coaxial lines,” IEEE Trans. Microwave Theory Tech., vol. 35, pp. 925–928, Oct. 1987. [2] S. S. Stuchly, C. L. Sibbald, and J. M. Anderson, “A new aperture admittance model for open-ended waveguides,” IEEE Trans. Microwave Theory Tech., vol. 42, pp. 192–198, Feb. 1994. [3] C. L. Li and K. M. Chen, “Determination of electromagnetic properties of materials using flanged open-ended coaxial probe—full-wave analysis,” IEEE Trans. Instrum. Meas., vol. 44, pp. 19–27, Feb. 1995. [4] E. Nyfors and P. Vainikainen, Industrial Microwave Sensors. Norwood, MA: Artech House, 1989. [5] N. Marcuvitz, Waveguide Handbook. New York: McGraw-Hill, 1951. [6] T. Morawski and W. Gwarek, Theory of Electromagnetic Field. Warsaw, Poland: WNT, 1978 (in Polish).

Bogdan A. Galwas was born in Poland on October 31, 1938. He received the M.Sc. degree in 1962, the Ph.D. degree in 1969, and the habilitated doctors degree in 1976, all in electronic engineering, from Warsaw University of Technology, Warsaw, Poland. In 1962, he joined the Faculty of Electronics, Warsaw University, as Lecturer. In 1986 he was promoted to Full Professor. His current research interests are microwave measurement systems, modeling, designing and measurement of microwave oscillators, theory and designing of microwave resonator sensors. He is the author of more than 100 scientific papers and two books in these areas.

Fig. 6. Calculated permittivity for silica–graphite mixtures for measurements in Fig. 5 and HP 85070 dielectric coaxial probe measurements.

the basis of the developed resonator sensor model the relative permittivity for the sample powders has been calculated and the results are presented in Fig. 6. together with the HP 85070 dielectric coaxial probe measurements. V. CONCLUSIONS Previously described quarter-wavelength resonator sensors are based on coaxial line opened to the half-space. In such a case the effect of radiation from line to open space strongly influences the resonator quality factor. The placing of dielectric sample inside a circular waveguide below cut-off removes the effect of radiation and therefore increases quality factors

Jerzy K. Piotrowski (M’89) was born in Tomasz´ow Mazowiecki, Poland, on May 10, 1952. He received the M. Sc. and Ph.D. (summa cum laude) degrees in electronics engineering from Warsaw University of Technology, Warsaw, Poland, in 1975 and 1988, respectively. He has been with the Institute of Microelectronics and Optoelectronics, Warsaw University of Technology, since 1975. From 1982 to 1984, he spent 20 months with the Technische Universitaet, Braunschweig, Germany, where he was engaged in the study of finline technique. He has published papers on Gunn oscillators, finlines, and coplanar waveguides. His areas of special interest include microwave and lightwave integrated circuits, computational electromagnetics, and microwave sensors.

Jerzy Skulski was born in Poland, on December 8, 1945. He received the M. Sc. degree in electronic engineering from Warsaw University of Technology, Warsaw, Poland, in 1970. In 1971, he joined the Electronics Faculty, Warsaw University of Technology, as Assistant Professor. He is now a Researcher. He has been engaged in the research and development of microwave amplifiers, generators, and measurement systems. His current research interest is in the area of microwave sensors.