PIERS Proceedings, Cambridge, USA, July 2–6, 2008 566 Measurement of the Dielectric Constant of Liquids Using a Hybrid Cavity-ring Resonator M. S. Kheir1 , H. F. Hammad1 , and A. S. Omar2 1 Faculty of Information Engineering and Technology German University in Cairo, Cairo, Egypt 2 Microwave and Communication Engineering University of Magdeburg, Magdeburg, Germany Abstract— A simple and efficient solution for extracting the dielectric constant of liquids utilizing microstrip ring resonators simultaneously with rectangular waveguide (RWG) cavities is presented. Employing both techniques in a single structure is a confirmation procedure rather than comparing the obtained results with any other standard method. The proposed structure is intended to be mechanically suited for holding liquid samples without enclosing any air gaps which enhances the measurement sensitivity. Since the structure is being totally enclosed, the loaded quality factor will be consequently increased due to the absence of radiation losses. The waveguide cavity acts as metallic enclosure for the ring circuit in order to maintain the design procedures as well. 1. INTRODUCTION Material characterization is an important field in microwave engineering since it is employed in various systems and applications ranging from high-speed circuits to satellite and telemetry applications . Several measurement techniques are already available nowadays and can be mainly classified into transmission-reflection, free-space, and resonance techniques. The later technique is of a great interest and wide range of application due to its higher accuracy and resolution. Among the resonant methods used in material characterization are waveguide cavities and printed-line resonators [3–11]. Rectangular and cylindrical waveguide cavities have been commonly used for a long time in characterizing low-loss materials [4–6] as they offer a high quality factor. However, performing material measurement with waveguides concurrently with another printed resonator has not been investigated yet and will be the goal of this work It is intended to use both structures simultaneously as a double-check procedure for measurement convenience and low fabrication cost. Using both methods consequently will definitely reduce measurement ambiguity. The key feature in this structure is that it is an ordinary microstrip ring resonator covered with a metallic enclosure which acts as a RWG as illustrated in Section 3. Above all, a practical solution for characterizing the electrical properties of liquids is strongly needed. 2. MEASUREMENT THEORY Napoli and Hughes  introduced a simple and accurate technique for determining the dielectric constant of integrated circuit substrates. It was assumed that the substrate material forms a parallel-plate waveguide cavity if it is metallized on both sides. Using the formula below the relative dielectric constant (εr ) can be easily obtained just by detecting the resonance frequency (fmn ) of this waveguide. r³ ´ c m 2 ³ n ´2 + (1) fmn = √ εr 2w 2l where c is the speed of light, m is the order of transverse resonance, n is the order of longitudinal resonance, w is the waveguide width, and l is the waveguide length. However, the resulting quality factor was not as high as expected. In a later work, Howell  suggested a slight modification to this method which significantly increased the quality factor and Progress In Electromagnetics Research Symposium, Cambridge, USA, July 2–6, 2008 567 offered a convenient way of measurement. In his work he short-circuited the ends of the parallelplate waveguide to eliminate the losses due to end-effect and fringe fields. The resulted resonator was a simple RWG with the resonance equation ¶ µ 2 c2 q2 p εr = + 2 (2) 4fpq a2 b where p and q are the transverse and longitudinal resonance modes respectively while a and b are the transmission line length and width. By observing the resonance frequency and applying the above-mentioned formulas, the effective dielectric constant can be calculated. Nevertheless, Robinson  also investigated the resonant modes that result from RWG cavities partially loaded with a microstrip line. This approach still can be a good approach for representing the modes of the metallic enclosure used in our proposed design. The guided wavelength (λg ) of this excited mode is given by λo λg = v (3) µ ¶2 u 1 λo u ¶− µ ¶µ u t h 1 2l 1− 1− b εr where h represents the substrate thickness, b is the cavity height (including the substrate material), and λo is the free space wavelength. 3. THE HYBRID CAVITY-RING STRUCTURE The detailed structure of the proposed hybrid resonator is shown in Fig. 1(a) with a separate illustration of the ring circuit structure in Fig. 1(b). It consists of three major parts; the microstrip ring resonator, the metallic enclosure and the common ground plane. This structure is made of Aluminum and is fed by an SMA coaxial-to-microstrip transition for measurement using the vector network analyzer (VNA). The details of the hybrid resonator structure are declared next. Metallic Enclosure Ring Resonator Ground Plane (a) (b) Figure 1: Exploded view of the proposed hybrid resonator (a) and top view of the used ring resonator (b). 3.1. The Microstrip Ring Resonator A gap-coupled microstrip ring resonator with an FR4-type substrate has a dielectric constant (εr = 4.4), a loss tangent (tan δ = 0.02) and a thickness (h = 1.5 mm) is used. The operation of the ring resonator is based on the well-known relation nλg = 2πr (4) where r is the mean radius of the ring and n is the harmonic order of resonance. Then the effective dielectric constant (εeff ) can be extracted from the above equation since λo λg = √ εeff (5) Meanwhile, the resonance frequency can by detected by observing the peaks of the magnitude and the rapid phase variation of the insertion loss (S21 ) of the ring. Considering that the ring is operating at its fundamental resonance. PIERS Proceedings, Cambridge, USA, July 2–6, 2008 568 3.2. The Waveguide Enclosure Another way for confirming the estimated εeff is to use the metallic enclosure which acts as a waveguide cavity with L-band standard dimensions  operating at its dominant mode TE10δ . When the cavity is perturbed by the material under test (MUT) the resulting resonance frequency will be deviated from its original resonance frequency. From this frequency shift the material properties can be evaluated using the Cavity-Perturbation theory . However, through the following section the details of the dielectric constant extraction procedures will be illustrated. 4. MEASUREMENT AND EXTRACTION PROCEDURES 1 2.4 2.6 2.8 1. 2 1. 4 1. 6 2 2. 2 2.2 Cav ity Reso na tor Ring Resonat or 2 1.8 1.6 Relative Dielectri c Co ns ta nt 1.4 1.2 22 20 18 16 14 12 10 8 6 4 2 Effective Dielectric Cons tant In the simulation phase, several materials with different dielectric constants have been tested and the resulting effective dielectric constant of the substrate has been extracted using a finite-elements method simulator. The detected resonance frequency of the overall structure is used in Equations (2) and (4) to calculate the respective εeff of the cavity and ring resonators. Fig. 2(a) shows the effective dielectric constants calculated in both cases while the results are in excellent agreement. In Fig. 2(b) the relative dielectric constant extracted at different resonance frequencies is plotted where the simulation points precisely fit a fourth order polynomial function. This curve can be efficiently used to extract the dielectric constant of any MUT using the proposed structure only by measuring its resonance frequency. 50 45 40 35 Simulation 30 Cu rve Fitting 25 20 15 10 5 1 1.8 2.4 2.6 2.8 Frequency (GHz) Fr equency (GHz) (a) (b) Frequency (GHz) (a) 0 -5 -10 -15 -20 -25 -30 -35 -40 -45 -50 0.5 1 1.5 2 2.5 3 Sij (dB) Figure 2: The extracted εeff from both resonators (a) and the estimated εr against frequency (b). (b) Figure 3: The measured S11 and S21 (a) and a photograph (b) of the resonator. As a measurement example the experimental prototypes have been filled with an unknown liquid. As shown in the S-parameters curve in Fig. 3(a) that the first resonance peak appears at 1.25 GHz. Such result typically corresponds to a liquid with εr = 40 according to the previously depicted graph. The measurement was performed by the Rohde and Schwarzr ZVB-20 network analyzer. Progress In Electromagnetics Research Symposium, Cambridge, USA, July 2–6, 2008 569 The photograph of this prototype is shown in Fig. 3(b) where the screw-hole in the middle of the enclosure is intentionally introduced for transferring the liquid into the structure. The structure was mechanically suitable for holding such liquids due to its sealed design. A screw is then used to close this hole which completes the upper metal boundary of the waveguide. 5. CONCLUSIONS A simple method for evaluating the dielectric constant of liquids has been proposed. It is based on using ring and RWG cavity resonators simultaneously in a single structure. By observing the resonance frequency of this hybrid resonator the effective dielectric constant can be extracted. 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