Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric Resonator Assisted by 3D Simulators

Transcription

1 Bulg. J. Phys. 38 (2011) Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric Resonator Assisted by 3D Simulators B.N. Hadjistamov, P.I. Dankov Faculty of Physics, University of Sofia, Sofia 1164, Bulgaria Received 6 January 2011 Abstract. In this paper the split-post dielectric resonator is investigated as a measurement tool for dielectric substrate parameters characterization by using a suitable 3D model, assisted by modern 3D electro-magnetic simulators. The dielectric parameters of a known substrate are measured by a set of different dielectric resonators in order to find the most appropriate measurement conditions and dielectric resonator shapes. Results are analyzed and presented in tabular form. PACS codes: d 1 Dielectric Substrates and Measurement of Their Parameters The measurement of dielectric substrate parameters is one of the most important things connected with modern electronics, computer and communication hardware [1]. The main reason is the manner of design of the electronic devices, based on electromagnetic or schematic simulators, where precise knowledge of the substrate dielectric constant (ε r ) and loss tangent (tan δ ε ) is very important. Modern high-integrated active or passive devices, such as microwave integrated circuits, systems on chips, antenna-array panels, chip carriers, etc. are multilayered composite structures, and a possible inaccuracy in the dielectric parameters of the used materials could deteriorate the numerical simulations. Usually the catalogue data given by substrate producers is obtained by the IPC TM stripline test method and is for a limited number of frequencies (commonly 1 MHz or 10 GHz), which can be quite insufficient. Furthermore, this method gives information only for the normal to the surface dielectric parameters ε, tan δ ɛ, while substrate materials are usually composite materials and may be anisotropic (Figure 1). In our previous work we have established that most of the commercial reinforced laminates (with layers of woven glass, ceramic powders, organic filling, etc.) have a noticeable c 2011 Heron Press Ltd. 191

2 Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric... ', tan Ox Oz Oy ',tan ' ' r ' ' Figure 1. Anisotropy of the dielectric parameters. dielectric anisotropy (e.g. up to 15 25% for dielectric constant anisotropy ΔA ε =2 ε ε /(ε + ε ) and up to 50 80% for dielectric loss tangent anisotropy ΔA tan δɛ =2 tan δ ɛ tan δ ɛ /(tan δ ɛ +tanδ ɛ ). The characterization of anisotropic materials generally requires two techniques, one for the component of permittivity perpendicular to the plane of the sample and one for the in-plane permittivity. The two-resonators method [2,3], based on two cylindrical resonators with different modes TE011 and TM010 is suitable for determination of substrate anisotropy at a set of fixed frequencies (Figure 2a). A possibility of tuning the resonance frequency by moving the inner cylinder and working at lower frequencies is achieved by the tunable coaxial and re-entrant resonators [4,5] (Figure 2b). In this paper we investigate a new pair of measurement tools based on dielectric cylindrical, ring or prismatic resonators inserted into metal cavities the splitpost dielectric resonator SPDR (Figures 2c,3). The parameters determination is assisted by commercial 3D electro-magnetic simulators creating a suitable 3D model, which ensures high accuracy and computational efficiency. We investigate numerically a number of configurations with different dielectric resonators DR, in different frequency ranges in order to obtain the best measurement conditions and DR shapes. Finally, we present measurement data for the dielectric a) b) c) Legend: Resonance cavity Metalpost E-field orientation Dielectric Resonator Substrate Figure 2. Pairs of measurement cylindrical cavities for determination of dielectric parameters anisotropy: a) cylinder resonators, b) coaxial cylinder and re-entrant resonators, c) split-post dielectric resonators. 192

3 B.N. Hadjistamov, P.I. Dankov Figure 3. Split-post dielectric resonator with a set of dielectric resonators. parameters of a known substrate, analyze and compare these results with those from the pure split-cylinder resonator. We use DR based on high-quality sapphire and alumina with very high Q factors. 2 3D Model of the Split-Post Dielectric Resonator Analytical solutions of the split-post dielectric resonator, due to the complexity of the structure are difficult and give only approximate results. Instead, by using modern 3D electro-magnetic simulators we create and simulate a 3D model of the structure (Figure 4). There are three basic principles in the creation of the model, which ensure fast and accurate simulations. First, we draw a stylized model of the resonator as a pure cylinder, where the influence of the coupling loops, screws, diameter eccentricity and etc. is taken into account in equivalent diameter and surface conductivity of the model. This considerably facilitates the Legend: 1 finite conductivity; 2 E-fieldsymmetry (E fieldperpendicular tothe boundary surface); 3 H-fieldsymmetry (E fieldparalleltothe boundarysurface); 4 perfecth -walls; Figure 4. Equivalent 3D models of the considered cavities and their main boundary conditions. 193

4 Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric... drawing procedure and the simulation of the structure. Second, we define the cylindrical surfaces with an optimal number of line segments N = 144. Small values of N do not fit well, while big values considerably increase the computational time. In fact, a simple rule is that the width of the linear segment should be smaller than λ g /16 (λ g the wave length in the structure). Finally, taking advantage of the symmetry of the electromagnetic field of the modes of interest, we split the resonators and simulate just one quarter of them. This approach requires suitable symmetrical boundary conditions to be chosen for the splitresonator surfaces illustrated in Figure 4. The utilization of these split-cylinder 3D equivalents instead of the whole resonator cavities is a key assumption for the applicability of the 3D models and it solves several important problems: 1) it considerably decreases the computational time (up to several hundred times); 2) allows to increase the computational accuracy and 3) suppresses a possible virtual excitation of non-physical modes, which occur during simulations of the whole resonator near to the mode of interest. 3 Measurement Procedure and Error Analysis We use two cylindrical resonators, one split TE011 mode, for measurement of ε, tan δ ε and one TM010 mode for ε, tan δ ε, a piece of foam and a spacer, a set of dielectric resonators with different shapes, dimensions and materials (Figure 5, dimensions given in Table 1). For the analysis we use a sample Ro4003, substrate produced by the Rogers Corporation. The measurement procedure is as follows: first we measure the resonance frequency and quality factor of the empty resonators, from which we determine the equivalent diameters and wall conductivity of the 3D models by assuring a coincidence of the measured resonance parameters and the simulated ones. Doing this at the beginning of every measurement procedure makes it indepen- Figure 5. Picture of the used dielectric resonators. 194

5 B.N. Hadjistamov, P.I. Dankov dent of daily variations of temperature and other immeasurable factors like wall roughness and diameter eccentricity. The accuracy in determining the equivalent diameters is quite high in terms of micrometers. Next we put the supporting foam in the TE011 mode resonator and the spacer in the TM010 mode resonator, and again by achieving a coincidence of the measured and the simulated resonance parameters determine the dielectric constant and loss tangent of the foam and the spacer. Then the same is done with the dielectric resonators. Although the method can be used for measurement of ε, tan δ ε of the dielectric resonators themselves, we must note that in these parameters we put the uncertainties of their shape manufacturing, roughness, and dimensions measurement. Thus, we have a well calibrated 3D model which is used for determination of the substrate parameters. The main error comes from the measurement of the height of the sample. 4 Analysis of the Results We have done series of measurements of one and the same substrate with a set of different dielectric resonators (Table 1). The aim is to see which shapes, materials and dimensions are the most appropriate for dielectric substrate parameters determination. The analysis of the results is made in the following aspects: 4.1 Low vs.high Dielectric Resonators As our investigations show high dielectric resonators pull the E-field away from the sample (Figure 6). The substrate is in an inactive zone and the sensitivity of measuring its parameters is weak. This leads to uncertainties in the measurements (Table 1, No 2, 13). We recommend dielectric resonators with heights up to 2/3 of the height of the resonator. Figure 6. Low vs. high dielectric resonators. High DR pull the E-field away from the sample. 195

6 Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric... Table 1. Experimental data for the dielectric and resonance parameters of SPDR with a set of different dielectric resonators (sample Ro4003, h =0.5 mm; PR prismatic resonator, RR ring resonator, CR cylindrical resonator) DR (dimensions,mm) TE 011 moderesonator TM 010 m ode resonator (D eq = ;H = 30.16; eq = 5.7M S/m) (Deq=30.045;H = 12.12; eq = M S/m) f,ghz/q (DR) 0 Em ptyresonator / foam /spacer / Alum inapr1 (19.1 x 18.4x12) 3 Alum inapr2 (19.8 x 19.6x6) 4 Alum inapr3 (19.3 x 11.9x6) 5 Alum inapr4 (19 x 6.8x6) 6 Alum inadr5 (12.5 x 11.1x6) 7 Alum inapr6 (12.6x7x6) 8 SapphirePR1 (17.7 x 12.5x6.6) 9 SapphirePR2 (10.3x8.0x5.3) 10 QuartzPR (12.8 x 12.3x9.3) 11 Alum inarr1 (20.5 x 10.3x3.3) 12 Alum ina RR 2 (20.5 x 10.3x5.2) 13 Alum inarr3 (20.5 x 10.3x8.5) 14 Alum ina CR 1 (9.5x8.95) 15 Alum ina CR 2 (8.8x8.5) 16 CR red (8x10.1) / / / / / / / / / / / / / / / 1453 tan (DR) f,g H z/q (sam ple) 1/ / / / / / / / / / / / / / / / / / tan f,ghz/q (sam ple) (DR) / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Nodata / / / / / / / / / / / / / / 2125 tan (DR) f,ghz/q tan (sam ple) (sam ple) 1/ / / / / / / / / / < / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Dielectric Resonators with Prismatic Forms We have investigated dielectric resonators made from one and the same material Alumina, but with different prismatic forms (Table 1, No 2 7). The results show that in the case of TE011 mode resonator, where the E-field is concentrated mostly in the dielectric resonator, DRs with big difference in their horizontal dimensions are not appropriate (Table 1, No 5). The SPDR in this case has lower quality factor and the mode is not well defined (Figure 7a). 196

7 B.N. Hadjistamov, P.I. Dankov a) b) Figure 7. Dielectric resonators with different prismatic forms. The electro-magnetic mode is not well expressed in SPDR with DR with big difference in their horizontal dimensions a). 4.3 Symmetrical Dielectric Resonators Cylindrical and ring dielectric resonators, made of Alumina with different dimensions are investigated (Table 1, No 11 15). Small cylindrical resonators concentrate the E-field in a small part of the substrate (Figure 8a). Better results are obtained by ring DR, where the field is stronger and more widely distributed (Figure 8b). a) b) Figure 8. E-field distribution in SPDR with: a) cylindrical DR, b) ring DR. 4.4 Dielectric Resonators with Different Dielectric Constants As can be seen (Table 1, No 17, 18), dielectric resonators with dielectric constants, which differ much from that of the sample, lead to a lack of sensitivity to the presence of the substrate (very small change in the resonance frequency) and are not appropriate for parameters measurements. We recommend DR with dielectric constants close to that of the substrate or up to 3,4 times bigger. 197

8 Measurement of Dielectric Substrate Parameters Using Split-Post Dielectric... 5 Conclusions The pair of TE011 mode and TM010 mode split-post dielectric resonators offer a good possibility for measurement of dielectric parameters anisotropy. The method has the following advantages: Higher quality factors, compared to those of the pure split cylindrical resonators. This leads to better sensitivity in the dielectric loss tangent determination. Possibility of tuning the resonance frequency by using a set of appropriate dielectric resonators. Appropriate are DR with heights up to 2/3 of that of the cylindrical resonator and dielectric constants close to that of the sample or up to 3 4 times bigger. Good measurement conditions are achieved by using ring dielectric resonators. References [1] J. Baker-Jarvis, B. Ridldle, M.D. Janezic, Dielectric and Magnetic Properties of Printed Wiring Boards and Other Substrate Materials, National Institute of Standards and Technology, Technical Note 1512, Boulder, CO, USA. [2] P.I. Dankov (2006) IEEE Trans. Microwave Theory and Technique [3] P.I. Dankov, V.P. Levcheva, V.N. Peshlov (2005) Utilization of 3D Simulators for Characterization of Dielectric Properties of Anisotropic Materials, 35th European Microwave Conference EuMW 2005, Paris, France, Oct.2005, p.515. [4] B. Hadjistamov, V. Levcheva, P.I. Dankov (2007) In: Meetings in Physics at University of Sofia 7, edited by A. Proykova, Heron Press, Sofia, p. 55. [5] P.I. Dankov, B. Hadjistamov (2007) Characterization of Microwave Substrates with Split-Cylinder and Split-Coaxial-Cylinder Resonators, 37th European Microwave Conference, Munich, Germany, Oct.2007, p