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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 2, FEBRUARY 2005

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Dielectric Constant, Loss Tangent, and Surface Resistance of PCB Materials at -Band Frequencies

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Victor N. Egorov, Vladimir L. Masalov, Yuri A. Nefyodov, Artem F. Shevchun, Mikhail R. Trunin, Victor E. Zhitomirsky, and Mick McLean

Abstract--This paper develops the theoretical approach and describes the design of a practical test rig for measuring the microwave parameters of unclad and laminated dielectric substrates. The test rig is based on a sapphire whispering-gallery resonator and allows the measurement of the following parameters: dielecof the dielectric substrate in the range from 2 to tric constant of the dielectric substrate in the range 10, loss tangent from 10 4 to 10 2 , and microwave losses of copper coating of the substrate in the range from 0.03 to 0.3 . Measurements of numerous commonly used microwave printed-circuit-board materials were performed at frequencies between 30­40 GHz and over a temperature range of 50 C to 70 C.

()

(tan )




+

Index Terms--Anisotropy, complex permittivity, dielectric resonator (DR), resonance spectrum, surface resistance, whispering-gallery (WG) modes.

I. INTRODUCTION SSENTIAL parameters needed for the efficient design of integrated microwave circuits are dielectric properties ( and ), the degree of passive intermodulation, and the microwave copper resistance of the printed-circuit-board (PCB) substrate on which the active elements are mounted. As components are increasingly miniaturized and frequencies increased, the need for accurate dielectric measurements of low-loss substrate materials increases. The properties of these materials should be known over a wide temperature range. Resonant measurement methods represent the most accurate way of obtaining the dielectric constant and loss tangent with unclad thin materials [1], [2]. The high value of the unloaded of the resonator enables measurements of the quality factor smallest losses in the test materials. Methods based on bulk resonators have been developed in numerous laboratories and the results widely published [1]­[5]. The cylindrical cavity
Manuscript received January 5, 2004; revised February 16, 2004. This work was supported by the National Measurement System Directorate of the U.K. Department of Trade and Industry. The work of Y. A. Nefyodov was supported by the Russian Science Support Foundation. V. N. Egorov and V. L. Masalov are with the East-Siberian Research Institute of Physico-Technical and Radioengineering Measurements, Irkutsk 664056, Russia (e-mail: egorov@irk.ru; masalov@niiftri.irkutsk.ru). Y. A. Nefyodov, A. F. Shevchun, and M. R. Trunin are with the Institute of Solid-State Physics, Russian Academy of Sciences, Chernogolovka, Moscow 142432, Russia (e-mail: nefyodov@issp.ac.ru; shevchun@issp.ac.ru; trunin@issp.ac.ru). V. E. Zhitomirsky and M. McLean are with Scientific Generics, Cambridge GB2 5GG, U.K. (e-mail: Victor.Zhitomirsky@genericsgroup.com; Mick.McLean@genericsgroup.com). Digital Object Identifier 10.1109/TMTT.2004.841219

E

has been used to measure both the in-plane dielectric parameters for thin dielectric samples and surface resistance [6]­[8]. Howof bulk resonators does not ever, at room temperature, the exceed 10 in the millimeter-wavelength band. The open hemispherical resonator [3], [4], [9] is a very sensitive instrument for in-plane dielectric measurements of very low loss and flat specimens with diameters much greater than the wavelength. There are two problems with this approach: nonflatness of real samples and large resonator sizes, which limit the application of this technique for measurements in a wide temperature range. Microstrip-based tests [10] do not allow the dielectric and ohmic losses to be measured separately. The nonreproducibility of the rig connection impedance limits the accuracy of this method. A dielectric split resonator [11] made from thercylindrical mostable high-permittivity ceramic has been successfully used for in-plane dielectric film measurements at frequencies below 10 GHz, but it was found unsuitable for measurements at higher frequencies due to increased loss tangent in ceramic materials . and, hence, decrease of In all the above-mentioned methods, the interface surface of the specimen is placed along the microwave -field. At the same time, most PCBs operate with the electric field primarily normal to the plane of the sheet. An incident electromagnetic field should, therefore, have an electric-field component orthogonal to the sample surface. The sapphire disk "whispering at approximately 40 000 gallery" (WG) resonator [12] has at room temperature in the range of 40 GHz (wavelength of approximately 8 mm) and a typical diameter approximately 1.5 . There are two WG-mode types: quasi- (or ) and ) with a high value for a large azimuth quasi- (or . They can be used for dielectric substrate mode index measurements with orthogonal and tangential microwave -fields, respectively. A significant and universal problem with making dielectric measurements with an orthogonal field is the so-called "residual air-gap," which exists due to the microroughness at the contact between the flat resonator and specimen surfaces. As a result, an effective "residual air gap" should be taken into consideration in the electrodynamic model of the measured structure. The goal of this paper is to evaluate both theoretically and experimentally the uncertainties of the sapphire disk WG dielectric-resonator (DR) technique for measurements of out-of-plane dielectric properties of thin materials using up to five different modes. Acceptable accuracy of measurement resonance

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Fig. 1.

(a) DR 1 above a metallic plane with dielectric layer 3 inserted in between, the residual air gap 2 is also shown. (b) Dielectric layer in the split DR.

was provided for both extremely thin substrates with a thickness down to 30 m, as well as for very thick substrates with a thickness exceeding 1 mm. This is possible because the DR achieves a substantial filling factor value even with very thin substrates. A high- factor of the DR also helps to accurately measure very small changes to the resonance frequency. An accuracy of 1% for permittivity measurements of thin dielectric materials and a resolution of the order of 10 for their loss tangent has been shown at 40 GHz. Our test method also allows the measurement of the effective microwave surface resistance of laminated metal at the interface between the laminated material and dielectric. II. ELECTRODYNAMICS A. Measurement Structure Basic Below we describe the resonance mode structure of a dielectric cylinder [see Fig. 1(a)] with diameter and height , which is separated from a metallic plane by a dielectric layer of height and a gap of height . If the component of the electric is an even function of , then the field in the -direction (metallic surface) behaves as a so-called "electric plane wall" for which the following boundary conditions are satisfied: . The electrodynamic structure of the modes in such a case is equivalent to the modes of the split DR with a dielectric layer of double height in the slot [see Fig. 1(b)]. The relative permittivity of a DR is characterized by a tensor

is represented in the form of linear combination of standing - and -waves, which forms a hybrid standing or wave along the -axis. Transverse (on , coordinates) field distribution in gap 2, the dielectric layer 3 and top space 4 is assumed the same as in disk 1. The longitudinal wavenumand of the - and -waves, respectively, are the bers same and are equal to the longitudinal wavenumber of the hy. The boundary conditions brid wave in disk 1: , for inside and outside field within the limits components at define the equation of a circular "dielectric post resonator" with single axis anisotropy [13]

(1)

where , , , and are the Bessel and Hankel functions of the order and their derivaand are the inside and outside transverse tives, , , and wavenumbers, respectively, . For , this equation is reduced into the equation of an isotropic "dielectric post resonator" [14], [15]. For modes with odd longitudinal index , the boundary conditions at , , , and result in the characteristic equation

which determines its electric properties, and by a scalar for are related to the the magnetic properties. Symbols and components of in the direction along the optical (geometrical) axis and in the plane perpendicular to this axis, respectively. We for the isotropic dielectric layer, and , for the use , ambient isotropic space, which includes both the top space 4 and gap 2. We analyze the electromagnetic resonance modes by the method of approximate separation of variables with one-mode approximation of the fields at all fractional volumes of the resonator [9]. In this approach, an electromagnetic field at frequency inside the resonator within the boundaries

[13]

(2)


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where , dinal wavenumbers in regions

, and are the longitu(Fig. 1)

Fig. 2. Schemes for measurements of: (a) ", tan , (b) R (d) q , R .

, (c) Q

, and

The set of (1) and (2) defines the values , , and , which depend on the relative dielectric sample per. Equation (1) does not explicitly depend mittivity on and for determination of , one should solve (1) and (2) and at the measured resonant in series with the values of frequencies. The electrodynamic model described by (1) and (2) does not take into account an influence of the part of the dielectric sample , , i.e., outside the resonator. If this sample at volume is taken properly into account, the resonant frequencies will decrease and, hence, (1) and (2) (which do not take this into account) will overestimate values for . The dielectric sample volume outside the resonator is exposed to only a small part of the total electromagnetic energy. This enables one to correct the value of the dielectric constant by the perturbation method (3) and , where are the total resonator energy and electric field energy outcan be found by numerical side the resonator disks. Factor differentiation of (1) and (2) with respect to the ambient media is of the order of 0.01­0.02. permittivity [16]. B. Dielectric Permittivity and Loss-Tangent Measurements of Nonmetallic Substrates For measurements of the dielectric permittivity and loss tangent of the substrate, the foil is removed from both sides of the microwave PCB sample. The sample (substrate) is clamped between the plates of the split DR [see Figs. 1(b) and 2(a)]. In the experiment, the values of the resonant frequencies of modes are determined. The basic data for calculating the dielectric permittivity of the sample using (1) and (2) are: 1) resonant of modes with known azimuth index ; frequency 2) dimensions and of the DR; 3) sapphire dielectric per, ; and 4) the thickness of the sample. The mittivities value of a residual air-gap is determined by the roughness of the surfaces of both the measured sample and the faces of the resonator and cannot be measured directly. One can estimate this value from the condition that the measured value should not be dependent on the frequency of the measurements in a narrow frequency interval, which is defined by the frequen, , cies of neighboring (by azimuth index)

and resonance modes. The frequency dispersion of low-loss dielectric samples in such a narrow frequency range is usually negligible in comparison with the uncertainty of the real measurements. The problem of the unknown residual air gap makes an additional contribution to inaccuracy, which slightly reduces the measured value . Uncertainty of the measurements depends on the frequency and is reduced with the increase of the azimuth index of the resonant mode. directly absorbed by the The electromagnetic power sample [dielectric layer 3 in Fig. 1(b)] and electromagnetic stored in the sample layer are connected by the energy , where is the dielectric loss relationship angle of a measured sample. In the ordinary approximation of the additive contribution of different losses, the power is connected with the total power loss and the unloaded of the resonator by the following equation: quality factor

(4) is a dielectric loss power in the resonator dielecwhere is a partial quality factor of these disks, tric disks only, is the radiant loss, and is the radiant quality factor of the resonator. It is easy to satisfy the condition by choosing dimensions of the DR. In this case, from (4), we get (5) is a filling factor of the resonator. The where can be obtained from the value of the stored envalue of ergy by integrating the field components over the corresponding volumes of the resonator

(6) where is the energy of the electric or magnetic field stored in the -volume of the resonator. Another way to calcuis by numerical differentiation of the function late


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obtained from (1) and (2) at measured resonant frequencies of the resonator with a sample inside [16] (7) The quantity in (5) is the unloaded quality factor of the resonator with a hypothetical sample, which has the dielectric . The permittivity of the real sample, but has no loss is close to the unloaded of the split resonator value without a sample and can be found from the equation (8) where , , and . Here, and are the energy stored in the longitudinal and transverse components of electric field in the sapand are phire disks with a sample between them; the components of the loss tangent tensor of sapphire in the direction of optic axis and in the plane perpendicular to this axis, respectively. and are Similarly to (6) and (7), the coefficients calculated via integration of longitudinal and transverse components of vector or by numerical differentiation of the resonant frequency dependences (9) (13) C. Surface-Resistance Measurements Under Dielectric To measure the surface resistance of the metallic foil on its interface with the dielectric material, disk 1 is pressed against unclad surface of the sample [see Figs. 1(a) and 2(d)]. In order , we will use values of the filling factor for to determine the laminated sample and the unloaded quality factor of of an unclad sample measured in the resonator, as well as accordance with the procedure described in Section II-B. Similarly to (4) and taking into account (5), the unloaded quality of the resonator pressed onto the dielectric sample factor with a copper laminated layer is defined as (10) where is the total loss power, factor due to ohmic loss in the metallic foil, and loss power, which is equal to is a partial is an ohmic . Neglecting the where contribution of the longitudinal component of the magnetic field is calculated in [17]. in (12), a geometric factor III. EXPERIMENT A. Measurement Cell A simplified schematic of the measurement cell is shown in Fig. 3. A sample is placed between polished sapphire disks with diameter of 12.51 mm and a height of 2.54 mm, which are arranged inside a thick-wall aluminum shield with an inner diameter of 25 mm. The diameter of the shield was chosen to exclude any influence of the metal wall on either the resonant frequencies or the quality factors of the sapphire disks. The aluminum shield is placed inside a thermal isolation chamber. The lower sapphire disk is attached to the post guide and clamped to the sample through the spring with the pressure of approximately three bars. We took special care to prepare "nearly ideal" DRs. Sapphire disks were cut from the same piece of a carefully oriented sapphire single crystal of very high chemical purity. The dimensions of both disks were identical to an accuracy of within 1 m. The -axis of both the disks was perpendicular to their faces. The faces of each disk were parallel with the accuracy better than 1 m across the disks diameter. Surface roughness reduced to 2 nm after polishing. The deviation from flatness of each surface was less than 0.5 m across each disk's diameter. As a result, the problem of the "residual air-gap" was significantly reduced even when the two disks were brought into contact without a "soft" dielectric film between them. Moreover, because these two disks

Fig. 3. Measurement cell diagram.

From (10)­(12), we get the surface resistance of the laminated dielectric sample

(11) where is the tangential component of the microwave magnetic field on the surface of the metal; is the surface area at the interface between the metallic foil and the dielectric layer. Total stored in the resonator can be found by integrating energy the magnetic-field energy in partial resonator volumes

(12)


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in close mechanical contact constitute a near-perfect monolithic crystal, no measurable splitting of the resonance curves has been detected. To simplify the process of changing dielectric samples, the post guide is designed to be axially moveable and have no radial free play. The aluminum shield with sapphire disks and sample can be moved toward and away from the microwave microstrip line by a stepper motor (not shown) in order to tune the coupling of the transmission line with the DR. The latter was included into the line as a directional coupler. Coupling change had not resulted in the resonance frequency shift. Semirigid coaxial cables connect the microstrip to standard 2.9-mm connectors outside the cell thermal isolation. The measuring cell is placed in a stainless-steel vacuum cryostat with a temperature control system. For low-temperature measurements, liquid nitrogen is evaporated from the cryostat and its vapor flows around the resonator and the aluminum shield. Rhode&Schwarz SMR-40 and Gigatronics-8541C were used as the generator and power meter, respectively. B. Experimental Procedure and Results The procedure for taking measurements of dielectric constant, loss tangent, and surface resistance of one-side laminated dielectric samples is described below. First, the resonant spectrum (resonator output microwave power versus frequency ) of the upper DR is measured. For this measurement, the lower resonator is moved away by a maximum distance of 3 mm from the upper resonator and does not influence the measured quantities. Thereupon we determine the resonant frequencies , loaded quality factors , and coupling coefficients of modes of the upper resonator in the range GHz. At room temperature C, the unloaded quality factors of the modes with are equal to 35 790, 40 850, 45 360, 44 970, 37 080, respectively. The maximum quality factor corresponds to the mode. The further increase of azimuth index results in a drop in due to the increase of the sapphire loss tangent. The measured values of resonant frequencies and quality factors for modes of the single resonator at different temperatures within the range C are saved into computer memory as calibration constants. We proceed with similar measurements with both sapphire disks pressed together and determine the values of resonant fremodes of this doubled quencies and quality factors for resonator at the same temperatures C. The results obtained are also stored into the computer memory for further calculations of the dielectric constant, loss tangent, and surface resistance of laminated dielectric samples. The measured frequencies of the double resonator are significantly lower than corresponding frequencies of the single one. The difference decreases when the azimuth number increases. For example, it is equal to 4406 MHz for and 3637 MHz for . This approximately corresponds to the theoretical calculations for the double resonator. Results of theoretical calculations using (1) and (2) are shown in Table I along with the measured resonant frequencies. In these calculations, we used sapphire permittivities of

TABLE I RESONANT F
REQUENCIES OF

HE

M

ODES

and [18]. The discrepancy between the calculated and measured frequency values does not exceed 1.3% for the single resonator and 0.5% for the doubled resonator. Dielectric sheet samples used for measurements of the dielectric constant and loss tangent have planar dimensions 25 50 mm , thickness up to 1 mm, and a one-side copper-laminated square surface of 25 25 mm . The sample is held with force between the upper and lower resonators [see Fig. 2(a)] providing the sapphire disks are in the center of the square 25 25 mm surface. When the sample is clamped inside the split DR, the are shifted down compared measured resonant frequencies to the frequencies of the single resonator. The problem of identification of the mode arises. Fortunately, however, modes are the highest, and secfirst the coupling of the ondly, the frequency difference between the nearest and modes is almost independent for . If the mode identification was correct, the results of calculations for all the modes give very close values for both the permittivity and loss tangent. The mean values of and are calculated using results obtained for all modes. The results are weighted according to the uncertainty of the resonance curve fitting. Examples of such results obtained for a set of samples at room temperature are shown in Table II. Below mean values, the coefficients and are shown. These values are introduced as correction coefficients describing the influence of the absolute uncertainty (in micrometers) in measurements of the thickness of the sample. The error for permittivity can then be found by the formula . Similarly, the error in the loss tangent value is given by . The test rig allows measurements at different temperatures. Such measurements are made in a similar fashion to those at room temperature. The only difference is that preliminary calibration of the resonance frequencies and quality factors of the single and double resonator are performed in the range of temperatures. The temperature is stabilized at exactly the same values for measurements with and without the sample, which helps to compensate almost completely for the temperature dependence of sapphire dielectric properties. An example of and temperature dependences obtained by this scheme for two samples (NY9220 0.01 in and Tly5a0200) is presented in Figs. 4 and 5, respectively. The method of surface resistance measurements of the laminated dielectric samples is illustrated in Fig. 2(b)­(d). Two approaches are possible here, which are: (I) direct measurements and (II) measurements using a calibrated reference copper foil. Let us consider them separately.


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S

AMPLES

P

ARAMETERS AT

TABLE II ROOM T

EMPERATURE

Fig. 4. Temperature dependences of permittivity in NY9220 and Tly5a0200 (Taconic).

2

0.01 in (Nelco)

Fig. 5. Temperature dependences of loss tangent in NY9220 and Tly5a0200 (Taconic).

2

0.01 in (Nelco)

(I) The direct method of the surface resistance measurements is based on the calculation of using (13). In this case, the sample is placed into the resonator as shown in Fig. 2(d), and

the quality factor of the upper resonator with laminated dielectric sample is measured. Using the previously determined quality factor of the resonator without a sample and the sample loss tangent (obtained by measuring the nonclad


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of this sandFig. 2(c)]. The quality factors wich structure are measured for different resonance modes. The values at resonant frequencies are found by the following formula: (15) In contrast to determined during the first in (15) determine the step, the quality factors losses in the reference foil, taking into account the electromagnetic-field distribution in the structure of Fig. 2(c). Step 3) The same distribution of the field occurs in the geometry shown in Fig. 2(d). The quality factor related to the ohmic loss at the interface between the metal foil and the dielectric material is determined in accordance with (14). The surface resistance of the metal foil at the resonant frequencies of the modes is found as , where the value of the reference foil measured at the first step is linearly approximated to the appropriate frequency of the third measurement step. The advantage of method (II) in comparison with the direct method (I) is that the surface resistance does not depend on the calculation of the geometric factor in (13) and, hence, the accuracy of method (II) is higher, especially for thicker samples. IV. CONCLUSION In this paper, we have presented a novel technique for the measurement of the dielectric constant and loss tangent of dielectric substrates with reasonable accuracy for substrate thickness ranging from 10 to 1000 m. For the first time, a resonance technique with the electric field of electromagnetic radiation orthogonal to the surface of the substrate has been demonstrated. The high sensitivity for thin samples is made possible by the high unloaded quality factor of the "WG" resonator and substantial filling factor value. There is no fundamental restriction on the maximum thickness of substrate, while its dielectric permittivity is lower than the one of sapphire. When the dielectric thickness increases, the measurement structure shown in Fig. 1 gradually turns to a single DR on the dielectric half-space. Experimental results do not show any influence of the "residual air-gap" problem, which is explained by the optical-quality sapphire polishing, elasticity, and/or flatness of most of the samples, as well as by pressure applied between the sapphire disks and substrate. The method also provides measurements of the surface resistance of metal films. The presence of copper film in the resonator reduces the quality factor by an order of magnitude. The accuracy of surface resistance measurements at the interface between a metallic film and a dielectric layer is strongly influenced by the substrate thickness, dielectric constant, and loss tangent. and , the 15%­20% accuIn the case of was shown experimentally for dielectric substrate racy of mm. Such materials are widely used thickness at 30­40 GHz.

Fig. 6. Evolution of resonance curves of the HE mode in the sample RO3003 0.0 (Rogers) for direct measurement of surface resistance.

2

part of the sample as described above), the value of tained as follows:

is ob(14)

where filling factor is calculated for the laminated sample. Factor has appeared before as a denominator in the righthand side of (13). It characterizes an ohmic loss in the metal lamination at the interface with dielectric material. The geometric factor is calculated elsewhere [17]. Fig. 6 illustrates the frequency shifts and quality-factor variations for measurements of at the mode. The accuracy of the direct surface resistance measurements strongly depends on the thickness and the dielectric losses in the substrate. To obtain reliable results by this method, ohmic losses in the laminated metal must be comparable to dielectric losses. In case of copper foil, the applicability criteria for direct measurements can be written as , where the thickness of the substrate is expressed in m. In Table II, the data of the fourth, fifth, seventh, eighth, and ninth samples were obtained by direct measurements. (II) The second method to measure the surface resistance of laminated dielectric samples involves a few extra steps, which are shown in Fig. 2(b)­(d). Step 1) The smooth copper metal foil is chosen as a reference. The surface resistance of the foil (if unknown) is determined by measuring the quality factor of the upper resonator pressed against this foil [seeFig. 2(b)]. Using measurements at the resonance frequencies of several modes, the surface resistance can be calculated as , where . The expression for follows from (13) for the resonator located on a metallic plane without dielectric layer , but with an effective air-gap . In turn, an effective air gap can be found from (1) and (2), and the condition of equality of double resonator frequency to the frequency of the upper resonator on the metal surface (see [17]). Step 2) The reference foil is placed underneath the uncoated region of the dielectric sample, and they are held together between the disks of the split resonator [see


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ACKNOWLEDGMENT The authors are grateful to S. V. Ryzhkov, V. N. Kurlov, and G. E. Tsydynzhapov, all of the Institute of Solid-State Physics, Russian Academy of Sciences (ISSP RAS), Moscow, Russia, for technical help. The authors would like to thank Rhode&Schwartz, Munich, Germany, for providing the long-term loan of a microwave signal generator. The authors would also like to express their gratitude to the numerous companies that provided samples for their validation measurements. This list includes, but is not limited to Rogers, Chandler, AZ, Labtech, Presteigne, U.K., Spemco, Portsmouth, U.K., Isola, Cumbernauld, U.K., Sheldahl, Nelco, Lannemezan, France, Bookham Technology, Caswell, U.K., and Celestica, Telford, U.K. REFERENCES
[1] J. Baker-Jarvis, B. Riddle, and M. D. Janezic, "Dielectric and magnetic properties of printed wiring boards and other substrate materials ," NIST, Boulder, CO, Tech. Note 1512, 1999. [2] J. Baker-Jarvis, M. D. Janezic, B. Riddle, C. L. Holloway, N. G. Paulter, and J. E. Blendell, "Dielectric and conductor-loss characterization and measurements of electronic packaging materials," NIST, Boulder, CO, NIST Tech. Note 1520, 2001. [3] A. L. Cullen and P. K. Yu, "The accurate measurement of permittivity by means of an open resonator," in Proc. Roy. Soc., vol. 325, London, U.K., 1971, pp. 493­509. [4] R. J. Cook and R. J. Jones, "Comparison of cavity and open resonator measurements of permittivity and loss angle at 35 GHz," IEEE Trans. Instrum. Meas., vol. IM-23, no. 4, pp. 438­442, Dec. 1974. [5] M. N. Afsar and K. J. Button, "Millimeter-wave dielectric measurement of materials," Proc. IEEE, vol. 73, no. 1, pp. 131­153, Jan. 1985. [6] H. E. Bussey, "Standards and measurements of microwave surface impedance, skin depth, conductivity and ," IEEE Trans. Instrum. Meas., vol. IM-9, no. 3, pp. 171­175, Sep. 1960. [7] A. Hernandes, E. Martin, and J. M. Zamarro, "Resonant cavities for measuring the surface resistance of metals at band frequencies," J. Phys. E., Sci. Instrum., vol. 19, pp. 222­225, 1986. [8] G. Kent, "Nondestructive permittivity measurement of substrates," IEEE Trans. Instrum. Meas., vol. 45, no. 1, pp. 102­106, Feb. 1996. [9] L. A. Vainshtein, Open Resonators and Open Waveguides (in Russian). Moscow, Russia: Sov. Radio., 1966. [10] IPC-TM-650 Test Methods Manual, Inst. Interconnecting and Packaging Electron. Circuits, Northbrook, IL, 1997. [11] T. Nishikawa, K. Wakino, H. Tanaka, and Y. Ishikawa, "Precise measurement method for complex permittivity of microwave dielectric substrate," in Precise Electromagnetic Measurements Conf. Dig., Tsukba, Japan, 1988, pp. 155­156. [12] V. F. Vzjatyshev et al., A Possibility of Superhigh Quality Resonator Creation (in Russian). Moscow, Russia: Trudy Moskovskogo Energeticheskogo Instituta, 1978, vol. 360, pp. 51­57. [13] V. N. Egorov and I. N. Mal'tseva, "Azimuthal modes in anisotropic dielectric resonator" (in Russian), Electronnaja Technika. Serija 1, Electronica SVCH, no. 2, pp. 36­39, 1984. [14] B. W. Hakki and P. D. Coleman, "A dielectric resonator method of inductive capacities in the millimeter range," IRE Trans. Microw. Theory Tech., vol. MTT-9, no. 4, pp. 402­410, Jul. 1960. [15] W. E. Courtney, "Analysis and evaluation of a method of measuring the complex permittivity and complex permeability of microwave insulators," IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 8, pp. 476­485, Aug. 1970. [16] V. F. Vzjatyshev and V. S. Dobromyslov, The Mutual Correlation of Characteristics in Multilayer Waveguides and Resonators (in Russian). Moscow, Russia: Trudy Moskovskogo Energeticheskogo Instituta, 1979, vol. 397, pp. 5­7. [17] V. N. Egorov, V. L. Masalov, Y. A. Nefyodov, A. F. Shevchun, M. R. Trunin, V. Zhitomirsky, and M. McLean, "Measuring dielectric properties and surface resistance of microwave PCB's in the -band,", [Online]. Available: http://xxx.lanl.gov/ftp/cond-mat/papers/0312/0 312 151.pdf, 2003. [18] V. N. Egorov and A. S. Volovikov, "Measuring the dielectric permittivity of sapphire at temperatures 93­343 K," Radiophys. Quantum Electron., vol. 44, no. 11, pp. 885­891, 2001.

Victor N. Egorov was born in Irkutsk, Russia, in 1950. He received the M.Sc. degree in physics and electronics from Irkutsk State University, Irkutsk, Russia, in 1972, and the Ph.D. degree in microwave theory and technique from the Moscow Power Engineering Institute, Moscow, Russia, in 1985. Since 1975, he has been with the East-Siberian Research Institute of Physico-Technical and Radioengineering Measurements (VS NIIFTRI), Irkutsk, Russia, where he is currently a Deputy Director. His research interests are mainly concerned with low-noise microwave generators, high- resonators, and microwave parameters measurements.

Q

Vladimir L. Masalov was born in Arkhangel'sk, Russia, in 1941. He received the M.Sc. degree in physics and electronics from the Novosibirsk Electrotechnical Institute, Novosibirsk, Russia, in 1967. Since 1976, he has been with the East-Siberian Research Institute of Physico-Technical and Radioengineering Measurements (VS NIIFTRI), Irkutsk, Russia, where he is currently a Senior Researcher. His research interests are mainly concerned with low-noise microwave generators and superconducting resonators and DRs.

Q

X

Yuri A. Nefyodov was born in Chernogolovka, Russia, in 1977. He received the B.Sc. and M.Sc. degrees in physics and mathematics and Ph.D. degree in condensed matter physics from the Moscow Institute of Physics and Technology (MIPT), Dolgoprudny, Russia, in 1998, 2000, and 2003, respectively. Since 1997, he has been with the Institute of Solid State Physics, Russian Academy of Sciences (ISSP), Chernogolovka, Moscow, Russia, where he is currently a Researcher. His current research interests are mainly concerned with electrodynamics of anisotropic medium, especially with high- superconductors.

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Artem F. Shevchun was born in Leipzig, Germany, in 1979. He received the B.Sc. and M.Sc. degrees in physics and mathematics from the Moscow Institute of Physics and Technology (MIPT), Dolgoprudny, Russia, in 2000 and 2002, respectively. Since 2000, he has been with the Institute of Solid-State Physics (ISSP), Chernogolovka, Moscow, Russia, where he is currently a Junior Researcher. His current research interests are mainly concerned with microwave electrodynamics of superconductors.

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Mikhail R. Trunin was born in Moscow, Russia, in 1958. He received the M.Sc. degree in theoretical physics from Gorky State University, Nizhnii Novgorod, Russia, and the Ph.D. and D.Sc. (habilitation) degrees in condensed matter physics from the Institute of Solid-State Physics (ISSP), Chernogolovka, Moscow, Russia, in 1985 and 1999, respectively. Since 1980, he has been with the ISSP, where he is a Head of the Laboratory of Electron Kinetics. Since 2000, he has been a Professor with the Moscow Institute of Physics and Technology (MIPT), Dolgoprudny, Russia. His current research interests are concerned with low-temperature physics, superconductivity, and high-frequency electrodynamics of solids.


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Victor E. Zhitomirsky was born in Kharkov, Ukraine, in 1967. He received the B.Sc. and M.Sc. degrees in physics and mathematics and the Ph.D. degree in condensed matter physics from the Moscow Institute of Physics and Technology (MIPT), Dolgoprudny, Russia, in 1987, 1989 and 1993, respectively. He was a Researcher with the Institute of SolidState Physics (ISSP). He has held post-doctoral positions with the Max-Planck Institute fЭr FestkЖrperforschung, Stuttgart, Germany and Oxford University, Oxford, U.K. Since 2001, he has been with the Science and Technology Group, Scientific Generics (SG), Cambridge, U.K., an integrated business and technology consultancy, where he is currently a Senior Consultant. His current research interests are concerned with microwave techniques and disruptive technologies in the area of semiconductors and opto-electronics.

Mick McLean was born in London, U.K., in 1948. He received the B.Sc degree in logic with physics and M.Phil in computer simulation modeling from the University of Sussex, Sussex, U.K., in 1970 and 1979, respectively. Since joining the Science and Technology Group, Scientific Generics (SG), Cambridge, U.K., a business and technology consultancy group, in 1989, he has managed over 300 assignments involving technology management for private- and public-sector clients. He is also Director and General Manager of Technical Investment Services Ltd.--the specialist "due diligence" company within the Generics Group launched in January 2001.