ISSN 0735-2727, Radioelectronics and Communications Systems, 2009, Vol. 52, No. 6, pp. 324–329. © Allerton Press, Inc., 2009. Original Russian Text © S.L. Skripka, V.V. Danilov, 2009, published in Izv. Vyssh. Uchebn. Zaved., Radioelektron., 2009, Vol. 52, No. 6, pp. 65–74.
Electrodynamics of Wave Processes into Two-Connected Planar Wave Guide Structures S. L. Skripka and V. V. Danilov National Taras Shevchenko University, Kyiv, Ukraine Received in final form February 28, 2008
Abstract—There are represented three configurations of two-connected planar wave-guides, two of them have small dissipations. We research theoretically and experimentally dependences of wave impedance, integration level and dissipations of proposed waveguides on their geometrical parameters and dielectric fulfillment structure. Obtained results for planar waveguide are represented and compared with results, correspondent to standard microstrip line researches. DOI: 10.3103/S0735272709060065
Progress in development of fiber-optic telecommunication and the other information systems does not decrease reduce actuality of development of sub-millimeter wavelength band whose potential possibilities are used insufficiently now. At that, the main and the greatest constraint is an absence of passive waveguide systems, which provides a development of wideband planar waveguides and also integral components and structures, developed on this basis. Since, now the most of integral circuits are constructed in planar form due to simple and inexpensive production technology, so integration possibility of planar elements is the main parameter. The purpose of this work is electrodynamic analysis and experimental research of unscreened two-connected planar waveguide [1–6] and components, developed on its basis, and also comparison of its characteristics with non-symmetric microstrip transmission line. One of the most spread planar waveguide structures, which are applied in radio electronic circuits development, is so-called non-symmetric transmission line (MicroStrip Line). Electromagnetic field configuration and its main features are researched in papers [1–3, 6]. But as it is shown in this paper, this transmission line has its essential drawbacks. In particular, relatively wide ground conductor can result in surface wave propagation in it. It leads to coupling of closely located lines in a printed circuit board and their interaction. To eliminate this mutual interaction of closely located elements they must be located on a greater distance or each of them must be screened. Therefore presence of solid ground conductor in microstrip line restricts its integration level. ELECTRODYNAMIC ANALYSIS Now the most spread method of calculation of electrodynamic processes in waveguide structures with complex boundary conditions is finite difference time-domain (FDTD) method [7, 8]. This method allows to solve Maxwell’s equations for electrodynamic structures of any configuration. In this paper parameters of FDTD method were selected in following way: calculated volume dimensions Lx, Ly, Lz are greater than maximal wavelength, propagating in researched structure (Lx, Ly, Lz > 5l); calculation time T = nDt is greater than transient processes period; to prevent re-reflections of electromagnetic waves from boundaries of calculated volume, i.e. for anechoic chamber imitation, special boundary conditions, so-called Perfectly Matched Layers (PML), were stated [8]; to take into account dissipation at metallic surfaces we use Leontovich limit conditions [9]; to take into account dissipation into dielectrics we use mathematical model of polar dielectric [10]; in standard FDTD algorithm during object discretization in calculated volume its boundaries can be determined only accurate within Dx , Dy , Dz that leads to essential calculation errors in case of small object dimentions and complex configuration. To eliminate these errors at boundaries of complex object we apply a method of boundary conditions specifying, i.e. so-called Perfect Boundary Approximation (PBA) method [11, 12].
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ELECTRODYNAMICS OF WAVE PROCESSES INTO TWO-CONNECTED PLANAR WAVE GUIDE 325 y
y e
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PLANAR TWO-CONNECTED WAVEGUIDE Unscreened planar waveguide is the simplest waveguide structure, containing two metallic surfaces, which are separated by dielectric or air space [5, 6]. Three main waveguide configurations, shown in Fig. 1, where w is metal strip width, h is a distance between metallic strips (waveguide height), p is metallization thickness. In Fig. 1a construction of planar waveguide with standard dielectric fulfillment is represented. In Fig. 1b construction of waveguide with external dielectric fulfillment is shown. In case of construction, shown in Fig. 1b, there is two comparatively thick dielectric planes, acting as consoles for metallization, and main part of signal propagates in air directly between metallic strips. Such waveguide height is regulated by dielectric layers between planes. Another variant of waveguide construction is a construction with complex shape of dielectric fulfillment, which is shown in Fig. 1c. As it will be shown further, constructions, represented in Fig. 1b and Fig. 1c have essentially lower dissipation, than construction, shown in Fig. 1a, so these construction are more promising for their application in sub-millimeter wavelength range, where great amount of standard dielectrics have great dissipation. Main features of two-connected planar waveguide were researched in papers [2–6]. Authors [2, 3] researched screened waveguide construction that was achieved by its placing into rectangular waveguide or into infinite plane capacitor with grounded plates. In case of screened waveguide its main parameters, such as wave impedance and dissipation were derived by means of variation method of strip lines analysis taking into account metallization thickness in case of any waveguide mode [1–3]. In papers [5, 6] they have researched unscreened construction of planar waveguide. For single-mode waveguide the authors [5] have obtained a solution of wave equations by conformal mapping method, but not taking into account metallization thickness. Conductor strip thickness was taken into account in paper [6], but like paper [5], here field pattern was obtained only near waveguide boundary. Complex dielectric fulfillment construction variant, shown in Fig. 1c was not researched. Authors of all mentioned above papers did not research characteristics of waveguide structure, taking into account total electromagnetic field pattern, they considered there is only TEM wave in single-mode waveguide. Complex shape of dielectric fulfillment influence was not researched. Such important waveguide parameter as integration level was not considered. It is obvious that planar waveguide, like microstrip line, is two-connected waveguide, which is characterized by main quasi-TEM mode. The main mode of a waveguide differs from TEM mode of free space, because signal spreads along metallic stripes with finite conductivity, that leads to appearance of longitudinal components of electric and magnetic fields. Therefore the main task is definition of waveguide main parameters, such as wave impedance and dissipation taking into account total field pattern. RADIOELECTRONICS
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E^
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For definition of waveguide main parameters total field pattern were calculated taking into account dissipation, caused by finite conductivity of metallic surface and dissipation into dielectric substrate. During research process following parameters were selected: calculations were carried out in two frequency bands 20–40 GHz and 75–120 GHz; metallization width is a = l s / 8 where l s is wavelength, corresponding to frequencies 30 GHz and 94 GHz for each band; dielectric permittivity is e = 2.2; a value of dielectric dissipation is tand = 0.0009 in two frequency bands was selected taking into account this value of tand provides good correspondence of experimental and calculation results. INTEGRATION LEVEL Calculations of amplitude distribution of crosscut components E ^ and longitudinal components Ez of electrical field in XY plane of cross section of two-connected planar waveguide with height h, which are represented in Fig. 2. To define integration level of planar two-connected waveguide, i.e. a distance, which provides correct omission of two closely set waveguides interaction, we calculate dependence of amplitudes of cross-cut components E ^ of evanescent field on distance l to waveguide boundary for different values of height h. investigation results were compared with analogous results for microstrip line. As it is follows from calculation results evanescent field amplitude decrease dynamics from waveguide boundaries essentially depends on dielectric fulfillment shape. In turns evanescent field amplitude decrease dynamics on a top and a bottom of planar waveguide depends on dielectric permittivity e and does not depend on its height h and dielectric shape. As it is shown in Fig. 2, maximal electrical field amplitude at the top and the bottom of waveguide is 8–12 dB less than field amplitude at waveguide boundaries. It is clear that distance l e from waveguide boundary, when evanescent electric field amplitude decreases e times, in case of application of microstrip line and it is half as much again as in case of planar waveguide application. Therefore we can conclude that in case of the same geometrical dimensions of researched waveguide and microstrip line the first is characterized by greater integration level. But it should be noted that in case of waveguide with external dielectric fulfillment distance l e is greater than in case of waveguide with internal fulfillment, and decreases integration level of the first waveguide. Electrodynamic analysis of planar waveguide with complex dielectric fulfillment (Fig. 1c) dependently on parameter b shows that optimal integration level, i.e. minimal value of l e is achieved where b » h. If parameter b increases further, then a value of l e changes negligible. For multi-mode waveguide a value of l e does not depend on metallization width w. From the other hand, in case of multi-mode waveguide maximal amplitude of electrical field at the top and a bottom of waveguide is always 10–15 dB less than in case of TEM-mode. DISSIPATION Calculation results show that longitudinal component of electrical field Ez does not exceed a value –30 dB with regard to cross-cut component Ey (Fig. 2) in case of any conditions. If cross-cut components amplitudes are constant then longitudinal component amplitude Ez increases with height parameter h increase. It also should be noted that component Ez at the boundaries of waveguide is by a factor of ten RADIOELECTRONICS
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Calculation Integral dissipation, dB/m
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greater than in the middle. It allows to draw a conclusion that main dissipation of propagating wave, which is related to finite conductivity of metallic strips, appears at waveguide boundaries. This conclusion is proven by practically total lack of dissipation dependences on metallization width w in planar waveguide. Calculation results of dissipation dependences on height h in planar waveguide in comparison with microstrip line for frequencies 30 GHz and 94 GHz shows that planar waveguide with external fulfillment, as it was noted before, is characterized by lesser dissipation, than waveguide with internal fulfillment. If waveguide height h decreases up to l/10 dissipation in metal become essential that leads to exponential increase of integral dissipation. If waveguide height increases more than l/4, then the greatest part of signal propagates beyond the waveguide and its essential part irradiates into environment, that leads to increase of integral dissipation. If waveguide height is h < l/20 irradiation dissipation can be omitted. On a basis of obtained results we can draw a conclusion that optimal waveguide height, when integral dissipation are minimal, is h » 0.12l. Calculation results of dissipation in planar waveguide with complex dielectric fulfillment (Fig 1c) dependently on parameter b show that if 0 < b < h dissipation change in the range 4 dB/m, and if h < b < 10h, dissipation change in the range 0.5 dB/m. Therefore, optimal value of dissipation can be achieved if b » h with minimal production technology complication. WAVE IMPEDANCE Numerical calculations show that dependence of wave impedance of planar two-connected waveguide with internal dielectric fulfillment (Fig. 1a) on its geometrical dimensions, calculated by means of FDTD method, practically coincides with theoretical dependence, represented in paper [9] in case of d << h. It also should be noted that, independently on waveguide geometrical dimensions, wave impedance of planar waveguide Zpw is related with wave impedance of microstrip line Zml [1, 5, 6] with following relation: Z pw »1.5Z ml . Calculation of wave impedance of researched planar waveguide (Fig. 1), dependently on geometrical dimensions and dielectric permittivity, shows that Zpw of waveguides, represented in Fig. 1b and Fig. 1c can be calculated on a basis of derived in papers [5, 6] formula for a waveguide with internal dielectric fulfillment. For this purpose in formula, represented in papers [5, 6] we need to substitute real dielectric permittivity e by certain efficient value e eff . Further researches show that efficient dielectric permittivity e eff depends on real dielectric permittivity e in case of b = h by following relations: e eff = 0 .115(e - 1) + 1 for a waveguide shown in Fig. 1b and e eff = 0 .11(e - 1) + 1 for a waveguide, shown in Fig. 1c. As following researches show, formulas for efficient dielectric permittivity can be applied if 1.4 < e < 100. EXPERIMENTAL RESULTS With purpose of verification of electrodynamic analysis results, represented in previous paragraph experimental researches of electrodynamic characteristics of two-connected planar waveguide were carried out. RADIOELECTRONICS
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h = l / 65
Calculation
h = l / 20 h = l / 65 h = l / 20
Experiment
h = l / 65 h = l / 20
h = l / 65 h = l / 20
h = l / 65 h = l / 20
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Measurements were carried out by means of analyzing circuits HP8510B and R2403E, at that for correct connection of generator wave output and two-connected planar waveguide special junction with smallest reflection factor, whose standing-wave factor is Kst < 1.02 during experimental research following parameters were selected: measurements were carried out in two frequency bands 20–40 GHz and 75–120 GHz; Duroid RT5880 was selected as a material of planar waveguide samples (dielectric permittivity e = 2.2, dissipation factor is tgd = 0.0009). DISSIPATION Experimental and calculated dependences of dissipation in planar waveguide, dependently on height h for frequency 30 GHz is represented in Fig. 3a, for frequency 94 GHz it is shown in Fig. 3b. Experimental results, obtained with Duroid RT5880 of different thickness application, demonstrate good accordance with numerical calculations result. As it is shown in Fig. 3, disagreement between experimental and calculated results is in the range 10%. INTEGRATION LEVEL For measurement of evanescent electric field amplitude dependence on a distance from planar waveguide boundary near-field probe was developed. Construction of near-field probe on a basis of two-connected waveguide were researched in papers [13, 14]. It was shown that since two-connected waveguide in case of TEM-mode operation is dispersionless, then near-field probe, developed on its basis, has no supercritical operation mode near probe spike that leads to its sensitivity increase. Construction of a probe, developed for mentioned measurements, has following parameters: probe width was w = 1 mm for carrying out of researching in frequency band of 20–40 GHz and w = 0.4 mm for researches in frequency band of 75–120 GHz; probe height was h = 0.125 mm for 20–40 GHz band and h = 0.05 mm for researches 75–120 GHz; probe angle of conic sharpening was j = 90°, probes for two frequency bands were made on a basis on Duroid RT5880 and also in totally air construction; probe resolution was D » l / 100. Measurements results of evanescent electric field of cross-cut component E ^ dependences on distance l from waveguide boundary for different value of height h, obtained by means of probes, constructed on a basis of Duroid RT5880, in comparison with calculation results are represented in Fig. 4a measurements results, obtained by means of air probes, in comparison with calculation results are represented in Fig. 4b. In Fig. 4a we represent only results, obtained with application of probe with standard internal dielectric fulfillment, because experimental results for probes, developed on basis of Duroid RT5880, demonstrate bad concordance with numerical calculation results. At the same time, as it is shown in Fig. 4b, if we apply air probes, disagreement of experimental and calculation results is in the range of 6%; it allows to draw a RADIOELECTRONICS
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conclusion that probe with internal dielectric fulfillment, placed into researched object field, distort field pattern stronger, than probe with air fulfillment. CONCLUSIONS Numerical calculation results and experimental results show that two-connected waveguide has greater integration level and lesser dissipation, than standard non-symmetric microstrip line. It was also shown that two-connected planar waveguide with external dielectric fulfillment is characterized by essentially lesser dissipation than waveguide with internal fulfillment. Minimal experimental value of integral dissipation was L » 5.5 dB/m on a frequency 30 GHz and L » 14.2 dB/m on a frequency 94 GHz. As a result of good scalability of planar two-connected waveguide that is proven by carried out researches it can be used not only for millimeter, but also for sub-millimeter wavelength range. REFERENCES 1. I. J. Bahl and G. Ramesh, “Simple and Accurate Formulas for Microstrip with Finite Strip Thickness,” Proc. IEEE 65, 1611 (1977). 2. I. J. Bahl and P. Bhartia, “Characteristics of Inhomogeneous Broadside-Coupled Striplines,” IEEE Trans. Microwave Theory Tech. 28, No. 6, 529 (1980). 3. I. J. Bahl and P. Bhartia, “Characteristics of Inhomogeneous Broadside-Coupled Striplines,” IEEE Trans. Microwave Theory Tech. 30, No. 5, 679 (1982). 4. H. A. Wheeler, “Transmission-Line Properties of Parallel Wide Strips by a Conformal-Mapping Approximation,” IEEE Trans. Microwave Theory Tech. 12, 280 (1964). 5. H. A. Wheeler, “Transmission-Line Properties of Parallel Strips Separated by a Dielectric Sheet Approximation,” IEEE Trans. Microwave Theory Tech. 13, 172 (1965). 6. H. A. Wheeler, “Transmission-Line Properties of a Strip on a Dielectric Sheet on a Plane,” IEEE Trans. Microwave Theory Tech. 25, 631 (1977). 7. K. S. Yee, “Numerical Solutions of Initial Boundary Value Problems Involving Maxwell’s Equation in Isotropic Media,” IEEE Trans. Antennas Propag. 14, No. 3, 302–307 (1966). 8. J. P. Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” J. Computational Physics 114, No. 2, 185 (1994). 9. J. H. Beggs and K. S. Yee, “Finite-Difference Time-Domain Implementation of Surface Impedance Boundary Conditions,” IEEE Trans. Antennas Propag. 40, No. 1, 49 (1992). 10. R. Luebbers, “A Frequency-Depended Finite-Difference Time-Domain Formulation for Dispersive Materials,” IEEE Trans. Electromagn. Compat. 32, No. 3, 222 (1990). 11. G. Waldschmidt and A. Taflove, “Three-Dimensional CAD-Based Mesh Generator for the Dey–Mittra Conformal FDTD Algorithm,” IEEE Trans. Antennas Propag. 52, No. 7, 1658 (2004). 12. B. S. Chavannes, Nicolas, and N. Kuster, “A New 3-D Conformal PEC FDTD Scheme with User-Defined Geometric Precision and Derived Stability Criterion,” IEEE Trans. Antennas Propag. 54, No. 6, 1843 (2006). 13. V. V. Danilov, S. L. Skripka, and O. U. Nechyporuk, “Planar Waveguides and Resonators of mm- and Submm Bands,” in Proc. of VI Int. Kharkiv Symposium on Physics and Engineering of Microwaves “Millimeter and Submillimeter Wave and Workshop on Terahertz Technologies,” Kharkiv, Ukraine, June 2007 (Kharkiv, 2007), Vol. 1, pp. 234–236. 14. S. L. Skripka, V. V. Danilov and R. V. Osiyuk, “Planar TE Near-Field Probe,” in Bulletin of Kiev PhysicoMathematical Science University (Kyiv, 2007), No. 4, pp. 271–274.
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