# 10.1002@1098-2760(20000920)26 6 410 aid-mop19 3.0.co;2-y

код для вставкиoscillators in Lur’s form. In addition, experiments have been conducted at both the baseband and radio frequency to verify the validity of our design and the feasibility of the proposed secure communication systems. The circuit implementation is simple, and the communication quality is reliable. The system is useful for those analog communications where high privacy is required. REFERENCES 1. K.M. Cuomo and A.V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications, Phys Rev Lett 71 Ž1993., 65᎐68. 2. C.W. Wu and L.O. Chua, A simple way to synchronize chaotic systems with applications to secure systems, Int J Bifurc Chaos 3 Ž1993., 1619᎐1627. 3. H. Dedieu, M.P. Kennedy, and M. Hasler, Chaos shift keying: Modulation and demodulation of a chaotic carrier using selfsynchronizing Chua’s circuits, IEEE Trans Circuits Syst II 40 Ž1993., 634᎐642. 4. T.X. Wu and D.L. Jaggard, On chaotic electromagnetic wave propagation, Microwave Opt Technol Lett 21 Ž1999., 448᎐451. 5. J. Peinke, J. Parisi, O.E. Rossler, and R. Stoop, Encounter with ¨ chaos, Springer-Verlag, Berlin, Germany, 1992. 6. M. Vidyasagar, Nonlinear systems analysis, Prentice-Hall, Englewood Cliffs, NJ, 1993. 䊚 2000 John Wiley & Sons, Inc. PLANAR SIR MICROWAVE BANDPASS FILTER USING HIGH-PERMITTIVITY CERAMICS Cheng-Liang Huang,1 Pau-Yeou Yen,1 and Min-Hung Weng1 Department of Electrical Engineering National Cheng Kung University Tainan, Taiwan 70101, R.O.C. 1 Recei¨ ed 3 March 2000; re¨ ised 26 April 2000 Figure 4 Experiment at RF band; carrier at 462.5625 MHz, sine wave of 4 kHz Žinformation.@voltage amplitude of 0.1 V. Ža. Spectrum of transmitted RF signal. Žb. Scope view of hŽy. versus hŽx.. Žc. Original information Žtop. and recovered information Žbottom. gation. The lagged synchronization is also illustrated in Figure 4Žc.. By comparing with the original signal, the recovered signal is replicated, except that there is a time delay of about 30 s. Such a delay usually does not cause any harmful effect in a general voice communication system. 3. CONCLUSIONS In this letter, a secure communication system employing chaotic synchronization has been systematically investigated. Theoretical analysis has been developed based on the Rossler ¨ 410 ABSTRACT: High-permitti¨ ity dielectric ceramic materials ha¨ e been applied in the fabrication of a planar stepped-impedance resonator (SIR) microwa¨ e bandpass filter. The input r output ports of the filter are formed with transmission lines directly tapped to the resonators. The admittance matrix for the equi¨ alent circuit of the filter has been deri¨ ed and transformed to the scattering matrix to initially determine the required spec. Losses and other EM effects are taken into account to further modify the actual dimension of the designed filter. The designed structures are simulated using an IE3D simulator. Fabricated filters are measured by an HP8510B network analyzer. Sample results of the filter performances demonstrate responses in good agreement with the computer simulations. 䊚 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 26: 410᎐413, 2000. Key words: stepped-impedance resonator; bandpass filter; high-permitti¨ ity ceramics 1. INTRODUCTION As wireless communications are expanding worldwide in the market, miniaturization for personal communication equipContract grant sponsor: National Science Council of the Republic of China Contract grant number: NSC-87-2218-E-006-061 Contract grant sponsor: Foundation of Jieh-Chen Chen Scholarship, Tainan, Taiwan, R.O.C. MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 26, No. 6, September 20 2000 ment has become one of the most fundamental requirements in communication system technology. The filter is one of the most important components in communication systems. Compact size is an essential requirement in many microwave filter applications, such as cellular telephones. The high dielectric constant of ceramic material provides filters will small resonator sizes, as well as high quality factor Ž Qs. Ceramic material with a high Q-value Ž)10,000. and high dielectric constant provides a means to create small coaxial structures that could be coupled to form combline bandpass filters w1x. However, further miniaturization becomes marginal, and integration is not provided for this filter. Planar filters, such as parallel-coupled filters w2, 3x, interdigital filters w4, 5x, combline filters w6, 7x, hairpin filters w8x, ring filters, and disk filters w9x, provide good integration ability. Filters using uniform impedance resonators ŽUIRs. have been popularly used in microwave communication systems. However, they suffer from poor harmonic suppression since the center frequency of the second passband with r2 or r4 resonators is two or three times the fundamental frequency. Although capacitor-loaded UIRs can avoid this problem, their Q-factors are degraded due to the electric field concentration in the capacitor-loaded section. The steppedimpedance resonator ŽSIR. was developed as a solution to that problem. It exhibited the ability to shift the second passband frequency and a higher Q-value than that of the conventional capacitor-loaded UIR w10, 11x. A very small dielectric bandpass filter was fabricated with the introduction of the ceramic lamination technique w12x. Furthermore, a miniaturized two-stage bandpass filter in a combline configuration was also reported using the same technique w13x. Since all of the strip-line resonators and tapped lines were arranged in the same layer, it could save an additional layer, and simplify the manufacturing process owing to its simple structure. However, further miniaturization of the dimensions of the filter was constrained to its low-permittivity substrate material such as alumina. Although a multilayer structure could effectively reduce the size, it needed a flexible process w14x. By replacing the substrate material with high-permittivity dielectric ceramics, a smaller size can be obtained. In this paper, high permittivity ceramics ŽCa, Ba. O᎐Li 2 O᎐ Sm 2 O 3 ᎐TiO 2 ŽCBLST. with r s 97 were applied in the fabrication of a planar SIR bandpass filter. Analysis and simulation of the filter were also reported. The frequency response of the fabricated planar SIR filter was measured by an HP85105B network analyzer. Figure 1 filter Configuration of the planar SIR microwave bandpass Figure 2 Parallel-coupled strip lines network. The matrix elements are given by Y11 s Y22 s Y33 s Y44 s yj Y12 s Y21 s Y34 s Y43 s yj Y14 s Y41 s Y23 s Y32 s j Y13 s Y31 s Y24 s Y42 s j 1 2 1 2 1 2 1 2 Ž Ye q Yo . cot Ž Ye y Yo . cot Ž Ye q Yo . csc Ž Ye y Yo . csc Ž1. where Ye and Yo represent the admittances of the even mode and the odd mode, respectively. is the electrical length of the strip lines. If one side of the parallel-coupled strip lines Žports 3 and 4. is grounded, the admittance matrix can be simplified to the two-port matrix expressed as follows: yj Ys yj 1 2 1 2 Ž Ye q Yo . cot yj Ž Ye y Yo . cot yj 1 2 1 2 Ž Ye y Yo . cot . Ž2. Ž Ye q Yo . cot When coupled strip lines are cascaded as shown in Figure 3, the coupled SIR configuration is formed. The admittance 2. ANALYSIS AND IMPLEMENTATION OF PLANAR SIR BANDPASS FILTER Figure 1 shows the configuration of the planar SIR microwave bandpass filter. The filter was made of two r4coupled SIRs sandwiched by two high-permittivity CBLST ceramic layers. The CBLST ceramics exhibit the dielectric properties: r s 97, Q = f s 7300 at 7 GHz, and f ; q1.5 ppmr ⬚C. Two tapped lines were arranged in the same layer, and were connected to each resonator to form the inputroutput ports. Ground planes were accomplished by metallizing the top and bottom walls. With one end grounded and the other end opened, it formed a resonator structure. The transmission performance can be realized by obtaining the even- and odd-mode impedances of the parallel-coupled strip lines, as shown in Figure 2. The open-circuit admittance matrix, then, can be derived for the four-port Figure 3 lines Coupled SIR configuration with cascaded coupled strip MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 26, No. 6, September 20 2000 411 matrix of the proposed geometry can be expressed as follows: Ye2 q Ye1 tan 1 cot 2 w Y1, 2 x 2=2 s j 1 cot 2 y K e tan 1 2 Ye2 q Ye1 tan 1 cot 2 cot 2 y K e tan 1 sj q y 1 Ye2 q Ye1 tan 1 cot 2 1 1 2 cot 2 y K e tan 1 Yo 2 q Yo1 tan 1 cot 2 Ye2 q Ye1 tan 1 cot 2 cot 2 y K o tan 1 cot 2 y K e tan 1 Yo 2 q Yo1 tan 1 cot 2 Ye2 q Ye1 tan 1 cot 2 cot 2 y K o tan 1 cot 2 y K e tan 1 1 Yo 2 q Yo1 tan 1 cot 2 1 1 qj 1 y1 2 cot 2 y K o tan 1 and y q Yo 2 q Yo1 tan 1 cot 2 cot 2 y K o tan 1 Yo 2 q Yo1 tan 1 cot 2 cot 2 y K o tan 1 y1 1 Ž3. and yj w Y3 x 2=2 s yj 1 Ye3 q Yo 3 yj tan 3 2 1 Ye3 y Yo 3 yj tan 3 2 1 Ye3 y Yo 3 Y11 q Y12 s yj tan 3 2 tan 3 Ytotal s Y1, 2 q Y3 1 Ye2 q Ye1 tan 1 cot 2 1 1 2 cot 2 y K e tan 1 qj 1 Yo2 q Yo1 tan 1 cot 2 2 yj y yj cot 2 y K o tan 1 1 Ye3 q Yo 3 2 tan 3 1 Ye3 y Yo 3 2 tan 3 yj yj 1 1 1 y1 y1 1 1 Ye3 y Yo 3 2 tan 3 1 Ye3 q Yo 3 2 Ye2 tan 3 qj 1 2 ⭈ Ye2 q Ye1 tan 1 cot 2 cot 2 y K e tan 1 Ž7. where Yei and Yoi represent the admittances of the even and odd modes of the ith coupled strip lines, respectively. i is the electrical length of the ith coupled striplines. K e s Ye1rYe2 and K o s Yo1rYo 2 . The admittance for the entire circuit then can be obtained as sj 2 ⭈ Ž4. 1 Ye3 q Yo 3 2 1 . Ž5. tan 3 where yY12 is the coupling between ports 1 and 2. The admittance matrix of ports 1 or 2 to ground is denoted as Y11 q Y12 . They can be further converted to a scattering matrix to determine the parameters of the filter. The effects of losses and discontinuities on the SIR structure were also taken into account in practical filter design. An SIR microwave ceramic bandpass filter centered at 890 MHz with a 3 dB bandwidth of 45 MHz was designed based on the previously discussed method. Substrates were made of CBLST dielectric material, which has a very high permittivity of 97. The resultant dimensions of the filter were 0.8 mm = 0.6 mm = 0.1 mm. Figure 5 shows the computer simulation result by using IE3D. The insertion loss and return loss of the filter were y1.95 and y15 dB, respectively. Measurement of the filter response was accomplished by using an HP8510B network analyzer, and the result is illustrated in Figure 6. It was observed that the insertion loss and return loss at a center frequency of 1.015 GHz were y2.8132 and y7 dB, respectively. A 3 dB bandwidth of 90 MHz was measured in the experiment. 3. CONCLUSION An equivalent -network for the SIR bandpass filter is illustrated in Figure 4, which is useful in realizing the transmission characteristics, and can be expressed as yY12 s j 1 2 ⭈ Ye2 y Yo 2 tan 3 qj 1 2 yj Figure 4 412 ⭈ 1 2 By using coupled strip-line theory and an admittance matrix, a planar SIR microwave ceramic bandpass filter was designed Yo 2 q Yo1 tan 1 cot 2 cot 2 y K o tan 1 ⭈ Ye2 q Ye1 tan 1 cot 2 cot 2 y K e tan 1 Equivalent -network of the SIR bandpass filter Ž6. Figure 5 Response of the SIR filter by IE3D simulation MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 26, No. 6, September 20 2000 12. T. Ishizaki, M. Fujita, H. Kagata, T. Uwano, and H. Miyake, A very small dielectric planar filter for portable telephones, IEEE Trans Microwave Theory Tech 42 Ž1994., 2017᎐2022. 13. T. Ishizaki and T. Uwano, A stepped impedance comb-line filter fabricated by using ceramic lamination technique, IEEE MTT-S Dig 1994, WE1C-4, pp. 617᎐620. 14. C.-L. Huang and H.-S. Hsueh, Multilayer ceramic bandpass filter at microwave frequency, Microwave Opt Technol Lett 24 Ž2000., 258᎐260. 䊚 2000 John Wiley & Sons, Inc. Figure 6 Measured frequency response of the SIR filter and fabricated. The size of the filter can be further reduced owing to the introduction of high-permittivity dielectrics CBLST. The frequency response of the designed bandpass filter was found to agree well with the simulation result. The measured insertion loss of y2.8132 dB was higher than the result Žy1.95 dB. from simulation since that CBLST exhibits a Q = f value of 7300 at 7 GHz. It also expends the 3 dB bandwidth. A 14% frequency shift was observed due to the existence of a gap between the substrates. The pattern mismatch and the 90⬚ bend between resonators and inputroutput ports may also cause an error. With a cofiring process, improvement of the filter response would be expected, although the measured result still agrees well with the simulation. The planar SIR filter using high-permittivity ceramics can find many applications in today’s wireless communication systems. REFERENCES 1. C.-C. You, C.-L. Huang, and C.-C. Wei, Single-block ceramic microwave bandpass filters, Microwave J 37 Ž1994., 24᎐35. 2. S.B. Cohn, Parallel-coupled transmission line resonator filters, IRE Trans Microwave Theory Tech Ž1958., 223᎐231. 3. M. Makimoto and S. Yamashita, Bandpass filters using parallel coupled stripline stepped impedance resonators, IEEE Trans Microwave Theory Tech MTT-28 Ž1980., 1413᎐1417. 4. G.L. Matthaei, Interdigital band-pass filter, IEEE Trans Microwave Theory Tech MTT-10 Ž1962., 479᎐491. 5. S. Caspi and J. Adelman, Design of combline and interdigital filter with tapped-line input, IEEE Trans Microwave Theory Tech 36 Ž1988., 759᎐763. 6. G.L. Matthaei, Comb-line band-pass filter of narrow or moderate bandwidth, IEEE Trans Microwave Theory Tech MTT-11 Ž1963., 82᎐91. 7. J.A.G. Malherbe, Microwave transmission line, Artech House, Norwood, MA, 1979. 8. U.H. Gysel, New theory and design for hairpin-line filters, IEEE Trans Microwave Theory Tech MTT-22 Ž1974., 523᎐531. 9. J.S. Hong and M.J. Lancaster, Theory and experiment of novel microstrip slow-wave open-loop resonator filters, IEEE Trans Microwave Theory Tech 45 Ž1997.. 10. M. Makimoto and S. Yamashita, Compact bandpass filters using stepped impedance resonators, Proc IEEE 67 Ž1979., 16᎐19. 11. M. Makimoto and S. Yamashita, Bandpass filters using parallel coupled stripline stepped impedance resonators, IEEE Trans Microwave Theory Tech MTT-28 Ž1980., 1413᎐1417. COMPARISON OF MOMENT-METHOD SOLUTIONS FOR WIRE ANTENNAS ATTACHED TO ARBITRARILY SHAPED BODIES 1 J. M. Taboada,1 J. L. Rodrıguez, and F. Obelleiro1 ´ 1 Departamento de Tecnoloxıas ´ das Communicacions ´ E.T.S.E. Telecomunicacion ´ Universidade de Vigo 36200 Vigo, Spain Recei¨ ed 22 March 2000 ABSTRACT: A comparison of different testing procedures for subdomain moment-method formulations for arbitrarily shaped bodies, including attached wires, is presented here. It is shown that an accurate e¨ aluation of the impedance matrix elements leads to important benefits o¨ er the con¨ entional procedures. Otherwise, the use of an adapti¨ ely generated meshᎏmore refined nearby the sourcesᎏis shown to reduce the total number of unknowns, and therefore, the computational cost for a fixed problem. 䊚 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 26: 413᎐419, 2000. Key words: method of moments; attachments; Galerkin procedure; adapti¨ e meshing 1. INTRODUCTION The analysis of wire antennas mounted on complex conducting structures is addressed here. This problem requires a good description of the electromagnetic behavior of the whole body, including the coupling and junction effects between the antennas and the supporting structure. For these kinds of problems, the method of moments ŽMoM. w1x is the most suitable tool due to its accuracy and versatility. By means of this technique, an approximate induced current distribution is obtained in the form of a series of known expansion Ž basis. functions, usually defined over small portions of the body surface Žsubdomain basis.. However, the high computational cost of the MoM makes its application to electrically large objects prohibitive due to the large number of expansion terms required in order to accurately model the current distribution. Several subdomain MoM techniques have been developed and applied to complex structures with connected wires. In w2x and w3x, a point-matching w1x MoM approach considering special functions for wire-to-surface junctions was presented. In that work, the attachment points had to be located at the Contract grant sponsor: E. N. Bazan ´ Contract grant sponsor: CICYTrFEDER Contract grant number: Project Ref. 1FD97-0922 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 26, No. 6, September 20 2000 413

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