Coupled Microstrip Lines 1
475
Slh
4.0
I
I
2
1
I
4
I
I
6
Wlh
Figure 8.5 Even- and odd-mode effective dielectric constants for coupled microstrip lines (c, = 9.6, S/h = 0.05 to 5.0, W/h = 0.2 to 5.5) (from [la], O 1972 Van Nostrand Reinhold. Reprinted with permission.).
where K(k,)and K(k:)are the elliptic function and its complement with
8.3.2 Fullwave Analysis It was pointed out in Chapter 2 that quasi-static analysis for microstrip holds for wavelengths greater than the transverse dimensions of the line. At higher
[16] Bergandt, H. G., and R. Pregla, "Calculation of Even- and Odd-Mode Capacitance Parameters for Coupled Microstrips," Archiv. Elektr. k r . , Vol. 26, 1972, pp. 153-158. [17] Kowalski, G., and R. Pregla, "Calculation of the Distributed Capacitances of Coupled Microstrips Using a Variational Integral," Archiv. Elektr. ~bertr.,Vol. 27, 1973, pp. 51-52. [18] Gunston, M. A. R.., Microwave Transmission Line Impedance Data, London: Van Nostrand Reinhold, 1972, Ch. 6. 1191 Gladwell, G. M. L., and S. Coen, "A Chebyshev Approximation Method for Microstrip Problems," IEEE Trans., Vol. MTT-23, 1975, pp. 865-870. [20] Krage, M. K., and G. I. Haddad, "Frequency Dependent Characteristicsof Microstrip Transmission Lines," ZEEE Trans., Vol. MlT-20, 1972, pp. 678-688. [21] Knorr, J. B., et al., "Hybrid Mode Analysis of Planar Lines," Roc. 8th Asilomar Conf:, 1974. 1221 Knorr, J. B., and K. D. Kuchler, "Analysis of Coupled Slots and Coplanar Strips and Dielectric Substrate," DEE Trans., Vol. MTT-23, 1975, pp. 541-548. 1231 Kowalski, G., and R. Pregla, "Dispersion Characteristicsof Single and Coupled Microstrips," Archiv. Elektr. Ubertr., Vol. 26, 1972, pp. 276-280. 1241 Davies, J. B., and D. G. Corr, "Computer Analysis of the Fundamental and Higher Order Modes in Single and Coupled Microstrip," Electron. Lett., Vol. 6, 1970, pp. 806-808; see errata, Vol. 7, 1971, p. 284. 1251 Jansen, R. H., "Fast Accurate Hybrid Mode Computation of Nonsymmetrical Coupled Microstrip Characteristics," Roc. 7th European Microwave Conf:, Copenhagen, 1977, pp. 135-139. 1261 Jansen, R. H., "High-Speed Computation of Single and Coupled Microstrip Parameters Including Dispersion, High-Order Modes, Loss and Finite Strip Thickness," IEEE Trans., Vol. M7T-26, 1978, pp. 75-82. [27] Farr, E. G., et al., "A Frequency-Dependent Coupled-Mode Analysis of Multiconductor Microstrip Lines with Application to VLSI Interconnect Problems," IEEE Trans., Vol. MTT-34, 1986, pp. 307-310. [28] Tripathi, V. R, and H. Lee, "Spectral-Domain Computation of Characteristic Impedances and Multiport Parameters of Multiple Coupled Microstrip Lines," ZEEE Trans., Vol. M7T-37, 1989, pp. 215-221. [29] Bagby,J. S., et al., "Entire-Domain Basis MOM Analysis of Coupled Microstrip Transmission Lines," IE.55 Trans., Vol. MTl-40, 1992, pp. 49-57. [30] Tzuang, C. K. C., and J. T. Kuo, "Modal Current Distributions on Closely Coupled Microstrip Lines: A Comparative Study of the SDA Basis Functions," Electron. Lett., Vol. 26, 1990, pp. 464-465. [31] Mu, T. C., et al., "Characteristics of Multiconductor, Asymmetric Slow Wave Microstrip Transmis sion Lines," IEEE Trans., Vol. MTT-34, 1986, pp. 767-772. 1321 Marx, K. D., "Propagation Modes, Equivalent Circuits and Characteristic Terminations for Multiconductor Transmission Lines with Inhomogeneous Dielectrics," E E E Trans., Vol. MTl-21, 1973, pp. 450-457. [33] Tripathi, V. K., "On the Analysis of Symmetrical Three-Line Microstrip Circuits," IEEE Trans., Vol. MlT-25, 1977, pp. 726-729. 1341 Janiczak, B. J., "Phase Constant Characteristic of Generalized Asymmetric Three-Coupled Microstrip Lines," h c . IEE, Pad H, Vol. 132, 1985, pp. 23-26. 1351 Qian, Y., and E. Yamashita, "Characterization of Picosecond Pulse Crosstalk Between Coupled Microstrip Lines with Arbitrary Conductor Width," IEEE Trans.,Vol. MTT41,1993, pp. 1011-1016. 1361 Kitazawa, T., and R. Mittra, "Analysis of Asymmetric Coupled Striplines," E E E Trans., Vol. MTT33, 1985, pp. 643-646. 1371 Getsinger, W. J., "Dispersion of ParallelGoupled Microstrip," IEEE Trans., Vol. MTl-21, 1973, pp. 144-145. 1381 Hammerstad, E., and 0.Jensen, "Accurate Models for Microstrip Computer-Aided Design," IEEE MlT-S Digest, 1980, pp. 407-409. 1391 Kirschning, M., and R. H. Jansen, "Accurate Wide-Range Design Equations for Parallel Coupled -
~
Coupled Microst@ Lines
'
1 519
Microstrip Lines," IEEE Trans., Vol. MTT-32, 1984, pp. 83-90; see also corrections, IEE Trans., Vol. MTT-33, 1985, p. 288. [40] Napoli, L. S., and J. J. Hughes, "Characteristics of Coupled Microstrip Lines," RCA Reuzew,Vol. 31, 1970, pp. 479-498. [41] Rizzoli, V., "Resonance Measurement of Even and Odd Mode Propagation Constants in Coupled Microstrips," Znt. M i m a v e Symp. Ihgest, 1975, pp. 106-108. [42] Garg, R., and I. J. Bahl, "Characteristics of Coupled Microstrip Lines," Trans., Vol. MTT-27, 1979, pp. 700-705; see also corrections, IEEE Trans., Vol. MlT-28, 1980, p. 272. [43] Bedair, S. S., "On the Odd-Mode Capacitance of the Coupled Microstriplines," lEEE Trans., Vol. MTT-28, 1980, pp. 1225-1227. [44] Akhtarzad, S., et al., "The Design of Coupled Microstrip Lines," D E E Trans., Vol. MTT-23, 1975, pp. 486-492. [45] Shamanna, K. N., et al., "Parallel-Coupled Microstrip Line is Easy to Determine with Nomograms," Electron. Design, Vol. 11, May 24, 1976, pp. 78-81. [46] Avdeyev, E. V., and V. I. Potapova, "Nomograms for Coupled Open Microstrip Lines," Telecomm. Radio Eng., Part 2, Vol. 28, 1973, pp. 89-93. [47] Shamasundara, S. D., and N. Singh, "Design of Coupled Microstrip Lines," lEEE Trans.,Vol. MTT25, 1977, pp. 232-233. [48] Shamasundara, S. D., et al., "Apply Standard Curves to Strange Substrates," Mimowaves, Vol. 16, September 1977, pp. 116-1 17. [49] Dalby, A. B., "Interdigital Microstrip Circuit Parameters Using Empirical Formulas and Simplified Model," IEEE Trans., Vol. MTT-27, 1979, pp. 744-752. [50] Tripathi, V. K., and C. L. Chang, "Quasi-TEM Parameters of Non-Symmetrical Coupled Microstrip Lines," 1nt.J Electron., Vol. 45, No. 2, 1978, pp. 215-223. [51] Kal, S., et al., "Normal-Mode Parameters of Microstrip Coupled Lines of Unequal Width," IEEE Trans., Vol. MTT-32, 1984, pp. 198-200. [52] Bedair, S. S., "Characteristics of Some Asymmetrical Coupled Transmission Lines," IEEE Trans., Vol. MTT-32, 1984, pp. 108-110. [53] Bedair, S. S., "Characteristics of Asymmetrical Coupled Shielded Microstrip Lines," A-oc. I B , Part H, Vol. 132, 1985, pp. 342-343. [54] Allen, J. L., "Non-Symmetrical Coupled Lines in an Inhomogeneous Dielectric Medium," Int. J. Electron., Vol. 38, 1975, pp. 337-347. [55] Llinner, I. J. P., "A Method for the Computation of the Characteristic Immitance Matrix of Multiconductor Striplines with Arbitrary Widths," IEEE Trans., Vol. MTT-22, 1974, pp. 930-937. [56] El-Deeb, N. A., et al., "Design Parameters of Inhomogeneous Asymmetrical Coupled Transmission Lines," lEEE Trans., Vol. MTT-31, 1983, pp. 592-596. [57] Kollipara, R. T., and V. K Tripathi, "Dispersion Characteristics of Moderately Thick Microstrip Lines by the Spectral Domain Method," IEEEMimaveGuided WaveLett.,Vol. 2,1992, pp. 100-101. [58] Jansen, R. H., "A Comprehensive CAD Approach to the Design of MMIC's up to MM-Wave Frequencies," lEEE Trans., Vol. MlT-36, 1988, pp. 208-219. [59] Bedair, S. S., and M. I. Sobhy, "Accurate Formulas for the Computer-Aided Design of Shielded Microstrip Circuits," Proc. IEE, Part H, Vol. 127, 1980, pp. 305-308. [60] Rama Rao, B., "Effect of Loss and Frequency Dispersion on the Performance of Microstrip Directional Couplers and Coupled Line Filters," IEEE Trans., Vol. MTT-22, 1974, pp. 747-750. [61] Tien, C. C., et al., "Effects of Metal Thickness and Finite Substrate Width on Leaky Waves in Coupled Microstrip Lines," lEEE MTT-SBgat, 1992, pp. 499-502. [62] Shamasundara, S. D., and K. C. Gupta, "Sensitivity Analysis of Coupled Microstrip Directional Couplers," IEEE Trans., Vol. MTT-26, 1978, pp. 788-794. [63] Buntxhuh, C., "High Directivity Microstrip Couplers Using Dielectric Overlays," IEEE GMTT Symp. Digest, 1975, pp. 125-127. [64] Wolters, K. C., et al., "Analysis and Experimental Evaluation of Distributed Overlay Structures in Microwave Integrated Circuits," lEEE GMTT Symp. Bgzst, 1968, pp. 123-130.
