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Prof. David R. Jackson Dept. of ECE

ECE 5317-6351 Microwave Engineering. Fall 2011. Prof. David R. Jackson Dept. of ECE. Notes 10. Waveguides Part 7: Planar Transmission Lines. Stripline. Common on circuit boards Fabricated with two circuit boards Homogenous dielectric (perfect TEM mode). TEM mode.

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Prof. David R. Jackson Dept. of ECE

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  1. ECE 5317-6351 Microwave Engineering Fall 2011 Prof. David R. Jackson Dept. of ECE Notes 10 Waveguides Part 7: Planar Transmission Lines

  2. Stripline • Common on circuit boards • Fabricated with two circuit boards • Homogenous dielectric • (perfect TEM mode) TEM mode (also TE & TM Modes) Field structure for TEM mode:

  3. Stripline (cont.) • Analysis of stripline is not simple • TEM mode fields can be obtained from static analysis • Closed stripline structure is analyzed in the Pozar book

  4. Stripline (cont.) Inductance / unit length For lossless TEM mode: Capacitance / unit length We can find Z0if C is known

  5. Stripline (cont.) From static, conformal mapping solution (S. Cohn) Exact solution: K elliptical integral

  6. Stripline (cont.) Curve fitting this exact solution: Effective width Fringing term Z0 as W The factor of 1/2 in front is from the parallel combination of two PPWs. Note:

  7. Stripline (cont.) Inverting this solutionto find W for given Z0:

  8. Stripline (cont.) Attenuation Dielectric Loss: (TEM formula)

  9. Stripline (cont.) Conductor Loss:

  10. Microstrip • Inhomogeneous dielectric  No TEM mode Cannot phase match across dielectric interface • Requires advanced analysis techniques • Exact fields are hybrid modes (Ezand Hz) For d /0<< 1  dominate mode is quasi-TEM

  11. Microstrip (cont.)

  12. Microstrip (cont.) For the equivalent TEM problem: Actual problem W d W d Equivalent TEM problem

  13. Microstrip (cont.) Effective permittivity: Limiting cases: (narrow strip) (wide strip)

  14. Microstrip (cont.) Characteristic Impedance:

  15. Microstrip (cont.) Inverting this solution to find W gives Z0: where

  16. Microstrip (cont.) Attenuation Dielectric loss: “filling” factor Conductor loss: very crude (“parallel-plate”) approximation (More accurate formulas are given later.)

  17. W t er d Microstrip (cont.) More accurate formulas for characteristic impedance that account for dispersion and conductor thickness:

  18. W t er d Microstrip (cont.) where Note:

  19. Microstrip (cont.) r "A frequency-dependent solution for microstrip transmission lines," E. J. Denlinger, IEEE Trans. Microwave Theory and Techniques, Vol. 19, pp. 30-39, Jan. 1971. Frequency variation r W

  20. W t er d Microstrip (cont.) More accurate formulas for conductor attenuation:

  21. W t er d Microstrip (cont.) Note: It is necessary to assume a nonzero conductor thickness in order to accurately calculate the conductor attenuation. The perturbational method predicts an infinite attenuation if a zero thickness is assumed. Practical note: A standard thickness for PCBs is 0.7 [mils] (17.5 [m]), called “half-ounce copper”. 1 mil = 0.001 inch s

  22. TXLINE This is a public-domain software for calculating the properties of some common planar transmission lines. http://web.awrcorp.com/Usa/Products/Optional-Products/TX-Line/

  23. TXLINE (cont.) TX-Line™ Transmission Line Calculator TX-Line is a FREE, easy-to-use, Windows-based interactive transmission line calculator for the analysis and synthesis of transmission line structures. TX-Line enables users enter either physical characteristics or electrical characteristic for common transmission medium such as: Microstrip Stripline Coplanar waveguide Grounded coplanar WG Slotline TX-Line runs on Microsoft® Windows® 2000-SP4, XP-SP2, Vista-SP1, Windows® 7

  24. Microstrip (cont.) REFERENCES L. G. Maloratsky, Passive RF and Microwave Integrated Circuits, Elsevier, 2004. • I. Bahl and P. Bhartia, Microwave Solid State Circuit Design, Wiley, 2003. R. A. Pucel, D. J. Masse, and C. P. Hartwig, “Losses in Microstrip,” IEEE Trans. Microwave Theory and Techniques, pp. 342-350, June 1968. R. A. Pucel, D. J. Masse, and C. P. Hartwig, “Corrections to ‘Losses in Microstrip’,” IEEE Trans. Microwave Theory and Techniques, Dec. 1968, p. 1064.

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