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

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

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

For lossless TEM mode: We can find Z 0 if C is known Inductance / unit length Capacitance / unit length Stripline (cont.) 4

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

Curve fitting this exact solution: Effective width Z 0 as W Stripline (cont.) Note: The factor of 1/2 in front is from the parallel combination of two PPWs. 6 Fringing term

Inverting this solution to find W for given Z 0 : Stripline (cont.) 7

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

Stripline (cont.) Conductor Loss: 9

 Inhomogeneous dielectric   No TEM mode Cannot phase match across dielectric interface  Requires advanced analysis techniques  Exact fields are hybrid modes ( E z and H z ) For d / 0 << 1  dominate mode is quasi-TEM Microstrip 10

Microstrip (cont.) 11

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

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

Microstrip (cont.) 14 Characteristic Impedance:

Inverting this solution to find W gives Z 0 : where Microstrip (cont.) 15

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

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

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

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

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

21 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. d W rr t s Practical note: A standard thickness for PCBs is 0.7 [mils] (17.5 [  m]), called “half-ounce copper”. 1 mil = inch

22 TXLINE This is a public-domain software for calculating the properties of some common planar transmission lines.

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, I. Bahl and P. Bhartia, Microwave Solid State Circuit Design, Wiley, R. A. Pucel, D. J. Masse, and C. P. Hartwig, “Losses in Microstrip,” IEEE Trans. Microwave Theory and Techniques, pp , June R. A. Pucel, D. J. Masse, and C. P. Hartwig, “Corrections to ‘Losses in Microstrip’,” IEEE Trans. Microwave Theory and Techniques, Dec. 1968, p