Notes 10 ECE 5317-6351 Microwave Engineering Waveguides Part 7: Fall 2015 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 (also TE & TM Modes) Field structure for TEM mode: Electric Field Magnetic Field

Stripline (cont.) Analysis of stripline is not simple. TEM mode fields can be obtained from an electrostatic analysis (e.g., conformal mapping). A closed stripline structure is analyzed in the Pozar book by using a numerical method. w b / 2 a

Stripline (cont.) For lossless TEM mode: We can find Z0 if C is known Inductance / unit length For lossless TEM mode: Capacitance / unit length We can find Z0 if C is known

From static, conformal mapping solution (S. Cohn) Stripline (cont.) From static, conformal mapping solution (S. Cohn) Exact solution: K = complete elliptical integral of the first kind

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

Stripline (cont.) Inverting this solution to find w for given Z0:

Stripline (cont.) Attenuation Dielectric Loss: (TEM formula) t b w Rs

Stripline (cont.) Conductor Loss: Note: We cannot let t  0 when we calculate the conductor loss.

Microstrip For h /0 << 1  dominant mode is quasi-TEM w h Inhomogeneous dielectric  No TEM mode Note: Pozar uses (W, d) Cannot phase match across dielectric interface Requires advanced analysis techniques Exact fields are hybrid modes (Ez and Hz) For h /0 << 1  dominant mode is quasi-TEM

Microstrip (cont.) Part of the field lines are in air, and part of the field lines are inside the substrate. Figure from Pozar book The flux lines get more concentrated in the substrate region as the frequency increases.

Microstrip (cont.) Equivalent TEM problem: Actual problem w h h The effective permittivity gives the correct phase constant. The effective strip width gives the correct Z0. h Equivalent TEM problem

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

Microstrip (cont.) Characteristic Impedance: This formula can also be used for an air line:

Microstrip (cont.) Inverting this solution to find w gives Z0: where This formula can also be used for an air line:

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

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

Microstrip (cont.) where Note: h w er t

Effective dielectric constant Microstrip (cont.) Quasi-TEM region Frequency variation (dispersion) Effective dielectric constant 7.0 8.0 9.0 10.0 11.0 12.0 Parameters: r = 11.7, w/h = 0.96, h = 0.317 cm Frequency (GHz) “A frequency-dependent solution for microstrip transmission lines," E. J. Denlinger, IEEE Trans. Microwave Theory and Techniques, Vol. 19, pp. 30-39, Jan. 1971. Note: The flux lines get more concentrated in the substrate region as the frequency increases.

Microstrip (cont.) More accurate formulas for conductor attenuation: t This is the number e = 2.71828 multiplying the term in parenthesis. h w er t

Microstrip (cont.) Note: s t er h 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. h w er t s Practical note: A standard metal thickness for PCBs is 0.7 [mils] (17.5 [m]), called “half-ounce copper”. 1 mil = 0.001 inch

Planar Transmission Lines h w er b er w Microstrip Stripline h w er g h w er g Coplanar Waveguide (CPW) Conductor-backed CPW h er s h er s Slotline Conductor-backed Slotline

Planar Transmission Lines (cont.) h w er s h w er s Coplanar Strips (CPS) Conductor-backed CPS Stripline is a planar version of coax. Coplanar strips (CPS) is a planar version of twin lead.

TXLINE This is a public-domain software for calculating the properties of some common planar transmission lines. http://www.awrcorp.com/products/optional-products/tx-line-transmission-line-calculator (AWR is now National Instruments)

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

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.