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Surface-Wave Losses of Coplanar Transmission Lines

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Surface-Wave Losses of Coplanar Transmission Lines C-5 SURFACE-WAVE LOSSES OF COPLANAR TRANSMISSION LINES Dayalan P. Kasilingam and David B. Rutledge Department of Electrical Engineering California Institute of Technology Pasadena, California 91125 Abstract. Coplanar transmission lines lose energy to the wave is fast, and radiation will occur in the surface waves when the propagation constant of the dielectric in the manner of a leaky wave antenna. surface-wave mode exceeds that of the transmission The radiation peak is at an angle ~. given by line. This happens when the substrate thickness is an appreciable fraction of a wavelength. The losses should become important in integrated circuits at (l) near-millimeter wavelengths because it is hard to make the substrate thickness small compared to a wavelength. In this paper we have developed a theory based on where k is the guide propagation constant along the reciprocity for predicting these losses. We also line ana ~ is the propagation constant of the utilized the quasi-static approximation method to substrate mode, This is illustrated in Fig. 2a. In derive expressions for propagation constants and line a thick substrate radiation is in a semi-cone of impedances. Experimental measurements were made for angle~ (Fig, 2b), This formula indicates that the the surface-wave losses in the two strip line, the two slot line and the three wire line, and the results obtained were consistent with the theory, Integrated circuits are now eeing fabricated at near-millimeter wavelengths. 1- Coplanar trans­ mission lines (Fig, l) are often the most convenient guides at these frequencies, but it can be hard to make the substrate thickness small compared to a wavelength. This means that the lines will radiate radiation into substrate modes, in constrast to the way these a b lines behave at microwave frequencies. Much infor­ mation is available on other engineering characteris­ tics of these lines,5,6 but not on surface-wave losses. F,i g. 2 Radiation by coplanar transmission 1 ines. Understanding these losses is important in designing (a) into surface-wave modes integrated-circuits at these wavelengths, not only to (b) into a thick substrate in a semi minimize losses, but also because this radiation cone of angle 1/J. could be useful. In this paper we study the losses line will begin to suffer losses to a particular of various transmission lines on different substrates. mode when the mode propagation constant 8 exceeds the guide propagation constant kz. Each mode has a -i.- w __.!.._ w frequency at which ~ first exceeds kz and this turn-on frequency is somewhat larger than the usual cut-off frequency, This is shown for a two strip line in Fig. 3. The TE1 and ™1 modes' cut-off thickness is indicated by the broken line. Also shown on the figure are the experimentally measured values of k . (a) (b) The radiation patterns of these surface waves can te observed by putting the transmission line on a --- quadrant of a circular disk (Fig. The edge is 4). tapered to prevent reflections, A vertically polarized receiving horn picks up the TM waves and a horizontally polarized horn picks up the TE waves. Typical surface-wave radiation patterns for a coplanar two strius transmission line and a coplanar ..(c) slot line are sh~n in Fig, (5). Surface wave radiation patterns for elementary dipoles and slots 7 have also been derived from reciprocity. Fig. 1 Coplanar Transmission Lines: (a) two-slot line (b) two-strip line (c) three wire We have recently developed a theory, based on 1 ine. reciprocity and the quasi-static approximation method which gives the surface-wave attenuation constant of It is easy to understand how this radiation coplanar transmission lines. In all cases we find occurs. At an interface, waves propagate along metals simple formulas with losses propo.rtional to the at a velocity that is intermediate between the velocity inverse of the effective guide thickness he• The of light in air and the velocity of light in the effective guide thickness is a term from the ray dielectric. As far as the dielectric is concerned, picture of waveguide propagation in integrated optics, 0149-645X/83/0000-0187 $01.00 © 1983 IEEE 113 1983 IEEE MTT-S DIGEST 0.2 0.4 4k0 1.0 X\ X kd en_ ... Q) 0.8 .: ): c: 0 0 0.. (/) ~TEX -c: kz kz , 0 Q) 0.6 u N c: 2k0 0 .Q E 0 ... -Cl 0 0 0. z ....0 0.. ko \X 0.2 0.4 Angle, degrees Substrate Thickness, h/~ 0 Fig. 5 Measured radiation pattern for a two Fig. 3 Dispersion curves for surface-waves as a function of thickness with Er = 12. strip line (strip width 2mm, strip kd and kz are tl:le propagation constants spaci:1g 1 mm, 5 GHz, actual thickness in the dielectric and the line is 12. 5 mm, tr = 12) . respectively. a function of width for both two slot line and two strip line on different dielectrics. Fig. Sa and Fig. 8b show the frequency dependences of the losses for a two slot line and a two strip line, respectively. Air Fig. 6 Effective thickness: ray picture, h h + 2z . e = o Fig. 4 Disk for measuring surface-wave losses for a two strip line. ... 1.0 and is given by the actual thickness plus the apparent .< penetration depth of the ray (Fig. 6). At high 'm frequencies the effective thickness tends towards the '0 0.8 physical thic~ness of the substrate. The quasi-static ~ approximation enables us to derive analytic express­ rn ions for the characteristic impedances of the coplanar ~ 0.6 transmission lines. It also gives estimates for the c: propagation constants. The_ attenuation constant due 0 to TM and TE modes in a two slot line are as following 0.4 -0 '0 3 0 Sin ~J Sined 0::: 0.2 (2) he KK' 0 2 2 0 o.os 0.10 0.15 0.20 0,25 0.30 Sin4 Sined Cos ed W 2 149.6 Cos ~ Transmission-line width, w/~d -----ch--;-;;KK,..,,----''---...;! (:~.--) dB /m (3) 11+ 1/E:r e d Fig. 7 Theoretical losses for lines with a strip or slot spacing equal to l/3 the where ~ and e are those shown in Fig. 2a and Fig. 6. total width. The dielectric constants W is the widtR of the slot and K, K' are elliptic are indicated. The substrate thickness integrals defined by Wen,9 Fig. 7 show the losses as is assume·d to be much greater than :\d. 114 As shown in Fig, 3, the measured values of the ~ propagation constant were found to be smaller then lmm their quasi-static approximation, by 5-10 percent. This means the wave in the transmission line propa­ 2.5cm~-- gates at a velocity raster then the phase velocity 20 , E ' predicted by the quasi-static approximation. A .......... ' plausible explanation for this discrepancy is yet to Ill ' ', Theory "0 ' be found. Daviesll et. al, show that the propagation ' constant and impedance of the coplanar transmission ,; 40 ' ' line are not equal to their quasi-static values when 0 ' the substrate is of finite thickness, but the values 0 ' we measured still do not agree with the modified ::J c: ' \ values they obtained. Kitazawal2 et al have predicted .,_Q) ' .... 60 that the propagation constant decreases with increases <t ' ' in metal thickness, Even this premise does not ex­ ' plain the magnitude of our discrepancy. ' ' ' The conduction losses for the two strip line are eo ' also shown in Fig, Sb, These losses are comparatively small in the S band. They remain small even at near­ millimeter frequencies although the surface resistance 2 3 4 5 6 does increase with frequency, At 90 GHz, the conduc­ Frequency, GHz tion loss attenuation constant, ac is approximately 45 dB/m for the line we experimented with. 0 ----------------~ We have in this paper tried to quantifY the effects of surface waves in coplanar transmission E -5.0 lines, The most significant conclusion is that at 11 Ill frequencies above the "turn on frequencies the ''0 -10.0 surface wave losses dominate all other loss mechamisms, up to submillimeter frequencies, The theory derived ..:c: .!!! for surface wave losses also apply to lines at near­ -15.0 Total Surfac'l. -~ Wave Losses millimeter wavelengths and the losses are therefore -., indicative of the losses one would experience at the 8 -20.0 higher frequencies, We have also critically examined c: the quasi-static approximation method used frequently 0 in micro strip line and coplanar transmission line ; -25,0 analysis, .,c:"' ~ -30.0 Acknowledgements This research was supported ty Army Research 2,0 3,0 4,0 5,0 6,0 Office, Frequency, GHz References Fig. 8 (a) Measured losses, compared to theory for a two slot line. [J,] Clifton, B.J., Murphy, R.A., and Alley, G.D., (b) Measured losses (x) and theoretical (1979), 4th Int. Conf. on Infrared and Millimeter losses for two strip line. Broken Waves, IEEE Cat, no. 79CH 1384-7 MTT, 84.86. line indicates conduction losses. [2] Neikirk, D.P., Rutledge, D.B., Muha, M.S., Park, In all the cases the attenuation constant a was H. and Yu, C.X., (1982a), Appl. Phys. Lett., 40, calculated utilizing the equation 203-205. [3] Rutledge, D.B., Schwarz, S.E. Hwang, T-L., Angelakos, D,J,, Mei, K.K., and Yokota, S., (1980), a = Power loss/unit length 2(Power transmitted) (4) IEEE J. of Quantum Electron., QE-16, 508-516. [4] Yuan, L., Paul J., and Yen, P.-:11982), in 11 IEEE 11 The power loss per unit length was calculated using MTT-S International Symposium Digest, 374-375, [5] reciprocity.10 In effect we relate the surface wave Gupta, K.C., Garg, R.
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