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IMAPS paper rough draft-Paper due July 25, 2003
Application of Uniplanar Structures for High Frequency Material Characterization
Department of Electrical and Computer Engineering, University of Minnesota, 200 Union Street Southeast, Minneapolis, Minnesota, 55455 USA; email@example.com
Index terms — CPW resonator, wire bonds, loss tangent, dielectric constant
Resonator structures have offered a useful means for acquiring electrical properties of materials. Conventional microstrip topologies have been predominantly used, where ring resonators have been shown to be suitable for characterization up to 40 GHz [1-3]. In hybrid circuits, Coplanar Waveguide (CPW) topologies (Fig. 1) have become another option to conventional microstrip topologies in microwave integrated circuits (MICs) and monolithic microwave integrated circuits (MMICs). Coplanar Waveguide designs have less dependence on substrate thickness and less sensitivity to impedance changes, thus, presenting a more consistent method for extracting dielectric property information. The use of an open-circuited CPW “T” resonator introduced by  Peterson and Drayton illustrated the application of CPW resonator topologies up to the 30 GHz regime, about 10 GHz beyond conventional microstrip topologies.
This paper will describe design techniques using a shorted CPW “T” resonators, as well as, various CPW “ring” resonators to mitigate problems that arise due to the ground plane effects in open circuit designs. To attain the high frequency operation air-bridges or cross-overs are used to suppress odd mode excitation. In order to achieve material characterization up to 50 GHz, a short-circuited “balanced T” resonator topology is shown to exhibit more even and balanced transmission in the resonator than the shorted “T” resonator resulting in stronger resonant peaks.
In practice CPWs have ground planes of finite width as can be seen in Fig 1. To analyze line losses, this paper will take a look at the closed form expressions for skin effect conductor attenuation of the symmetric CPW with finite ground planes . The analysis technique is the conformal mapping method introduced by Owyang and Wu for the analysis of conductor losses in infinite ground symmetric CPWs  and later revised by Ghione for finite ground width CPWs in .
The loss tangent and the dielectric constant of DuPont’s Green Tape™ 943 LTCC material will be extracted as an expansion on this methodology. The use of the NIST MultiCal thru-reflect-line (TRL) calibration technique using integral calibration lines on the test substrates for improved measurement accuracy will also be discussed.
In finite ground CPWs (FGCPW), the ground to signal to ground configuration gives the advantages of balanced wave propagation, while the finite ground plane allows control of the cut-off frequencies for higher order modes, increasing the upper operating frequency. The main design criterion in a finite ground CPW designs are impedance (Zo) and aspect ratios c/b. In order to avoid mismatch with test equipment, a 50 ohms CPW line is needed for the design. This can be accomplished with Ansoft’s LineCalc software. Also, it has been shown in  that maintaining a c/b ratio greater than 3 approximates the infinite-plane ideal case for coplanar waveguides. The gap size, g, signal line width, s, and substrate height h are also main variables when dealing with FGCPWs in the Q-band.
Fig 1. Symmetric Finite Ground CPW
In order attain a balanced excitation in the stubs and to attain stronger S-parameter resonance peaks, the traditional T resonator is modified to have two symmetric stubs of equal length instead of just one (Fig 2). At every half-wavelength, a standing wave distribution exists along the shorted T-resonator stubs and presents well-defined resonant peaks. Under low loss conditions,
Where n is the resonant index (n = 1,2,3…), c is the speed of light in vacuum and Lstub is the effective physical length of the resonant stub.
Fig 2. a) standard T-resonator b) “Balanced-T” resonator
All circuits were tested up to 50 GHz on an HP 8510C network analyzer using Cascade on-wafer probe station. The calibration technique used was a Thru-Reflect-Line (TRL)  based on CPW design.
Fig 3. Simulation and measurement frequency response for a Balanced T resonator vs. a standard T resonator using Rogers’ RT6010.2LM substrate
Each CPW resonator is fabricated on Rogers’ RT 6010.2LM (Er = 10.2. loss tangent = .0023) substrate with a thickness of 25 mils and the effective length of the resonant stubs being 490 mils. The gaps between the ground planes and the signal lines are 4 mils throughout the CPW structure with the signal line being 6.5 mils wide. The experimental comparison between the Balanced T and the standard T resonator can be seen in Fig. 1. It is seen that in the Balanced T resonator that the resonant nulls are strong throughout the 50 GHz bandwidth. However, the peaks of the transmission data appear stronger in the standard T resonator than that of the Balanced T resonator. This is due to the resonant stub being twice as long in the Balanced T than the standard T resonator.
CPW structures exhibit two distinct transmission losses: dielectric losses and also ohmic or conductor losses. In order to calculate the conductor losses for a FGCPW, the skin-effect loss analysis needs to be utilized. The skin-effect loss analysis is based on the well-known expression of the per-unit-length conductor loss attenuation c:
where, Rs is the surface resistance, Zc is the line impedance, I is the total current carried by the line, J is the current density and the line integral is defined on the line periphery.
where K is the complete elliptical integral of the first kind, and
Once c is found one can subtract this result from T, (2), to give the remaining loss, d. Rearranging equation (5), one can find tan.
In order to investigate the dielectric constant,, the conformal methods for finite width ground planes on a finite thickness substrate can be discovered .
Knowing the resonant frequency and the stub length, once can find from (1), and hence eventually find from (6).
Fig 4. Dielectric constant extracted from “Balanced” T resonator
Fig 5. Dielectric constant extracted from “Balanced” T resonator
VI. FGCPW Ring-resonator
ince the ring resonator has no open ends it is almost free of radiative losses. The ring resonator design requires the determination of the guided wavelength (g) along the transmission line used. The ring will resonate when its mean circumference is a multiple integral of the guided wavelength:
Hence, theequation now becomes,
The CPW ring resonator has been analyzed for three different feed topologies:
Fig 6. Ring resonator w/ a) standard b) insert c) insert T feed geometries
The three different coupling structures are shown in Fig.2. Each CPW resonator is fabricated on LTCC 943 (Er = 7.4) substrate with a thickness of 22.8 mils and the effective radius of the resonant stub being 152.3 mils. The comparison of the S21 (insertion loss) parameters for all three of the CPW resonators is seen in Fig. 3.
Fig 7. S21 Comparison of the standard, insert, and insert-T resonator circuits
As can be seen from Fig. 3, the resonant peaks are strong for all three of the coupling geometries up to about 35 GHz. However, the insert-T seems to exhibit sharper and stronger resonant peaks than the standard and insert feeding geometries. Using the same approach as in (6), one can find the dielectric constant extracted from the ring resonators.
Fig 8. Dielectric constant extracted from the standard, insert, and insert-T ring resonator circuits
The authors would like to thank the Rogers Corporation for providing substrate materials for this investigation.
 J.W. Gipprich et.al., “Microwave Dielectric Constant of a Low Temperature Co-fired Ceramic”, 41st Electronic Components and Technology Conference (ECTC 91), pp. 20-25, 1991.
 R. Kulke et.al. “Investigation of Ring Resonators on Multilayer LTCC” RAMP:, Rapid Manufacture of Microwave and power Modules, BE-97-4883
 D. I. Amey and J. P. Curilla, “Microwave properties of ceramic materials,” 41st Electronic Components and Technology Conference (ECTC 91), pp. 267-272, 1991.
 R.L. Peterson and R. F. Drayton, “A CPW T-Resonator Technique for Electrical Characterization of Microwave Substrates,” 57th Conference of the Automatic RF Techniques Group (ARFTG) Digest, pp. 88-90, June 12, 1998
 Ghione, G.; Goano, M., “The influence of ground-plane width on the ohmic losses of coplanar waveguides with finite lateral ground planes”
Microwave Theory and Techniques, IEEE Transactions on , Volume: 45 Issue: 9 , Sep 1997
Page(s): 1640 –1642
 Owyang and Wu
 Gupta, K.C., et al, “Microstrip Lines and Slotlines, 2nd edition”. Norwood: Artech House Inc., (put page number here), 1996.
 R. E. Collin, “Foundations for Microwave Engineering.” New York: McGraw Hill, 1992, pp.886-893
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