summary, the TE 01 and TE 03 modes are working modes for tem- peratures lower than 40°C. The TE 01 mode is the working mode up to 40°C. Then, the lossy load can induce a multimodal character for the waveguide, even for a frequency close to 2.45 GHz. Therefore, several centimeters after the discontinuity between the source and the waveguide, the applicator will select the mode(s) which offer(s) the lowest attenuation (according to tem- peratures TE 01 and TE 03 ). For the structure studied, we never observe the TE 02 , TE 03 , and TE 04 modes. However, these modes will participate in heating at the beginning of the application because all modes are excited due to the dielectric loss of the water pipe. So, during the microwave heating of the rod, we can consider several modes in order to forecast the electric-field distribution. Thus, knowledge of electromagnetic behavior of the loaded waveguide allows us to forecast the electric-field radial distribu- tion. Then, with a good choice of pipe diameter, it is possible to suggest a structure which will provide uniform heating over the available section of the cylindrical load. According to these results, the effect of dielectric losses upon the mode-propagation param- eters is a consequence. Obviously, it is not possible to deduce the behavior of lossy structures from the data of lossless ones. 6. CONCLUSION A powerful computer-aided-solution procedure has been designed for the study of high-power industrial applicators. Modes estab- lished for lossless structures have been extended to high-loss systems and limits of classical perturbation approaches can be completely avoided. Taking into account dielectric losses is a key goal for the design of optimized microwave industrial applicators for microwave heating of fluids within pipes. Moreover, dielectric tuning due to thermal dependency of dielectric properties must be taken into account. It has been shown that our approach provides an accurate means of trapping modes for lossy loaded cylindrical applicators. The information made available by this technique is a valuable contribution to a more precise understanding of electromagnetic distribution within the applicator. Moreover, our approach should enable the predictive control and design of optimized travelling- wave applicators. According this study, a viable alternative to the trial and error methods currently used to design microwave appli- cators for industrial heating applications has been proposed. REFERENCES 1. D.J. Hill, C.D. Rudd, and M.S. Johnson, Design and application of a cylindrical mode applicator for the in-line microwave preheating of liquid thermoset, J Microwave Power Electromagn Energy 33 (1998), 216 –230. 2. C. Stenzel, M. Brinkmann, J. Mu ¨ller, R. Schertlen, Y. Venot, and W. Wiesbeck, A novel microwave applicator for tailoring the energy input for hydrothermal synthesis of zeolites, J Microwave Power Electro- magn Energy 36 (2001), 155–168. 3. P.O. Risman, Microwave properties of water in the temperature range +3 to 140°C, Electromagn Rev 1 (1988), 3–5. 4. U. Kaatze, Complex permittivity of water as a function of frequency and temperature, J Chem Engg Data 34 (1989), 371–374. 5. P. Lampariello and R. Sorrentino, The ZEPLS program for solving characteristic equations of electromagnetic structure, IEEE Trans MTT 23 (1975), 457– 458. 6. A. Calmels, D. Stuerga, and P. Pribetich, Modeling propagation in high-power microwave devices, Microwave Opt Lett 21 (1999), 477– 482. 7. A. Calmels, D. Stuerga, and P. Pribetich, Modeling propagation high- power cylindrical microwave applicators, Microwave Opt Technol Lett 30 (2001), 192–195. 8. D. Stuerga, P. Pribetich, and C. Lohr, Microwave heating and elec- tromagnetic modeling: from concepts to applications in applicator design, Proc Euro Symp Numer Meth Electromagn, 2002, Toulouse, France. 9. J-L. Mousson, E. Michel, C. Lohr, P. Pribetich, and D. Stuerga, About trapping of modes, Proc 3 rd World Congress Microwave and Radiofreq Applic, 2002, Sydney, Australia. 10. D. Stuerga and P. Pribetich, 1A5-Modeling and design of high-power microwave applicators, Proc PIERS, 2003, Honolulu, Hawaii, pp. 49 –56. 11. R. Collin, Field theory of guided waves, 2 nd ed., IEEE Press, New York, 1991. © 2004 Wiley Periodicals, Inc. DE-EMBEDDING TECHNIQUES FOR EMBEDDED MICROSTRIPS J. M. Song, 1 F. Ling, 2 W. Blood, 3 E. Demircan, 4 K. Sriram, 4 G. Flynn, 5 K.-H. To, 3 R. Tsai, 3 Q. Li, 3 T. Myers, 3 M. Petras, 3 and A. Dengi 2 1 Department of Electrical and Computer Engineering Iowa State University 2215 Coover Hall Ames, Iowa 50011 2 Neolinear Inc. 583 Epsilon Dr. Pittsburgh, PA 15238 3 Motorola, Inc. 2100 E. Elliot Rd. Tempe, AZ 85284 4 Motorola, Inc. 3501 Ed Bluestein Blvd. Austin, TX 78721 5 Teravicta Technologies, Inc. 2535 Brockton Dr. Austin, TX 78758 Received 10 December 2003 ABSTRACT: Three parameters are needed to model symmetrical adapters, but not enough equations can be found to solve them. The proposed two-impedance model with one shunt and one series imped- ance gives consistent results when applied to three different lengths of embedded microstrip transmission lines. This model can be used with more complicated structures than the single-impedance model. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 42: 50 –54, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20204 Key words: de-embedding; microstrips; embedded devices 1. INTRODUCTION In order to characterize on-wafer circuitry for any device, it is necessary to gain test access to that circuitry. This is generally accomplished by placing test access ports (pads, vias, intercon- nects, buffers, and so on) on the silicon and the circuit to be tested. For most low frequencies, techniques have been developed which ensure that the effect of the test access ports on the measurement is negligible. However, for high-frequency (1 GHz) parametric measurements, it is generally not possible to gain access to the circuit under test without significantly impacting the measurement being made. In this case, it is standard practice to attempt to characterize the effect of the test access ports, or adapters, on the measurement, and then separate their effect from actual measure- ment in order to obtain the response of the target. This process is know as de-embedding. 50 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 42, No. 1, July 5 2004