convergence of the S-parameters. On the other hand, the number of modes in region b significantly affects the conver- gence, which is expected, as there are more interactions between modes in the midregion than in the outer regions. The interactions are especially strong for structures with small midregion lengths. More modes are therefore generally needed in the midregions for double- as well as multiple-step discontinuities in order for the convergence to occur. Our double- and triple-step S-parameter data were obtained with eight modes in the outer regions and ten modes in the midregion. V. CONCLUSIONS Frequency-dependent analysis for cascaded multiple-step dis- continuities of a shielded asymmetric multilayer CPW has been presented using the mode-matching method. The eigen- modes of the shielded asymmetric multilayer CPW, needed for the implementation of the modal analysis, has also been formulated based on the spectral-domain technique. The analyzed CPW step discontinuities are general in the sense that they can accommodate any form of structural asymme- tries in the strip, the slots, or in the ground planes which, to the authors’ best knowledge, have not been reported. The analysis has been validated through very good agreement between our computed results and those published previously for a symmetric CPW step. Computed S-parameters with and without the enforcement of the modal orthogonality have been found to be in very good agreement. All of the compu- tations have also satisfied the conservation of power almost exactly with and without the orthogonality assumption. Since asymmetric multilayer CPWs are capable of achieving an improved impedance range and additional design flexibility, their use in MICs and MMICs is expected to grow and, consequently, discontinuity analyses such as those reported here are needed for accurate design. REFERENCES 1. A. K. Sharma and T. Itoh, Guest Eds., IEEE Trans. Microwa  e Ž Theory Tech. Special Issue on Modeling and Design of Coplanar . Monolithic Microwa  e and Millimeter-Wa  e Integrated Circuits , Vol. 41, Sept. 1993. 2. R. N. Simons and G. E. Ponchak, ‘‘Modeling of Some Coplanar Waveguide Discontinuities,’’ IEEE Trans. Microwa  e Theory Tech., Vol. 36, Dec. 1988, pp. 17961803. 3. C. W. Kuo, T. Kitazawa, and T. Itoh, ‘‘Analysis of Shielded Coplanar Waveguide Step Discontinuity Considering the Finite Metallization Thickness Effect,’’ 1991 IEEE MTT-S Int. Symp. Dig., pp. 473475. 4. C. W. Kuo and T. Itoh, ‘‘Characterization of Shielded Coplanar Type Transmission Line Junction Discontinuities Incorporating the Finite Metallization Thickness Effect,’’ IEEE Trans. Mi- crowa  e Theory Tech., Vol. 40, Jan. 1992, pp. 7380. 5. T. W. Huang and T. Itoh, ‘‘Full-Wave Analysis of Cascaded Junction Discontinuities of Shielded Coplanar Type Transmis- sion Line Considering the Finite Metallization Thickness Effect,’’ 1992 IEEE MTT-S Int. Symp. Dig., pp. 995998. 6. K. M. Rahman and C. Nguyen, ‘‘On the Analysis of Single- and Multiple-Step Discontinuities for a Shielded Three-Layer Copla- nar Waveguide,’’ IEEE Trans. Microwa  e Theory Tech., Vol. 41, Sept. 1993, pp. 14841488. 7. V. Radisic et al., ‘‘Experimentally Verifiable Modeling of Copla- nar Waveguide Discontinuities,’’ IEEE Trans. Microwa  e Theory Tech., Vol. 41, Sept. 1993, pp. 15241533. 8. H. Jin and R. Vahldieck, ‘‘Full-Wave Analysis of Coplanar Waveguide Discontinuities Using the Frequency Domain TLM Method,’’ IEEE Trans. Microwa  e Theory Tech., Vol. 41, Sept. 1993, pp. 15381542. 9. S. J. Chung and T. R. Chrang, ‘‘Full-Wave Analysis of Disconti- nuities in Conductor-Backed Coplanar Waveguides Using the Method of Lines,’’ IEEE Trans. Microwa  e Theory Tech., Vol. 41, Sept. 1993, pp. 16011605. 10. A. M. Tran and T. Itoh, ‘‘Full-Wave Modeling of Coplanar Waveguide Discontinuities with Finite Conductor Thickness,’’ IEEE Trans. Microwa  e Theory Tech., Vol. 41, Sept. 1993, pp. 16111615. 11. F. Alessandri et al., ‘‘A 3-D Mode Matching Technique for the Efficient Analysis of Coplanar MMIC Discontinuities with Finite Metallization Thickness,’’ IEEE Trans. Microwa  e Theory Tech., Vol. 41, Sept. 1993, pp. 16251629. 12. M. R. Lyons, J. P. K. Gilb, and C. A. Balanis, ‘‘Enhanced Dominant Mode Operation of a Shielded Multilayer Coplanar Waveguide via Substrate Compensation,’’ IEEE Trans. Micro- wa e Theory Tech., Vol. 41, Sept. 1993, pp. 15641567. 13. T. Itoh and R. Mittra, ‘‘Spectral-Domain Approach for Calculat- ing the Dispersion Characteristics of Microstrip Lines,’’ IEEE Trans. Microwa  e Theory Tech., Vol. MTT-21, July 1973, pp. 496499. 14. A. Wexler, ‘‘Solution of Waveguide Discontinuities by Modal Analysis,’’ IEEE Trans. Microwa  e Theory Tech., Vol. MTT-15, 1967, pp. 508517. 15. Q. Zu, K. J. Webb, and R. Mittra, ‘‘Study of Modal Solution Procedures for Microstrip Step Discontinuities,’’ IEEE Trans. Microwa  e Theory Tech., Vol. 37, Feb. 1989, pp. 381387.  1997 John Wiley & Sons, Inc. CCC 0895-247797 ACTIVE MMIC WIDEBAND TIME DELAY M. Dousti, 1 B. Delacressonniere, 1 F. Temcamani, 1 and J. L. Gautier 1 1 ENSEA-EMO 95014 Cergy Pontoise Cedex, France Recei  ed 15 July 1997 ABSTRACT: In this letter, we show how acti  e elements can be effec- ti  ely employed in the design of an important microwa  e time delay. We present analytical and computer-simulated results for an acti  e time delay, and layout design using microwa  e monolithic integrated circuit ( ) MMIC technology.  1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 382385, 1997. ( ) Key words: phase shift; monolithic microwa  e integrated circuit MMIC ; time delay; all-pass cell 1. INTRODUCTION    The design of MMIC transverse 1, 2 and recursive 3 active filters is based on two important elements: the gains  , and i the time delays  . The purpose of this letter is the design of an active time delay, matched to 50  at both input and output, which represents an important pure time delay   1.5 ns. This circuit operates in a bandwidth of 800 MHz around the central frequency f  4 GHz. This time delay is realized by 0 cascading two all-pass cells. The losses in the MMIC induc- tors are compensated by adding active elements. MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 16, No. 6, December 20 1997 382