диафрагмированные волноводные фильтры / 1e07c81e-12e7-4422-aa68-6a7da896f19c

Figure 3 Effective area and mode-field diameter versus wavelength for the large-effective-area dispersion-flattened fiber

The effective area Aeff and the mode-field diameter MFD are calculated from ‚8„9ƒ

ies from 75 to 100 ‹m2, while MFD varies from 9.56 to

10.92 ‹m. At • ‡ 1.55 ‹m, Aeff ‡ 90.46 ‹m2 and MFD ‡ 10.45 ‹m. Clearly, as noted from Figure 3, the larger the

wavelength, the larger the effective area and mode-field diameter. Larger Aeff amounts to smaller nonlinearities, while larger MFD implies higher bending losses; thus, we have the

tradeoff between Aeff and MFD. The values for Aeff and MFD for the dispersion-flattened fiber presented here are

comparable with those of large-effective-area dispersionshifted fibers reported by others ‚3„4ƒ. Microbending losses of the proposed fibers were also examined using the method described in ‚10ƒ. These losses were found to be in the same range as those of conventional single-mode fibers. This observation on microbending loss, the results for mode-field diameter, and the fact that index differences between neighboring layers are less than 1% suggest that the total losses of the proposed fibers should be in the same range as those of existing low-loss single-mode fibers.

CONCLUSION

A large-effective-area dispersion-flattened fiber consisting of a depressed index central core and three cladding layers has been proposed. Transmission properties of the fiber have

been theoretically analyzed. The proposed design provides less than 0.7 psŠnm Ž km dispersion and an effective area of 75„100 ‹m2 in the wavelength range 1.48 ‹m Œ • Œ 1.58 ‹m, and predicts low bending, microbending, scattering, and absorption losses.

ACKNOWLEDGMENT

H. T. Hattori gratefully acknowledges the financial support of the Brazilian Research Council ŽCNPq..

REFERENCES

1.P. Nouchi, P. Sansonetti, S. Landais, G. Barre, C. Brehm, J. Y. Boniort, B. Perrin, J. J. Girard, and J. Auge, ‘‘Low-Loss SingleMode Fiber with High Nonlinear Effective Area,’’ OFC’95 Tech. Dig., 1995, p. 260„261.

2.Y. Liu, A. J. Antos, and M. A. Newhouse, ‘‘Large Effective Area Dispersion-Shifted Fibers with Dual-Ring Index Profiles,’’ OFC’96 Tech. Dig., 1996, pp. 165„166.

3.T. Kato, S. Ishikawa, E. Sasaoka, and M. Nishimura, ‘‘Low Nonlinearity Dispersion-Shifted Fibers Employing Dual-Shaped Core Profile with Depressed Cladding,’’ OFC’97 Tech. Dig., 1997, p. 66.

4.S. Arai, Y. Akasaka, Y. Suzuki, and T. Kamiya, ‘‘Low Nonlinear Dispersion-Shifted Fiber,’’ OFC’97 Tech. Dig., 1997, p. 65.

5.D. Marcuse, ‘‘Single-Channel Operation in Very Long Nonlinear Fibers with Optical Amplifiers at Zero Dispersion,’’ J. Lightwa‘e Technol., Vol. 9, 1991, pp. 356„361.

6.M. J. Adams, An Introduction to Optical Wa‘eguides, John Wiley & Sons, Chichester, 1981.

7.A. W. Snyder and J. D. Love, Optical Wa‘eguide Theory, Chapman and Hall, New York, 1983.

8.G. P. Agrawal, Nonlinear Fiber Optics, Academic Press, Boston, 1989.

9.K. Petermann, ‘‘Constraints for Fundamental-Mode Spot Size for Broadband Dispersion-Compensated Single-Mode Fibers,’’ Elec- tron. Lett., Vol. 19, 1983, pp. 712„714.

10.D. Marcuse, ‘‘Microdeformation Losses of Single-Mode Fibers,’’ Appl. Opt., Vol. 23, 1984, pp. 1082„1091.

’1997 John Wiley & Sons, Inc.

CCC 0895-2477Š97

FULL-WAVE ANALYSIS OF ASYMMETRIC CPW – MICROSTRIP OVERLAP TRANSITIONS FOR MMIC INTERCONNECTS AND PACKAGING

L. Kadri,1 P. Pannier,1 E. Paleczny,1 P. Kennis,1 and F. Huret1

1 Institut d’Electronique et de Microelectronique´ du Nord U.M.R. CNRS 9929

Domaine Scientifique et Universitaire de Villeneuve d’ Ascq B.P. 69, 59652 Villeneuve d’Ascq Cedex, France

Recei‘ed 17 July 1997

ABSTRACT: In this letter, an asymmetric o‘erlay transition between a CPW and a microstrip is studied. The mode con‘ersion phenomenon is characterized by an efficient spectral-domain analysis associated with the matrix pencil posttreatment and described by a generalized scattering matrix. ’ 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 328„332, 1997.

Key words: MMIC; interconnects; packaging; coplanar wa‘eguide; microstrip

I. INTRODUCTION

‘‘Generally, on-wafer measurements of microstrip based MMIC’s require via holes as ground contact. For the production of these circuits, a closely spaced row of vias at the chip edges may affect the stability of the thinned wafer during the backside processing, and an excess number of vias may reduce the yield’’ ‚1ƒ. To avoid these, in ‚1ƒ, the necessary ground plane interconnects are achieved using quarter-wave structures printed at the sides of the microstrip input lines. Indeed, wavelengths at millimeter-wave frequencies, especially in conjunction with GaAs or alumina substrates, are rather small. Consequently, quarter-wave stubs become small enough to be compatible with the size of MIMICs. Another possibility consists of using a CPW„microstrip overlap transition in order to create a process to check the S-parameters of the microstrip circuits without via holes. The process is to use an electromagnetic coupling between an open-end coplanar probe and the circuit.

From another point of view, the problem of electromagnetic coupling from a coplanar to a microstrip line may find applications in the design of millimeter-wave monolithic integrated circuits. Indeed, since MICs are typically composed of a variety of different types of transmission lines, low-loss connection between the different propagation media, like CPW to microstrip, is of considerable concern in the design of components like filters, balanced mixers, multipliers, switches, etc. In ‚2ƒ, a transition has been developed for coupling a microstrip line on one surface to a coplanar waveguide on another. The main idea was to transfer energy via electromagnetic coupling rather than with wire bonds in order to improve performance and reduce the cost of integrated or hybrid circuits. In ‚3ƒ, a novel concept for millime- ter-wave MMIC interconnects and packaging has been proposed. This concept is also based on electromagnetic field coupling. The transition from microstrip to coplanar line through a carrier substrate is one of the basic transitions of this novel concept for MMIC interconnect techniques. In ‚4ƒ, CPW„microstrip transitions are used in order to realize bandpass filters. The effects of changes in the structural dimensions of an overlay transition between a CPW and a microstrip line have been characterized in ‚5ƒ. Finally, to check possible tolerances with respect to the adjustment of top and bottom metallization, the influence of a lateral shift between the two planes ŽFig. 1. has been investigated in ‚6ƒ. Nevertheless, only variations of the return loss were presented in this tolerance analysis. Moreover, when a lateral shift is taken into account, the discontinuity becomes asymmetric, and the mode conversion between the coplanar even mode and the spurious slot-line odd mode of the coplanar

waveguide has to be studied. With this in mind, in this letter, an overlay transition between a microstrip and a coplanar waveguide is investigated. A generalized full-wave model is used for the evaluation of the mutual electromagnetic coupling between the two transmission lines. The boundary condition on the slots and microstrip line are applied to the structure, and the related spectral-domain integral equations are solved using Galerkin’s method of moments. Green’s functions for the stratified layer are calculated by applying a transmission line approach ‚7ƒ. Given the magnetic current distribution on the slots and the electric current distribution on the microstrip line, the matrix pencil approach is employed to extract the modal amplitudes of all of the modes ‚8ƒ. In order to exhibit mode conversion, this multiport scattering problem is described by a generalized scattering matrix.

II.FULL-WAVE ANALYSIS

A. Coupled Integral Equations and Moment Method. Since the spectral-domain method is well known ‚7, 9ƒ and the derivation of the Green’s functions is similar to ‚7ƒ, it will be described only briefly.

The structure of interest is shown in Figure 1. The electric

surface current Js on the microstrip line and the electric field Es across the apertures have both x- and y-components. The ground plane and substrate extend to infinity in the x- and y-directions. An application of the equivalence principle al-

lows the aperture to be closed and replaced with a fictitious magnetic current Ms below the ground plane and ŠMs above the ground plane ŽFig. 2.. Therefore, we can decom-

pose the original problem into two equivalent half-space problems ‚10ƒ. One of these problems, problem 1, is valid in the region z ‹ 0 where only the source ŠMs radiates in the presence of the infinite perfect electric conductor plane. The

second problem, problem 2, is valid in the region z Π0 where the fields are generated by the magnetic current Ms and the electric current Js. The total electric and magnetic

fields in the two regions can be written as follows:

The different fields Hi, Ei should be expressed in terms of Green’s functions of the two regions …10†. These dyadic Green’s functions are obtained using a procedure for deriving the TEˆTM decomposition of the fields in the spectral domain and equivalent transmission line models …7†.

The coupled integral equations are obtained by enforcing the following boundary conditions.

1. The total tangential magnetic field is continuous across

2. The total tangential electric field is zero along the microstrip line surface:

In these equations, Eexc represents the electric field due to an eventual voltage gap generator on the microstrip line …11†. This excitation affects only region 2. Jexc vanishes everywhere on the plane of the slot apertures, except at the position of the eventual electric current sources exiting the coplanar waveguide …12†.

In the next step, the previous coupled integral equations, expressed in the Fourier domain, are solved using the wellknown Galerkin moment method. The microstrip line and the aperture region in the CPW are first divided into a finite number of rectangular cells. The basis and testing functions for the electric and magnetic surface currents are the rooftop functions …7†. The unknown coefficient vectors of basis functions on the microstrip and slot apertures are calculated solving the final system of linear equations. The scattering parameters of the discontinuity are computed from the resulting current distribution.

B. Extraction of Scattering Matrix. The magnetic current along the coplanar waveguide section can be described by the superposition of the even and odd modes. When a lateral shift ŽFig. 3. is taken into account, the discontinuity becomes asymmetric, and a mode conversion between the CPW coplanar Ževen mode. and slot-line Žodd mode. modes has to be studied.

With this in mind, given the magnetic current distribution on the slots and the electric current distribution on the microstrip line, the matrix pencil approach is employed to extract the modal amplitudes of all of these modes. Numerical matched loads are used in order to ‘‘numerically measure’’ the scattering parameters in the way that they are defined: that means with nonreflective generators and matched loads on each port …13ˆ15†. In order to exhibit mode conversion, this multiport scattering problem is described by a general-

Figure 3 Three-port model of the studied transition. W ‚ 0.2 mm, Wm ‚ 0.2 mm, S ‚ 0.1 mm, g ‚ 0.5 mm, d ‚ 1 mm

ized scattering matrix:

The different wave amplitudes are described in Figure 3. The subscripts o and e stand, respectively, for the odd slot-line and even coplanar modes. The subscript m stands for the microstrip mode. For example, •oe is the reflection coefficient of the odd mode due to an incident even mode of unit amplitude in the CPW.

When scattering parameters between two modes with different field maps are calculated Žfor example, •eo and •oe; Tem and Tme., these values are highly sensitive to the definition used to obtain the characteristic impedance. For a passive device, this difficulty has been overcome by using the reciprocity theorem.

III. NUMERICAL RESULTS AND DISCUSSION

In the first step, a thin slot discontinuity in the ground plane of a microstrip line, shown in Figure 4, was studied in order to validate our numerical method. Good agreement was obtained between calculation and measurement …7†, as can be seen from Figure 5. Having demonstrated the accuracy of this method, the asymmetric CPWˆmicrostrip overlap transition shown in Figures 1 and 3 has been studied.

One of the primary objectives of this study is to use an electromagnetic coupling between an open-end coplanar probe and a microstrip in order to check the S-parameters of microstrip circuits without via holes. Consequently, consider-

Figure 4 Thin slot discontinuity in the ground plane of a microstrip line. h € 31 mil, Wm € 55 mil, L € 1 in, Ws € 0.05 in, •r € 4.7

Figure 5 Magnitude of the measured and computed S-parameters for the discontinuity shown in Figure 3

ing that the incident mode is the fundamental coplanar Ževen. mode, incoming power may be transferred naturally from the fundamental microstrip mode. Nevertheless, power also can be reflected back by the spurious slot-line Žodd. mode. These power transfers are described by the scattering parameters „ee, „oe, and Tem.

Figure 6 shows the variation of the S-parameters „ee and Tem versus the lateral displacement m of the CPW…micro-

Figure 6 Variation of the S-parameter magnitudes versus the lateral displacement of the CPW…microstrip transition shown in Figures 1 and 4

Figure 7 Variation of the S-parameter magnitude versus the lateral displacement of the CPW…microstrip shown in Figures 1 and 4

strip transition at 20 GHz. As expected, the coupling between the even coplanar and the microstrip modes is most important for m € 0. This topology is naturally the better configuration. When the lateral shift becomes important, the outgoing power in the microstrip line can be neglected. All of the power is reflected by the coplanar mode. The studied structure naturally becomes a simple CPW open end as shown by the return loss evolution in Figure 6.

Concerning the mode conversion, Figure 7 shows the variation of the S-parameter „oe versus the lateral displacement at 20 GHz. First of all, we must notice that this parameter presents a very low value, whatever the lateral displacement may be. This result can be explained easily. Indeed, in the CPW circuit, the two ground planes are connected from the plane P Žshown in Fig. 3. and have the same potential. A ‘‘small’’ coupled slot-line Žodd. mode persists because the two ground planes are connected behind the asymmetric transition.

On the other hand, the value of the S-parameter „oe is maximum when the microstrip line is placed within one of the two slots of the CPW.

Finally, we present in Table 1 the percentage of incident power that is converted into the transmitted microstrip mode, the percentage of incident power that is reflected back as a coplanar Ževen. mode, and also the percentage that is converted into a reflected slot-line Žodd. mode. Naturally, the incident mode is the fundamental coplanar Ževen. mode. The frequency is 20 GHz. When the transition is symmetric, 45% of the incident CPW power is converted to a transmitted microstrip mode. The most significant observation is that only 0.1% of the incident CPW power is converted into a reflected

TABLE 1 Power Conservation Check for the Studied Transition Shown in Figures 1 and 4 at 20 GHz

slot-line mode when m € 0.2 mm. Meanwhile, this negligible fraction corresponds to the maximum of mode conversion.

IV. CONCLUSION

In this letter, an asymmetric overlay transition between a CPW and a microstrip line was studied. The mode conversion has been characterized by a spectral-domain analysis and the matrix pencil posttreatment.

The mode conversion between the coplanar Ževen. mode and the spurious slot-line Žodd. mode was found to be insignificant, whatever the lateral displacement between the top and bottom metallization may be. Concerning the studied structure, it appears that tolerance requirements of this lateral shift can be determined neglecting the mode conversion phenomenon in the CPW.

REFERENCES

1.G. Strauss, P. Ehret, and W. Menzel, ‘‘On Wafer Measurement of Microstrip-Based MIMICs without Via Holes,’’ 1996 IEEE MTT-S Dig., pp. 1399…1402.

2.J. J. Burke and R. W. Jackson, ‘‘Surface-to-Surface Transition via

Electromagnetic Coupling of Microstrip and Coplanar Waveguide,’’ IEEE Trans. Microwa†e Theory Tech., Vol. 37, Mar. 1989,

pp.519…524.

3.G. Strauss and W. Menzel, ‘‘A Novel Concept for MM-Wave MMIC Interconnects and Packaging,’’ 1994 IEEE MTT-S Dig.,

pp.1141…1144.

4.W. Menzel, W. Schwab, and G. Strauss, ‘‘Investigation of Coupling Structures for Coplanar Bandpass Filters,’’ 1995 IEEE MTT-S Dig., pp. 1407…1410.

5.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.

6.G. Strauss and W. Menzel, ‘‘Millimeter-Wave Monolithic Integrated Circuit Interconnects Using Electromagnetic Field Coupling,’’ IEEE Trans. Comp., Packag., Manufact. Technol. B, Vol. 19, May 1996, pp. 278…282.

7.A. B. Kouki, R. Mittra, and C. H. Chan, ‘‘Analysis of a Thin Slot

Discontinuity in the Reference Plane of a Microstrip Structure,’’

IEEE Trans. Microwa†e Theory Tech., Vol. 41, Aug. 1993, pp. 1356…1361.

8.Y. Hua and T. Sarkar, ‘‘Matrix Pencil Method for Estimating Parameters of Exponentially Damped‡Undamped Sinusoids in Noise,’’ IEEE Trans. Acoust., Speech, Signal Processing, Vol. 38, May 1990, pp. 814…824.

9.T. Becks and I. Wolff, ‘‘Analysis of 3-D Metallization Structure by a Full-Wave Spectral Domain Technique,’’ IEEE Trans. Mi- crowa†e Theory Tech., Vol. 40, 1992, pp. 2219…2227.

10.M. Kahrizi, T. Sarkar, and Z. A. Maricevic, ‘‘Analysis of a Wide Radiating Slot in the Ground Plane of a Microstrip Line,’’ IEEE Trans. Microwa†e Theory Tech., Vol. 41, Jan. 1993, pp. 29…36.

11.L. P. B. Katehi and N. G. Alexopoulos, ‘‘Frequency-Dependent

Characteristics of Microstrip Discontinuities in Millimeter-Wave Integrated Circuits,’’ IEEE Trans. Microwa†e Theory Tech., Vol. MTT-33, Oct. 1985, pp. 1029…1035.

12.N. I. Dib, L. P. B. Katehi, G. E. Ponchak, and R. N. Simons, ‘‘Theoretical and Experimental Characterization of Coplanar Waveguide Discontinuities for Filter Applications,’’ IEEE Trans. Microwa†e Theory Tech., Vol. 39, May 1991, pp. 873…881.

13.C. Delabie, Y. Delplanque, P. Pribetich, and P. Kennis, ‘‘Matched Loads Simulation Using Ghost Basis Functions for Moment

Method Analysis: Application to Microwave Planar Circuits,’’ Microwa†e Opt. Technol. Lett., Vol. 7, Sept. 1994, pp. 632…637.

14.P. Pannier, L. Kadri, J. F. Carpentier, F. Huret, and P. Kennis,

‘‘Full-Wave Spectral Domain Analysis of Coplanar Discontinuities Using Numerically Matched Loads,’’ Microwa†e Opt. Tech- nol. Lett., Vol. 10, Dec. 1995, pp. 350…353.

15.P. Pannier, L. Kadri, C. Seguinot, P. Kennis, and F. Huret, ‘‘Multimode Matched Loads Simulation for Moment Method Analysis: Application to the Characterization of Asymmetric Discontinuities in Coupled Microstrip Lines and CPW,’’ to be submitted.

ˆ 1997 John Wiley & Sons, Inc.

CCC 0895-2477‡97

MILLIMETER-WAVE BANDPASS FILTER IN BILATERAL FINLINE WITH WINDOW-CUT RESONATORS

S. K. Koul1 and B. Bhat1

1Centre for Applied Research in Electronics Indian Institute of Technology

Hauz Khas, New Delhi 110 016, India

Recei†ed 11 July 1997

ABSTRACT: An E-plane bandpass filter in bilateral finline featuring minimum insertion loss in the passband is proposed. The filter consists of a cascade of inducti†e strips and window-cut half-wa†e resonators formed by cutting out the dielectric substrate in the region of the resonator sections. It is demonstrated that such filters can be designed using the closed-form expressions a†ailable for the metal insert filters. A typical Ka-band filter realized with fi†e window-cut resonator elements offers typically 1 dB insertion loss o†er a passband of about 0.5 GHz and a stopband rejection of greater than 50 dB at ‰0.75 GHz away from the center frequency. ˆ 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 332…334, 1997

Key words: E-plane circuits; millimeter wa†es; bandpass filters; windowcut resonators

1. INTRODUCTION

Bandpass filters with low passband insertion loss and high stopband attenuation are commonly required in communication and radar systems; particularly in diplexers and triplexers. For operation at millimeter-wave frequencies up to about 100 GHz, such filters are generally realized in either E-plane metal insert configurations Š1…6‹ or large gap finlines Š4…7‹ by cascading half-wave rectangular slot resonators coupled through inductive strips. In these filters, since the conductor loss reduces with an increase in the slot width of the resonators, the highest Q-factor is achieved by keeping the slot width equal to the waveguide height. In the E-plane metal insert configuration, a pure metal insert is mounted in the E-plane of a rectangular waveguide. Because of the complete absence of dielectric substrate, these filters offer the advantage of low-loss performance similar to that of conventional waveguides. However, the dimensional tolerance of these filters is as stringent as in an air-filled waveguide filter. The large-gap finline filter with gap width equal to the height of the waveguide, known as the E-plane finline filter, alleviates this problem to some extent by concentrating most of the energy within the dielectric substrate. This filter, however, includes in it the loss due to the dielectric substrate.

This letter presents an improved version of the E-plane finline filter in which the dielectric substrate in the region of