диафрагмированные волноводные фильтры / 29b9be85-40b0-45d2-baf4-697fb88d1f6e

P. Arcioni, M. Bressan, G. Conciauro, A.R. Olea-Garcia

Figure 3: Example of solenoidal and non-solenoidal basis functions obtained as combination of ”rectangular rooftops”: a and b: standard type; c strip-type; d and e: special type (at a gap); e, f: special type (at a tip).

transmission between gap pairs connected by a metallic path9. Strip-type basis functions along annular paths are also required to permit the correct representation of solenoidal currents when the surface is multiply connected.

All the following results are shown in the form of scattering parameters. The CPU times refer to a PC with a Pentium-III 450 MHz processor and 256 Mb RAM.

Fig. 4 shows the geometry and the frequency response of a coupled-line directional coupler on a silicon substrate ( r = 11:76, æ = 1=30 S=m). This component was designed to have a coupling of 15 dB at 40 GHz (no attempt was made to optimize its performance). In the BI-RME modeling, performed up to 50 GHz with an accuracy factor = 2:5, we considered 102 u-functions and 146 w-functions. The number of resonant modes was P = 3 and Q = 7. The results of the BI-RME analysis are in very good agreement with those of EMSightTM. This last code required 315 sec to compute 21 samples of the frequency response. This time has to be compared with 15 sec, required to obtain the complete wide-band modeling by the BI-RME method.

Other results refer to two coupled-line band-pass filters having the same metallization pattern, but different substrates. We first designed a three-resonator filter (see Fig. 5) with a 5%

9It is easily realized that the non-zero elements of the matrix K depend on the strip-type basis functions connecting the gaps. In the absence of any d.c. connection between the gaps we have K = 0 and, as expected from physical considerations, we find that the admittance matrix has no pole at ! = 0.

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P. Arcioni, M. Bressan, G. Conciauro, A.R. Olea-Garcia

Figure 4: Amplitude of the scattering parameters of a 40 GHz coupled-line directional coupler (dimensions in m) obtained through the BI-RME method (solid lines) and through the code EMSightTM (markers).

bandwidth around 30 GHz, considering the same silicon substrate of the previous example. In this case the analysis was performed up to 70 GHz, in order to include the first replica of the pass-band. In the BI-RME analysis we used an accuracy factor = 2:5, and we considered 94 u-functions and 147 w-functions. The number of resonant modes was P = 9 and Q = 13. The agreement of the BI-RME modeling with the EMSightTM results is excellent, in particular in the pass-band. Then we considered the effect of a silicon oxide layer ( r = 3:9) between the silicon and the metal pattern (see Fig. 6). The oxide layer was considered lossless in the simulations, and all the parameters affecting the accuracy of the analysis were left unchanged. As shown in the frequency responses reported in Fig. 6, the band-pass is displaced and deformed by the presence of the oxide layer. Also in this case an excellent agreement with the EMSightTM results was found. In both cases the advantage of using the BI-RME approach is dramatic, since it avoids the large number of repeated analyses required by EMSightTM to determine the large number of samples necessary to adequately represent the rapid variations of the frequency response. In fact, the CPU time was 420 sec for the EMSightTM analysis and only 12 sec for the BI-RME modeling10.

10The CPU time is practically the same for the two structures: in fact, the most time-consuming part of the algorithm is the filling time of the matrices of Table I, whereas the calculation of the resonant modes and of the modal impedances (i.e., of the quantities affected by the presence of the oxide) takes a negligible time

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P. Arcioni, M. Bressan, G. Conciauro, A.R. Olea-Garcia

Figure 5: Insertion loss of a 30 GHz coupled-line band-pass filter (dimensions in m), obtained through the BIRME method (solid lines) and through the code EMSightTM (markers).

Figure 6: Insertion loss a filter differring from the previous one for the insertion of a SiO 2 layer.

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P. Arcioni, M. Bressan, G. Conciauro, A.R. Olea-Garcia

5 CONCLUSIONS

Though the computer code used in the examples was far from being optimized, the results demonstrated that the use of the BI-RME method can give rise to a time saving of more then one order of magnitude, with respect to a typical commercial code based on the SDA. Apart from this advantage, the BI-RME method has the unique feature of yielding directily the mathematical model of a microstrip structure, starting from the field analysis. This model represents the structure like a lumped-element network, and can be used in the computer aided design of complex electronic circuits that include the microstrip structure as a part.

A APPENDIX

Using an evident matrix symbolism, Equation (16) becomes

where ^`m is defined in Table I. In matrix form we can write:

T

where the last approximation is valid provided the frequencies is not very low. Then the relationship between the d- and b-variables can also be written as:

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P. Arcioni, M. Bressan, G. Conciauro, A.R. Olea-Garcia

REFERENCES

[1] G. Conciauro, P. Arcioni, M. Bressan, L. Perregrini, “Wideband Modeling of Arbitrarily Shaped H-Plane Components by the Boundary Integral - Resonant Mode Expansion Method”, IEEE Trans. on Microwave Theory Tech., vol. MTT-44, no. 7, July 1996,pp.1057-1066.

[2]P. Arcioni, M. Bressan, G. Conciauro, L. Perregrini, “Wideband Modeling of Arbitrarily Shaped E-Plane Components by the Boundary Integral - Resonant Mode Expansion Method”, IEEE Trans. on Microwave Theory Tech., vol. MTT-44, no. 11, Nov. 1996, pp. 2083-2092.

[3]P. Arcioni, M. Bressan, G. Conciauro, L. Perregrini, “A Fast Algorithm for the Wideband Analysis of 3-D Waveguide Junctions”, Proc. of the Second Int. Conf. on Computation in Electromagnetics, Nottingham, UK, April 12–14, 1994, pp. 311-314.

[4]G. Conciauro, L. Perregrini, P. Belloni, “Wideband Analysis of E-Plane Metal Insert Filters by the 'Boundary Integral - Resonant Mode Expansion' Method”, Proc. of 24rd European Microwave Conference, Bologna, Sept. 4–7, 1995, pp. 742-745.

[5]P. Arcioni, M. Bressan, G. Conciauro L. Perregrini, “Generalized Y-Matrix of Arbitrarily H-plane Waveguide Junctions by the BI-RME Method”, Proc. of the 1997 IEEE MTT-S Int. Symposium, Denver, CO, June 8–13, 1997, pp. 211–214.

[6]P. Arcioni, M. Bressan, G. Conciauro, “Generalized Admittance Matrix of Arbitrary E- plane Waveguide Junctions by the BI-RME Method”, Proc. of the 1999 IEEE MTT-S Int. Symposium, Anaheim, CA, June 13–19, 1999, pp. 1699-1702.

[7]P. Arcioni, M. Bressan, G. Conciauro, “A new algorithm for the wide-band analysis of arbitrarily shaped planar circuits”, IEEE Trans. on Microwave Theory Tech., vol. MTT-36, no. 10, Oct. 1988, pp. 1426-1437.

[8]G. V. Eleftheriades, J. R. Mosig, “On the Network Characterization of Planar Passive Circuits Using the Method of the Moments”, IEEE Trans. on Microwave Theory Tech., vol. MTT-44, no. 3, March 1996, pp. 438-445.

[9]R.H. Jansen, “The Spectral-Domain Approach for Microwave Integrated Circuits”, IEEE Trans. on Microwave Theory Tech., vol. MTT-33, no. 10, Oct.1985, pp. 1043-1056.

[10]L. B. Felsen, N. Marcuvitz, “ Radiation and Scattering of Waves”, Prentice-Hall, Englewood Cliffs, N.J., 1973, Sec. 5.2.

[11]G. Conciauro, M. Bressan, “Singularity Expansion of Mode Voltages and Currents in a Layered, Anisotropic, Dispersive Medium Included between Two Ground Planes”, IEEE Trans. on Microwave Theory Tech., vol. MTT-47, no. 9, Sept. 1999, pp. 1617-1626.

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