• Deeb Tubail
  • Talal Skaik




coupling coefficients, coupling matrix, diplexer, resonators, Ttopology


Diplexers are used to separate or combine two bands of frequencies and they are designed by combining channel filters using distribution circuit or alternatively designed based on coupled resonator circuits. Design parameters of coupled resonator circuits such as coupling coefficients, self-resonant frequencies and external couplings are done using optimization techniques. However, optimization techniques are not always efficient particularly for large set of parameters and hence more efficient approaches are required. In this paper, numerical solution instead of optimization is proposed to synthesize coupled resonator diplexers and obtain coupling coefficients directly from equations. The proposed direct approach achieves the desired characteristics for any given number of resonators and some numerical examples are given to demonstrate the validity of the proposed approach. One of the given examples is compared to a diplexer in literature synthesized using optimization technique and implemented using cavity resonators.


[1] J. Hong, M. Lancaster, Microstrip Filters for RF/Microwave Applications, Wiley Interscience Publication, New York, 2001.
[2] D. Pozar, Microwave Engineering, 4th edition, Wiley, 2012.
[3] S. Amari, "Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique," IEEE Trans.
Microw. Theory Tech, vol. 48, no. 9, pp. 1559-1564, 2000.
[4] A. Atia, A. Zaki, E. Atia, "Synthesis of general topology multiple coupled resonator filters by optimization," in Proc. of IEEE MTT-S
Int. Microwave Symposium, Baltimore, USA, 1998, pp. 821-824.
[5] B. Jayyousi, M. Lancaster, "A gradient-based optimization technique employing determinants for the synthesis of microwave coupled
filters," in Proc. of IEEE MTT-S Inter. Microwave Symposium, USA, June 2004, pp. 1369-1372.
[6] M. Lancaster, “Radio frequency filter”, W.I.P.O patent WO/01/69712, 2001.
[7] T. Skaik, M. Lancaster, F. Huang, "Synthesis of multiple output coupled resonator microwave circuits using coupling matrix
optimization," IET Journal of Microwaves, Antenna and Propagation, vol. 5, no. 9, pp. 1081-1088, June 2011.
[8] T. Skaik, T., M. AbuHussain, "Design of diplexers for E-band communication systems," in Proc. of the 13th Mediterranean Microwave
Symposium, Lebanon, Sept. 2013.
[9] T. Skaik, M. Lancaster, "Coupled resonator diplexer without external junction," Journal of Electromagnetic Analysis and Applications,
vol. 3, no. 6, pp. 238-241, June 2011.
[10] T. Skaik, M. Lancaster, M. Ke, Y. Wang, "A micro-machined WR-3 waveguide diplexer based on coupled resonator structures," in
Proc. of the 41st European Microwave Conference, UK, Oct 2011, pp. 770-773.
[11] W. Xia, X. Shang, M. Lancaster, "All-resonator-based waveguide diplexer with cross-couplings," in Electronics Letters, vol. 50, No.
25, pp. 1948-1950, 2014.
[12] F. Loras-Gonzalez, I. Hidalgo-Carpintero, S. Sobrino-Arias, A. Garca-Lamprez, M. Salazar-Palma, "A novel Ku-Band dielectric
resonator triplexer based on generalized multiplexer theory," in Proc. of IEEE MTT-S International Microwave Symposium, 2010,
Anaheim, CA, 2010, pp. 884-887.
[13] T. Skaik, "Novel star junction coupled resonator multiplexer structures," Progress in Electromagnetics Research Letters, vol. 31, pp.
113-120, April 2012.
[14] D. Tubail, T. Skaik, "Synthesis of coupled resonator based multiplexers with generalized structures using coupling matrix
optimization," IET Electronic Letters, vol. 51, no. 23, pp. 1891-1893, Nov 2015.
[15] A. Garcia-Lamperez, M. Salazar-Palma, T. Sarkar, "Compact multiplexer formed by coupled resonators with distributed coupling," in
Proc. IEEE Antennas and Propagation Society International Symposium, USA, 2005, pp. 89-92.
[16] T. Skaik, D. Tubail, "Novel multiplexer topologies based on coupled resonator structures," in Proc. of the 15th Mediterranean
Microwave Symposium, Lecce, Italy, Dec. 2015.
[17] X. Shang, Y. Wang, X. Wenlin, M. Lancaster, "Novel multiplexer topologies based on all-resonator structures," IEEE Transactions
Microwave Theory and Techniques, vol. 61, no. 11, pp. 3838-3845, 2013.
[18] Y. Wang, M. Lancaster, "An investigation on the coupling characteristics of a novel multiplexer configuration," in Proc. of European
Microwave Conference (EuMC), Nuremberg, 2013, pp. 900-903.




How to Cite

Deeb Tubail, & Talal Skaik. (2019). A DIRECT APPROACH FOR COUPLING MATRIX SYNTHESIS FOR COUPLED RESONATOR DIPLEXERS. Journal of Microwaves, Optoelectronics and Electromagnetic Applications (JMOe), 16(4), 942–953. https://doi.org/10.1590/2179-10742017v16i41077



Regular Papers