LPF is set at 20 GHz. Figure 9 shows the photograph of the final filter, which has the size of 18 3 35.8 mm 2 and is fabricated by a single-layer PCB process on RT/Duroid 5880 substrate with thick- ness of 0.254 mm. The filter is measured by using an Agilent N5245A vector network analyzer and shown in Figure 10. From the measured results in the Figure 10, this filter has a central frequency of 8.55 GHz, a 3-dB fractional band width of 22.2% and return loss better than 18.8 dB in the whole pass- band. The insertion loss is 1.45 dB at the center frequency and keeps below 1.8 dB from 7.8 to 9.2 GHz, about 0.8 dB worse than that of the simulated. As shown in Figure 10, the measured upper 3-dB cut-off frequency is lower than that of the simulated one about 200 MHz, which might be caused by the variation of substrate’s permittivity and the inaccuracy in fabrication. In addition, it exhibits a strong sideband suppression better than 65 dB at 12.5 GHz. What is more, the characteristic of upper stop- band suppression is less than 30 dB until 45 GHz. The upper stopband characteristic with LPFs is much improved compared with the case without LPF. In Figure 11, whatever for measured and simulated results, both variations of the group delay of S 21 are less than 0.2 ns, which is quite smooth for a microwave fil- ter. The proposed filter can be used as a linear phase filter in wireless communication and digital microwave system. Here, some comparisons between our design and previous SIW-based filters with similar technologies are summarized in Table 2. Obviously, this work has advantages of controllable bandwidth, much wider stopband rejection, better return loss, lower insertion loss, and relatively compact size. Specially, the proposed bandpass filter has a wider stopband performance compared with the SIW cavity-based bandpass filters [11], which is integrated with LPFs. 5. CONCLUSION In this letter, the bandpass filter based on SIW and DGS technol- ogy are designed, fabricated, and measured. The measured results are in good agreement with the simulated ones. The proposed fil- ters have advantages of controllable fractional bandwidth, low insertion loss, wide stopband, and relatively small size, so that they can be widely used in microwave and millimetre-wave sys- tems to suppress the unwanted harmonics and spurs. ACKNOWLEDGMENT This work is supported by the China Fundamental Research Fund for the Central Universities under Grant ZYGX2013J006. REFERENCES 1. Y. Cassivi, L. Perregrini, P. Arcioni, M. Bressan, K. Wu, and G. Conciauro, Dispersion characteristics of substrate integrated rectan- gular waveguide, IEEE Microwave Wireless Compon Lett 12 (2002), 333–335. 2. D. Deslandes and K. Wu, Integrated microstrip and rectangular waveguide in planar form, IEEE Microwave Wireless Compon Lett 11 (2001), 68–70. 3. D. Ahn, J.S. Park, C.S. Kim, J. Kim, Y.X. 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GENERAL EXPRESSION FOR TUNABLE MATCHING NETWORK EFFICIENCY IN THE CASE OF COMPLEX IMPEDANCES Vitor Freitas, Jean-Daniel Arnould, and Philippe Ferrari Universit e de Grenoble-Alpes, CNRS, IMEP-LAHC, Campus Minatec, 3 Parvis Louis N eel, CS 50257, 38016 Grenoble, France; Corresponding author: arnould@enserg.fr Received 9 October 2014 ABSTRACT: The design of matching networks is generally based on lossless devices, hence rendering difficult to anticipate their performance when both impedances are complex. To be more predictive in terms of insertion loss and matching impedance coverage, a rigorous method is proposed for the first time to calculate the efficiency of a tunable match- ing network based on the quality factor of its components, with source and load complex impedances. The method allows optimizing the topology of the matching network, depending on the location of the source and loading impedances in the Smith chart. It is the first time to our knowl- edge that a complete analytical formulas is given to predict the matching network’s efficiency in function of available components quality factors in the case of source and load complex impedance. V C 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:1160–1166, 2014; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.29039 Key words: impedance transformer; matching network; reconfigurable circuits; quality factor; efficiency formula; impedance coverage 1. INTRODUCTION Today’s mobile communication devices are used in almost all possible environments, including near body area, cars, on differ- ent surfaces, and of course in talking position near the head. The environment of the antenna and the resulting field distribu- tion around it has unfortunately an eminent impact on its input impedance [1,2]. The resulting mismatch between antenna and RF-front end reduces its power efficiency, linearity, and lowers the power of the input signal. To overcome this problem, a tunable matching network (MN) with very low insertion loss, high linearity, and a wide tuning range is required. A MN is a passive two-port network designed to provide narrow-band impedance and voltage trans- formation between the two ports. Some analytical descriptions of MNs are based on the assumption of lossless components [3]. 1160 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 57, No. 5, May 2015 DOI 10.1002/mop