## 1 Introduction
By introducing a slotline in the ground plane, common-mode transmission is avoided since the location of the slot is not compatible with the pattern of common-mode currents. In all these cases [29; 31; 32; 35], the use of slotted ground plane provides good CM rejection at the expense of increasing radiation losses and making difficult system integration (for many practical applications a solid ground plane is required). Lumped or quasi-lumped microwave resonators are not the only structures used to design balanced dual-band bandpass filters. Distributed structures have also been used for this purpose. Some works based on them can be found in the literature [36; 37; 38; 39; 40; 30]. For example, asymmetrical coupled lines [36] and substrate integrated waveguide (SIW) technology [37] are interesting recent approaches for balanced dual-band BPF design. These designs provide both good DM and CM response, but typically suffer from the problem of large electrical size. Moreover, both [36; 37] require the use of a large number of via-holes, which makes their performance very dependent on the accuracy of the implementation of such vias. In [38], a second-order dual-band filter based on coupled lines loaded with a pair of SIRs and open stubs was presented showing a wide CM rejection bandwidth and high selectivity in the narrow DM passbands. However, the introduction of SIRs increased the total size. Another approach based on stub loaded resonators (SLR) was presented in [39] showing a simple and compact design, easily adaptable to two or three passbands, that presents a good level of CM noise rejection. Nevertheless, the isolation between bands is relatively poor. In [40], a via-free composite right/left-handed (CRLH) resonator was presented showing an excellent CM suppression behavior, both in terms of bandwidth and rejection level. Nonetheless, the bandwidth of the DM passbands is too small for many applications. In [30], single-and-dual-band stub bandpass filters are presented whose input-output terminals are loaded with resistively terminated _Kth_-order bandstop filters. Thanks to resistive loading, common-mode is neither transmitted nor reflected, but absorbed in the resistors. This technique leads to good results for both DM and CM, but the prize to pay is the complexity in the design and the use of lumped resistors, which are not always desirable at high frequency applications. The use of magnetic coupling to design balanced single-band BPFs was proposed in [26] as an alternative to the most commonly employed electric coupling. It was demonstrated that magnetic coupling provides inherent strong common-mode rejection when compared with electric coupling. For the simple case of two coupled open-loop resonators, the electric coupling occurs when the resonators are placed in such a way that the gaps of the resonators are placed face-to-face. The boundary conditions under differential- and common-mode excitations barely affect the charge distribution around the open ends of the loops, in such a way that the coupling level for both excitation modes is expected to be similar. By contrast, in the case of magnetically coupled resonators, the open sides are in the opposite orientation. In such case the coupling between resonators can be assimilated to the coupling between two microstrip transmission lines [26]. When common-mode excitation is applied, the symmetry plane of the open loop becomes a virtual open circuit (vanishing currents at that plane) and the coupling mechanism among adjacent resonators remains electrical in nature. On the contrary, a short-circuit condition appears at the same point when differential-mode excitation is applied. Currents around that point are important and the coupling mechanism between adjacent resonators becomes magnetic in nature. For a required coupling level of the differential-mode signal, which is imposed by the filter design specifications, magnetic coupling leads to larger separation between resonators when compared with the electric coupling case [41].