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In this paper the problem of designing simple low-cost planar microwave bandpass filters with strongly asymmetric characteristics, filters that can very efficiently attenuate one of the two adjacent channels, is investigated. In case of a fourth-order filter, the usual quadruplet structure leads to two transmission zeros located one on each side of the passband, but higher attenuation can be obtained for one of the two adjacent channels by designing filters with two transmission zeros in the same (upper or lower) stopband. The new topology investigated in this paper offers the possibility of designing such quadruplets with two transmission zeroes situated both on the same side of the passband, in prescribed and controlled positions. Filters with this novel structure can provide very high attenuation not only at a single frequency, but in a larger adjacent frequency band.