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This paper presents a generalized direct synthesis technique for lossy reciprocal and nonsymmetrical microwave filters. The procedure handles multiple complex coupling among resonators and finite-Q resonators. A coupling matrix model with complex entries is used as the basis for the analysis. New mathematical definitions are introduced to find the necessary properties of the complex coupling matrix. Synthesis verification examples include symmetrical, asymmetrical and different loss level lossy functions. A lossy four-pole Chebyshev filter in Ku-band has been designed, fabricated and tested using mixed combline and microstrip technologies for the first time. This design has the advantage of having the signal passing through at least two resonators for any possible signal path, which eliminates unwanted source to load coupling to a great extent.