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Lossy synthesis techniques allow filters consisting resonators with finite quality factor (Q) to be synthesized and designed while preserving prescribed in-band flatness. It is achieved at the expense of an overall constant additional insertion loss. As microstrip resonators generally suffer from low quality factor, using lossy synthesis techniques can be a good approach to design high performance narrow-band microstrip filters. In this paper, a lossy 3rd order Chebyshev filter with 5% fractional bandwidth, based on microstrip technology is synthesized and designed. The filter is centered at 2.6 GHz with the lossless return loss of 20 dB and a loss factor of 3.5 dB. At first, the complex coupling matrix corresponding to the filter characteristic is synthesized. Then, it is transformed into a realizable form using trigonometric rotations. Afterwards, hyperbolic rotations are employed to evenly distribute the loss among resonators. The synthesized filter network is implemented using hairpin resonators with the Q of 180. The simulation and optimization process is performed using a full-wave electromagnetic simulator (HFSS). Experimental evaluations illustrate that there is a reasonably good agreement between simulated and measured results.

Synthesis and Design of Narrow-Band Micrwave Lossy Filter Based on Microstrip Technology