Advanced Coupling Matrix and Admittance Function Synthesis Techniques for Dissipative Microwave Filters

In this paper, novel approaches to synthesize admittance function polynomials and canonical <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +2 coupling matrices for narrowband lossy filters are presented. The methods are simpler and more general than the ones found in the literature. The polynomial synthesis approach is fully analytical and also very useful for lossless polynomial synthesis with simpler derivations. The coupling matrix synthesis method is based on a lossy transversal network model, which can also accommodate direct source to load coupling. Unlike the lossless transversal coupling matrix, the lossy coupling matrix model requires the assumption of complex <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> -inverters and additional resistive elements in the network. The complex <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> -inverter circuit model is defined and explained in detail in this paper. The lossy transversal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +2 matrix can be systematically rotated to obtain a number of practical realizations. Parallel-coupled pairs and folded lossy configurations are shown as examples. Moreover, the synthesis of novel networks with different return-loss levels at source and load is presented. A performance comparison with a predistorted filter is also included in this paper.