Physical interpretation of frequency-dependent S/L coupling in multi-mode bandpass filter and its design approach for generation of multiple finite transmission zeros

This paper introduces a new physical interpretation of a frequency-dependent source/load (S/L) coupling to multi-mode filter designs, thereby successfully generating (N + 1) transmission zeros (TZs) greater than the number of resonant modes N. It is made clear by a transmission-line based analysis with the help of a parameter-extraction technique that the frequency-dependent S/L coupling essentially appears in a dual-mode loop resonator filter fed by parallel-coupled input/output lines. As an example, a dual-mode bandpass filter having a sharp roll-off response and high attenuation at the upper stopband is developed, which can be realized by three finite TZs with a very simple structure. The validity of the design technique is verified by simulations and measurements.