“…Wolff first demonstrated a microstrip dual-mode filter in 1972 [1] and therefore, the number of resonators had been reduced by half, resulting in a compact size. Since then [2,3,4,5,6], multi-mode filters have been widely used in wireless communications systems [7,8,9,10,11,12,13,14,15,16]. On the other hand, high performance, light weight, good outband rejection and low cost can't be ignored for filter designers.…”