Compact planar quasi-elliptic function filter with inline stepped-impedance resonators

Compact microstrip bandpass filters of orders N = 4, 6, and 8 with quasi-elliptic function responses are synthesized with inline stepped-impedance resonators. The filters have enhanced transition responses since two transmission zeros are generated on both sides of the passband. Existence of these two zeros is investigated by formulating the Y-matrix of the equivalent circuit for the filter and taking adjacent and nonadjacent coupling into account. Some matrix elements Y_j,j+2 representing coupling between two nonadjacent resonators are shown to have the opposite signs in both the lower and upper sides of the center frequency. This property leads to creation of the two transmission zeros on both sides of the passband. It is demonstrated that one more zero can be created in the rejection band by the tapped-line input/output scheme. Experimental circuits on substrates with ε_r = 2.2 and 10.2 are measured to validate the theory and design.