Finally, we employ the coupling pad (see also Fig. 5) to create two more transmission zeros (solid lines in Figs. 6 and7). The first transmission zero (Tz:1) is due to the parallel resonance that is formed by two components: (i) the electromagnetically coupled signal created between the resonators and (ii) the signal through the coupling pad. The second transmission zero (Tz:2) is due to the possible resonance through the fringe capacitance and inductance of the coupling pad with resonators and the ground plane. The dimensions of the various sections of the filter with coupling pad and pin-pad resonators are as follows: r ϭ 7.5, h ϭ s ϩ l ϭ 0.5 mm, W ϭ 0.6 mm; resonators: length ϭ 40 mm, spacing between the resonators ϭ 1 mm, input/output line location ϭ 4.5 mm from short-circuit end; pin-pad resonator 1: x ϭ y ϭ 7.25 mm, l ϭ 0.375 mm, d ϭ 0.1 mm; pin-pad resonator 2: x ϭ y ϭ 8.6 mm, l ϭ 0.375 mm, d ϭ 0.1 mm; coupling pad: length (along resonators) ϭ 4 mm, width ϭ 3 mm.
Note that the results presented in Figures 6 and7 have been obtained using IE3D and, therefore, include all electromagnetic effects.
4. CONCLUSION
The equivalent-circuit model for grounded pin-pad resonators offers an attractive solution for the creation of transmission zeros in LTCC filter components. The determination of the resonance frequency or, alternatively, the pin-pad design for a given frequency is simple and straightforward. The process has been validated through an LTCC filter design, which was shown to achieve a transmission zero per pin-pad resonator. Hence, this design can be used to suppress a second passband. An additional coupling pad can be used to create additional transmission zeros closer to the passband. Both the equivalent-circuit model and the LTCC filter designs were verified through computations using the commercially available field solver IE3D.