Generalized cross-coupled filters require implementation of both positive and negative cross-coupled elements. A positive element frequently uses inductive coupling, while a negative one uses capacitive coupling. Traditional methods for realizing capacitive couplings, which are difficult to adjust in practice, have included the use of capacitive probes in coaxial cavity. And this kind of n-order cross-coupled filters without the coupling between input and output ports can only produce 2-n transmission zeros at most. In this paper, we present a convenient method for capacitive coupling. Based on the method a four-order cross-coupled filter is realized, and the measured results match well with the theoretical prediction. Especially, there are three transmission zeros near the pass band.
2. Levy, R., "Filters with single transmission zeros atreal and imaginary frequencies," IEEE Trans. Microw. Theory Tech., Vol. 24, No. 4, 172-181, 1976.
3. Hongand, J.-S. and M. J. Lancaster, "Couplings of microstrip square open-loop resonators for cross-coupled planar microwave filters," IEEE Trans. Microw. Theory Tech., Vol. 24, No. 12, 2099-2109, 1976.
4. Shen, T., H.-T. Hsu, K. A. Zaki, A. E. Atia, and T. G. Dolan, "Full-wave design of canonical waveguide filters by optimization," IEEE Trans. Microw. Theory Tech., Vol. 51, No. 2, 504-510, 2003.
5. Ruiz-Cruz, J. A., M. A. E. Sabbagh, K. A. Zaki, J. M. Rebollar, and Y. Zhang, "Canonical ridge waveguide filters in LTCC or metallic resonators," IEEE Trans. Microw. Theory Tech., Vol. 53, No. 1, 174-182, 2005.
6. Yao, H. W., K. A. Zaki, A. E. Atia, and R. Hershtig, "Full wave modeling of conducting posts in rectangular waveguides and its applications to slot coupled combline filters," IEEE Trans. Microw. Theory Tech., Vol. 43, No. 12, 2824-2829, 1995.
7. Wang, C. and K. A. Zaki, "Full wave modeling of electric coupling probes comb-line resonators and filters," IEEE Trans. Microw. Theory Tech., Vol. 48, No. 12, 2459-2464, 1995.
8. Pozer, D. M., Microwave Engineering, 3rd Ed., 51-53, 2004.
9. Hong, J.-S. and M. J. Lancaster, "Microstrip Filter for RF/Microwave Applications," Wiley, 2001.
10. Zysman, G. I. and A. K. Johnson, "Coupled transmission line networks in an inhomogeneous dielectric medium," IEEE Trans. Microw. Theory Tech., Vol. 17, 753-759, 1969.
11. Rhodes, J. D., Theory of Electric Filters, Wiley, London, England, 1976.
12. Wenzel, R. J., "Solving the approximation problem for narrowband bandpass ¯lters with equal-ripple passband response and arbitrary phase response," 1975 IEEE MTT-S Int. Microwave Symp. Dig., 50, 1975.