Using the presented theory, the authors established a computer-aided-optimization (CAO) program to calculate the and matrices for a bandstop filter built on multilayer microstrip with a metallic diaphragm. When these matrices are determined, the filter response can be analyzed using an adapted numerical model.^{4} Although a number of CAO programs can be used for analyzing this filter, it is not the intention of this article to review the merits of a CAO program but to describe these simple-to-design structures for tunable bandstop filters.

To show the influence of the aperture half-width (s) on the properties of the bandstop filter, the authors analyzed a shielded bandstop filter using multilayer asymmetrical microstrip with metallic diaphragm. The cross section of this filter is presented in Fig. 4.

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The filter is characterized by the following features:

a bottom strip width (w_{1}) of 0.5 mm;

a top strip width (w_{2}) of 5 mm;

bottom material thickness (h_{1}) of 1 mm;

top material thickness (h_{2} = h_{3}) of 0.0825 mm;

separating lengths (s_{1} and s_{2}) of 3.25 and 1 mm, respectively;

strip thickness (t) of 0.01 mm;

diaphragm width (t) of 0.01 mm;

FR-4 substrate material (e_{r1} = e_{r2}) with dielectric constant of 4.7; and filter length (b) of 19.44 mm.

Figs. 5, fig. 6, and fig 7 provide plots of the elements of the inductance matrix as functions of the aperture halfwidth. The influence of the aperture half-width (s) on the elements of the capacitance matrix of the filter is shown in Figs. 8, 9, and 10. Figs. 5, 6, 7, 8, 9, and 10 clearly show the influence of the aperture half-width (s) on the bandstop filter's electromagnetic parameters (, ) and, consequently. on its rejection frequency, f_{0}.

To show the influence of the aperture half-width (s) on the bandstop filter's rejection frequency, f_{0}, the authors analyzed the filter response for the same physical and geometrical parameters mentioned above using an adapted numerical model.^{4}

Fig. 11 provides plots of the scattering coefficient (S_{21}) as a function of frequency for different values of the aperture half-width (s = 0.2, 0.4, and 0.6 mm, for example).

Fig. 11 shows that a minimum value of |S_{21}| = -93 dB is obtained at f_{0} = 1830 MHz for s = 0.2 mm. For s = 0.4 mm, the minimum value of |S_{21}| = -74.44 dB is obtained at f_{0} = 1810 MHz and for s = 0.6 mm, the minimum value of |S_{21}| = -79.76 dB is obtained at f_{0} = 1800 MHz.

Finally, Fig. 12 shows the rejection frequency, f_{0}, of the tunable bandstop filter constructed with multilayer microstrip with metallic diaphragm, versus the aperture halfwidth (s). The operating frequency range is 1796 to 1852 MHz, which was obtained for a half-width range between 0.05 and 1 mm.

In conclusion, a new structure for a tunable bandstop filter using shielded multilayer microstrip with a metallic diaphragm has been presented and simulated. The basic operating principle for the new structure is to control the tunable rejection frequency by means of adjusting the aperture half-width value. This new structure can be realized without major difficulties and with simple lowcost mechanical construction.

REFERENCES

1. N. Ben Ahmed, M. Feham, and S. Dali, "Design of Tunable Bandstop Filters using Multilayers Microstrip," Applied Microwave and Wireless, vol. 13, no. 7, July 2001, pp. 82-91.

2. D. Jaisson, "A Multilayer Microstrip Bandstop Filter for DCS," Applied Microwave & Wireless, 1998, pp. 64-70.

3. N. Ben Ahmed, M. Feham, and M. Kameche, "Finite Element Analysis Of Planar Couplers," Applied Microwave & Wireless, vol. 12, no. 10, October 2000, pp. 28-38.

4. A.R. Djordjevic, M. Bazdar, G. Vitosevic, T. Sarkar, and R. F. Harrington, Scattering Parameters of Microwave Networks with multiconductor transmission lines, Artech House, Norwood, MA, 1990.