Tunable bandstop filters are useful for a wide range of applications in eliminating unwanted signals and interference. Designing such filters can be greatly simplified with a new structure fabricated on multilayer microstrip substrates with a metallic diaphragm. This new structure overcomes the limitations of traditional tunable bandstop filter designs and supports simple, low-cost manufacturing processes.^{1} The new tunable filter architecture is well suited for rejecting unwanted carrier frequencies within the intermediatefrequency (IF) range of a DCS cellular communications system.

A bandstop filter using multilayer microstrip has been presented by D. Jaisson.^{2} Its design involves a doublelayer microstrip resonator coupled to a microstrip line. The filter was designed to operate on a center frequency (f_{0}) of 1842.5 MHz and reject unwanted carrier frequencies in the IF processing unit of a DCS receiver. What follows is the analysis of a shielded bandstop filter with metallic diaphragm and the design of a tunable bandstop filter.

This analysis is based on a numerical resolution of the electrostatic problem by the finite-element method (FEM).^{1,3} Then, the modeling of this structure is achieved by the determination of the inductive and capacitive matrix (, ) parameters and the scattering coefficient (S_{21}) of its equivalent circuit.

Fig. 1 shows a microstrip line with a parallel open stub, which brings about a stopband effect around a frequency, f_{0}. In a microwave integrated circuit (MIC), where space is limited, it might be preferred to use the most compact microstrip configuration possible. A possibility proposed by Jaisson^{2} consists of rotating the open microstrip structure and placing it on top of the access lines as shown in Fig. 2, with an additional layer of substrate between them.

The structure in Fig. 2 was selected in ref. 2 for use as a bandstop filter. Fig. 3 gives the equivalent circuit of the bandstop filter, where its output is matched to a characteristic impedance, Z_{co} = 50 O. Figure 3 shows that for a selected length, b, the bandstop filter consists of two coupled transverse electromagnetic (TEM) or quasi-TEM transmission lines. The left end of the top line is connected to that of the bottom line, and its right end is kept open.

Fig. 4 shows the cross section of the filter as having an inhomogeneous multilayer structure with metallic diaphragm and with asymmetrical microstrip construction. For asymmetrical strips,^{1,3} and using this numerical model, the filter capacitances C_{i}(er) can be computed for:

Vi = 1 V

(with all other conductors grounded).

Setting the voltage as V_{1} = V_{2} = 1 V yields capacitance C_{3}, with the coupling capacitance, C_{m}, calculated by the following relationship^{1,3}:

The filter inductances, L_{i} (i = 1, 2), are given in terms of the capacitances, as in the case of a single quasi-static line,^{1} and the mutual inductance, L_{m}, can be calculated from the following relationship:

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.