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 (f₀) 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 ([L], [C]) parameters and the scattering coefficient (S₂₁) of its equivalent circuit.

Fig. 1 shows a microstrip line with a parallel open stub, which brings about a stopband effect around a frequency, f₀. 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 Jaisson² 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 V₁ = V₂ = 1 V yields capacitance C₃, 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 [L] and [C] 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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