A single x-coupling-bypassing one resonator (also called a triplet)-may, under certain conditions, give rejection corresponding to approximately two extra filter poles. By convention inductive couplings are positive and capacitive couplings negative. Inductive couplings are indicated by unbroken lines and capacitive couplings by a capacitor symbol. In the schematic circuit diagram, the numbered black dots represent resonators the white circles represent source/load terminals (that is "connectors"). If the top-point of the two peaks-or alternatively the "valley" between them-is kept below approximately -30 dB, the influence of the I/O ports can be neglected.įigure 4 Three commonly used x-coupling configurations and their characteristics.Ĭouplings may either be inductive or capacitive and are often schematically represented, as shown in Figure 3. To minimize the influence of input and output connections on the coupling measurement, the resonators must be loosely connected to the input and output ports. Where Δf is the coupling bandwidth, which expressed in Hz, and M 12 is the normalized coupling coefficient between resonator 1 and 2. Therefore, the normalized coupling coefficient is given by If the coupling bandwidth is divided by the ripple bandwidth BW of the filter, the normalized coupling coefficient is obtained. In this case, the coupling is Δf MHz and is referred to as the coupling bandwidth. The coupling between the resonators results in a displacement Δf of the resonance frequencies. The two resonators are identical and are both resonating at frequency f 0. The corresponding measured transmission characteristic (S 21) is also shown. Two metallic resonators are enclosed in a metallic housing and loosely coupled to the in and output ports. To demonstrate the concept of coupling between adjacent resonators, the two-pole circuit in Figure 1 is used. It is shown how coupling coefficients can be measured.įigure 1 Two-pole box and associated transmission characteristic. In this section the coupling mechanisms in bandpass filters are investigated. To design microwave filters a basic understanding of coupling and coupling mechanisms is necessary. It is also demonstrated how coupling matrix synthesis may be used to better understand and explain differences between calculated and measured filter responses. The methods are validated through measurements on manufactured coaxial cavity filters. ![]() Emphasis is made on practical approaches and it is demonstrated that even fairly complex x-coupled filters can be made in just one iteration. In that case a couple of test circuits must be manufactured. ![]() Even though EM solvers in this article are used for the designs, the adopted methods may be applied even without EM solvers available. In this article, practical filter design using the coupling matrix synthesis and simple 3-D EM simulation techniques is demonstrated. The recent coupling matrix formulation leads to more accurate determination of practical filter characteristics highly complex filters with multiple non-adjacent couplings are now easily synthesized.Įven though a large number of articles dealing with coupling matrix synthesis have recently been published, almost none of them go into details about how to convert the synthesized matrices into physical filters. The coupling matrix representation of bandpass filters is convenient since, with matrix operations, it is possible to transform between topologies whereby the best suited topology for a given problem may be found. 2 The coupling matrix concept has also been reformulated to accommodate couplings directly from the source and the load to internal resonators. The coupling matrix concept was introduced in the 1970s, but general methods have recently been introduced for its synthesis. ![]() The other field that has had a major impact on filter design methods is advances within the coupling matrix representation of microwave filter circuits.
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