Smain Amari

Synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique

We propose a general approach to the synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique. The gradient of the cost function with respect to changes in the coupling elements between the resonators is determined analytically. The topology of the structure is strictly enforced at each step in the optimization thereby eliminating the need for similarity transformations of the coupling matrix. For the calculation of group delays, a simple formula is presented in terms of the coupling matrix. A simple recursion relation for the computation of the generalized Chebychev filtering functions is derived. Numerical results demonstrating the excellent performance of the approach are presented.

Adaptive synthesis and design of resonator filters with source/load-multiresonator coupling

The paper presents a universal and comprehensive synthesis technique of coupled resonator filters with source/load-multiresonator coupling. The approach is based on repeated analyses of a circuit with the desired topology; no similarity transformation is needed. Restrictions imposed by the implementation on the coupling coefficients such as signs and orders of magnitudes are straightforwardly handled within this technique. The technique is then used to synthesize and design filters with full or almost full coupling matrices by selecting, among the infinite number of solutions, the matrix that corresponds to the actual implementation. In such cases, analytical techniques and those based on similarity transformations cannot be used since they provide no mechanism to constrain individual coupling coefficients in order to discriminate between two full coupling matrices, which are both solutions to the synthesis problem. Using the technique described in this paper, a filter designer can extract the coupling matrix of a filter of arbitrary order and topology while enforcing relevant constraints. There is no need to master all the different existing similarity-transformation-based techniques and the topologies to which they are applicable. For the first time, detailed investigations of parasitic coupling effects, for either compensation or utilization, are made possible. The method is applied to the synthesis of a variety of filters, some of which are then designed and built and their response measured.

Coupling-Matrix Design of Dual and Triple Passband Filters

The concept of the conventional coupling matrix is extended to include designs of dual- and triple-band filters. The multiband response is created by either placing transmission zeros within the bandwidth of a wideband filter or using higher order resonances. Realizable topologies both in planar and waveguide technologies can be imposed and associated coupling coefficients enforced during optimization. The design process is verified by measurements and comparison with results of commercially available field solvers

Space-mapping optimization of planar coupled-resonator microwave filters

This paper presents an iterative technique for the design of planar coupled-resonator microwave filters, which exploits initial information on the equivalent circuit elements within the space-mapping technique. To accelerate the convergence of the design process, information on the dependence of the elements of the equivalent circuit on adjustable geometrical and physical parameters, which is available from the initial design step, is used. The technique is applied to design harmonic-reject planar filters. Results from applications to fourth- and sixth-order filters show that the successful designs are achieved with at most two iterations. A sixth-order harmonic-reject filter is then fabricated and measured.

Novel coupling schemes for microwave resonator filters

The paper presents novel coupling schemes for microwave resonator filters. Some of these solutions contain more than one main path between the input and output. These paths may be interacting or non-interacting. In other solutions, only some of the direct (main) couplings are zero. It is shown that higher-order filter characteristics can be obtained from lower-order sections, which are connected in parallel between the source and the load, by proper superposition of the individual lower-order responses. Possible applications of these solution to actual design problems are discussed.

New building blocks for modular design of elliptic and self-equalized filters

This paper introduces building blocks for modular design of elliptic, pseudoelliptic, and self-equalized filters. The first building block is of second order and generates two transmission zeros (TZs), which are either on the real or imaginary axis. Moving the zeros from the real axis (linear phase response) to the imaginary axis (attenuation poles) requires changing the sign of one coupling coefficient. The second building block is a structure of order three, called extended doublet, which allows the generation of two TZs practically anywhere in the complex plane. An important property of this block is its ability to move the two TZs from the real axis to the imaginary axis of the complex s-plane without changing the signs of its coupling coefficients. The third building block is of third order and generates two TZs, which can be moved from the real to the imaginary axis by changing the sign of one coupling coefficient. Simple waveguide structures to implement these blocks are introduced for validation, although this general approach is feasible for all resonator filter types. Higher order filters are designed modularly by cascading an arbitrary number of these building blocks. A novel concept, which allows the independent control of each pair of TZs in higher order filters, is then introduced. It is shown that the new concept allows a filter of order N to generate N TZs without directly coupling the source to the load even when the coupling coefficients are all assumed frequency independent. The same approach can be used to design and reduce the sensitivity of higher order elliptic and pseudoelliptic filters using other building blocks such as doublets or a mixture of building blocks of different orders and properties. Measured results and extensive computer simulation are presented to demonstrate the validity of the concept and the performance of the designed filters.

Characteristics of cross (bypass) coupling through higher/lower order modes and their applications in elliptic filter design

This paper presents a new set of results concerning the use of higher/lower order modes as a means to implement bypass or cross coupling for applications in elliptic filter design. It is shown that the signs of the coupling coefficients to produce a transmission zero (TZ) either below or above the passband are, in certain situations, reversed from the predictions of simpler existing models. In particular, the bypass coupling to higher/lower order modes must be significantly stronger than the coupling to the main resonance in order to generate TZs in the immediate vicinity of the passband. Planar (H-plane) singlets are used to illustrate the derived results. This study should provide very important guidelines in selecting the proper main and bypass couplings for sophisticated filtering structures. Example filters are designed, built, and measured to demonstrate the validity of the introduced theory.

Singlets, cascaded singlets, and the nonresonating node model for advanced modular design of elliptic filters

The singlet, which contains one resonator and generates one transmission zero, is introduced as the most basic building block for modular design of elliptic filters. Higher-order elliptic filters are designed by cascading singlets to generate the required transmission zeros. A novel model, the nonresonating node model (NRNM), which contains both resonating and nonresonating nodes is then introduced. The model allows a high level of modularity in the design of elliptic filters. Example filters are designed and measured to validate the model and the design approach.

Automated filter tuning using generalized low-pass prototype networks and gradient-based parameter extraction

A novel technique for automated filter tuning is introduced. The filter to be tuned is represented by a generalized filter low-pass prototype model rather than a specialized equivalent network. The prototype model is based on the minimum number of characteristic filter parameters to represent the filter transfer function correctly. The parameter values are found from a gradient-based parameter-extraction process using measured S-parameters. Automated filter tuning is performed as a two-step procedure. First, the parameter sensitivities with respect to the tuning elements are determined by a series of S-parameter measurements. Second, the parameter values of the filter are compared to the values of the ideal filter prototype found from a filter synthesis, thus yielding the optimal screw positions. This novel tuning technique has been tested successfully with direct coupled three-resonator and cross-coupled four- and six-resonator filters.

Synthesis of inline filters with arbitrarily placed attenuation poles by using nonresonating nodes

A general and direct synthesis technique of pseudoelliptic inline filters with arbitrarily placed attenuation poles (APs) (transmission zeros) at real frequencies is presented. The APs are brought about and independently controlled by dedicated resonators, which are coupled to nonresonating nodes. Simple rules to properly determine the phases of the reflection coefficients at the input and output are given. To reduce the effect of roundoff errors, especially for higher order filters, the extraction of the elements of the network is performed from the input and output simultaneously. Multiplicity and scaling properties of the solutions are discussed. Synthesis examples are presented to demonstrate the soundness of the procedure. Theoretical results are compared with measurement to demonstrate the validity of the presented theory.