This article proposes a fully analytical synthesis methodology for manifold multiplexers (MUXs). The core of this proposed method involves approximating the dispersive transmission line (TL) characteristics with finite-order rational functions. This allows the TLs to be treated as lumped elements that can be accommodated in circuit synthesis. In addition, a circuit transformation strategy is introduced that decomposes a star-connected MUX into two separate branches. By applying this transformation recursively, the initial star-connected topology gradually converts to the target manifold-coupled topology. During the transformation, an iterative procedure to modify filtering polynomials is developed to ensure that the channels’ transmission zeros (TZs) hold the prescribed ones, while maintaining the quasi-equiripple passbands. Compared with optimization-based synthesis approaches, the proposed method offers higher efficiency and stability while achieving a quasi-equiripple response. Its effectiveness is demonstrated through the synthesis of a quadruplexer and a manufactured contiguous triplexer.

This paper presents the results of a unique bandstop filter whose characteristics and performances push the boundaries of what is generally recognized as practicable. For the first time, the full extracted-pole technique is successfully applied to a bandstop filter possessing high order and wide stopband, thus verging on an ideal brick-wall filtering function. The implementation of the filter is based on parallel-coupled slab lines technology, where an advanced stepped-impedance bandstop resonator structure is employed. Such a resonator allows for the realization of a wide spurious-free passband while enabling the strong coupling coefficients required to obtain a wide stopband. The experimental results presented at the end of this paper, including a remarkable match between measurements and simulations, validate the feasibility of the proposed brick-wall bandstop filter.

The evolution of the communication technologies in the recent years has required more and more performing filtering subsystems. In particular, the very strict requirements in terms of selectivity, passband losses and compactness have required new and more effective synthesis solutions. Considering the compactness and the best use of the available footprint, the inline topology represents undoubtedly a very convenient solution. Unfortunately, in its classical implementation, it suffers from scarce selectivity (no transmission zeros can be introduced in the frequency response). Recently, various solutions have appeared in the literature, which allow introducing transmission zeros in true inline (and quasi-inline) filter topologies. This is obtained by means of new characteristic functions allowing additional degrees of freedom in the definition of the frequency response (which are exploited to impose the additional constraints necessary to make it possible the synthesis of the imposed topologies).In this talk two new frequency characteristics (namely the Reduced Chebycheff and the Bounded Chebycheff) are first introduced, and their features are illustrated and discussed (they are based on the use of complex reflection zeros in the filter response).Two types of true inline filters exploiting these characteristics are then analyzed in detail, namely the Path filters and the Extracted-zero filters. For each type, the specific synthesis procedure is described and several examples of synthesis of the prototype networks are presented. Some examples of real filters with the considered topologies (developed for 5G applications) are also presented.

This work presents a direct synthesis methodology for realizing codesigned filters that integrate low-pass/multi bandpass or high-pass/multi bandpass responses within a unified network. The proposed approach enables independent control over each subband—such as order, bandwidth, and return loss—while supporting flexible placement of transmission zeros (TZs) for enhanced out-of-band selectivity. The synthesis is built upon a new class of characteristic polynomials defined in the nonnormalized $\omega $ -domain, which intrinsically realizes composite low-pass and multi bandpass filtering behavior without requiring frequency transformation. These polynomials are then mapped to a transversal prototype comprising low-pass and bandpass blocks, which can be corresponded to a high-pass/multi bandpass form via $\omega $ -to-1/ $\omega $ inversion. The obtained transversal networks are then simplified into practical topologies through matrix-based manipulations. A series of examples, including synthesis and experimental validations, confirms the effectiveness and flexibility of the method. The proposed technique establishes a legitimate approach toward the integration of complex codesigned filtering functions based on simple resonator and coupling models.

The synthesis of duplexers without a common junction is presented. The input of the duplexers is realized on the first resonator of the TX or RX filter. The main advantage of the proposed solution is the improved feasibility, due to the much higher external Q required at the diplexer input (especially for wideband devices). The proposed solution is validated both through simulations and a manufactured prototype.

This article introduces a general multiport coupling matrix synthesis framework for star-junction multiplexers. Two types of star-junction multiplexers can be synthesized. The channel filters are directly connected to the common port in the first type and are connected to a common resonant node in the second type. To establish this general multiport coupling matrix synthesis framework, this article first investigates topological constraints on realizable multiport S-parameter rational functions. S-parameter rational functions of equi-ripple multiplexer responses complying with these constraints are constructed based on a novel Remez-like algorithm. A multiport coupling matrix can be analytically synthesized from the partial fraction expansions of the S-parameter rational functions. Finally, coupling matrix transformation strategies for star-junction multiplexers are introduced, which complete the general synthesis framework. Throughout the synthesis procedure, high-order polynomials are evaluated as products of first-order factors or as sums of first-order rational fractions with auxiliary denominators to enhance numerical stability. The proposed synthesis method allows flexible assignment of passband frequency ranges, number of reflection zeros (RZs) in each passband, in-band return loss levels, and prescribed transmission zeros (TZs). Moreover, for multiplexers of the second type, the common resonant node is utilized to produce an additional RZ in one of the passbands, improving the overall selectivity of the multiplexer. Several synthesis examples are provided to demonstrate the effectiveness and flexibility of the method. It is shown that the proposed method can accurately synthesize multiplexers of degrees as high as 300.

Microwave bandstop filters several finite transmission zeros are commonly synthesized as a sequence of frequency-invariant phase shifters followed by hung resonators. The physical realization however often involves transmission lines, whose phase delay introduces a linear variation with frequency and hence limit the design effectiveness to narrow band and heavy subsequent optimization. Leveraging a revisited version of classical cascade synthesis, the formulation presented here allows to include the known frequency variation of such components at synthesis time. The resulting compound technique yields a synthesized circuit much closer to its physical implementation up to relative bandwidth 13%.

Stopband filters are often implemented by a constant-impedance line tapped by blocks which create transmission zeros. The design of such filters today suffers from poor numerical accuracy of the available synthesis techniques and is thus analytically limited to low order or otherwise to very time-consuming symbolic computations, and only extensive circuit or electromagnetic optimizations can overcome such limitations. Traditional cascade synthesis methods can however be substantially revisited to allow for orders beyond 30 and hence find an ideal application in stopband filters with extreme selectivity requirements, as described in this work.

This article addresses the limitations in the analytical synthesis of star junction multiplexers, focusing on passband configuration flexibility, maximum achievable multiplexer order, and canonical channel settings, with the aim of eliminating uncertainties in existing approaches. The proposed method provides an optimal design approach by iteratively updating the allocation of reflection zeros (RZs) for various configurations. By introducing a set of techniques to enhance numerical accuracy, the new method significantly expands the order of synthesizable multiplexers to over 200, surpassing existing engineering requirement. Moreover, the new method offers flexibility in accommodating various channel filter configurations, including fully canonical, nonfully canonical filters, and their combinations. The effectiveness and generality of the proposed synthesis technique are validated through three synthesis examples and one design example, which includes fabrication and measurement, demonstrating its capability to address complex challenges in the synthesis of high-order multiplexers.

This paper presents a direct synthesis approach for lowpass/bandpass co-designed filters, allowing independent control of sub-band responses. The synthesis is based on a group of characteristic polynomials that provide combined lowpass and bandpass responses in the non-normalized frequency domain. A novel transversal array network is sequentially constructed to match the responses, which can be converted into practical topologies through matrix transformations. Synthesis and experimental results using a ladder-type model are proposed to validate the approach. The proposed technique offers significant advantages in sub-band performance control and out-of-band selectivity compared to traditional methods.

This letter introduces a stable star-junction multiplexer synthesis method based on rational function iteration. It reformulates the objective of allocating the common port reflection zeros (CPRZs) by iteratively adjusting the input admittance (IA) of individual channel filters (CFs), ensuring that the common port IA is perfectly matched at the predefined reflection zeros. This enables the proposed method to be applied to frequency-dependent reference impedance. Furthermore, the proposed iterative procedure inherently eliminates the need for high-order polynomial manipulation and provides improved numerical stability. Two examples of synthesis are presented to demonstrate the effectiveness of this approach.

The applicability of section extraction synthesis techniques for high-order microwave filters is traditionally hampered by numerical roundoff errors which cumulate at each step and quickly prevent correct extractions. A revisited version of cascade synthesis is instead proposed in this work which, instead of operating iteratively on the polynomial coefficients, requires only their evaluation at the transmission zeros. This technique allows a compact representation suited for extracting phase-shifter-extracted-pole blocks sequentially for fully-canonical filters. Good results are obtained up to order 18.

Advancements in compact, high-performance filtering structures are crucial for high performance communication systems. Applications such as massive MIMO antenna arrays require filters which are at the same time strongly selective and highly miniaturized. Traditionally, transmission zeroes in the filtering response have been obtained using cross-coupling between multiple resonators. Recently, techniques have been developed for the retrieval of transmission zeroes with inline topologies. In this work, two of such techniques are compared, the extracted-pole and the path filter. The size and performance of these topologies are evaluated by creating and comparing a test filter for each of them, working around 3.7 GHz with a 5.4% bandwidth. Substrate Integrated Waveguide (SIW) prototypes have been fabricated and measured.

In this paper two novel frequency-dependent coupling structures (FVC) in rectangular waveguide are introduced. The main features of these FVCs are: 1) only a transmission zero is generated (no reflection zeros in the waveguide monomodal band). 2) Very high values for the equivalent slope parameter can be realized. 3) The structure is relatively compact. The use of the novel structures in FVC filters is illustrated by the design of two test filters.

A comprehensive design procedure for quasi-inline filters using strongly coupled resonator quadruplets (SCRQs) is presented in this article. Just recently proposed, the SCRQ is a novel building block structure that allows for the generation of two transmission zeros and three passband poles in the response of microwave filters. This block belongs to the category of strongly coupled resonators, whose adoption has the following advantages: 1) reduced overall filter size (quasi-inline configuration can be realized) and 2) avoids the usage of capacitive couplings (only positive couplings are required). After a brief summary recalling the concept behind the working principles of the SCRQ, a suitable model for this new block is introduced, which is then used in an original synthesis procedure of higher order filters composed by an arbitrary number of cascaded SCRQs. In addition to several numerical synthesis examples, the design technique here introduced is validated through a manufactured prototype exhibiting a response with 11 poles and four transmission zeros.

This work presents an optimization method for coupled-resonators filter topologies relying on the computation of poles and zeros directly from the coupling matrix. The optimizer can therefore iteratively fill the non-zero elements of the coupling matrix, assess the resulting poles and zeros and compare them against the required response. The obtained overall difference between the two sets of roots is hence minimized according to a local strategy. The method has been tested up to 12th order responses implemented by a box section, with successful results. Such optimizer has been also compared with other approaches, revealing generally higher reliability than transverse-prototype optimization while suffering from a slightly slower execution speed.

This article presents a general synthesis method for achieving flexible bandwidth of a bandpass filter by cascading modular blocks. The synthesis utilizes a matrix procedure in the bandpass domain, enabling the extraction, relocation, and cascading of various bandpass blocks (including bandpass doublets, triplets, quadruplets, and boxes) together. These blocks can consist of capacitive or inductive couplings and can be further reduced through specific matrix transformations that introduce resonant couplings. The resulting prototype, incorporating transmission zeros (TZs) generated by each cascaded block, facilitates the realization of sharp selectivity without limitations on filter degree or bandwidth. Additionally, an N th-order in-line prototype composed of bandpass doublets in series is specially discussed, which allows for independent generation and control of massive finite TZs (with at least 1 TZ dedicated to 0), even in very wideband cases. To evaluate the proposed approach, numerous synthesis examples are presented, showcasing different orders, TZ allocations, and coupling pathways. Furthermore, an experimental design is demonstrated for the validation, which features a fifth-order low-temperature superconducting (LTS) filter with a passband of 3.5–6.5 GHz and 4 TZs at 0/1.9/7.6/8.1 GHz. The simulated and measured results are well correlated, thus showing the effectiveness of the proposed approach.

This paper introduces novel frequency-variant coupling (FVC) structure in rectangular waveguide. The key feature of this structure is its ability to generate two transmission zeros (TZs) and one pole, reducing by one the number of physical resonators in waveguide filters with frequency-variant coupling (FVC) presenting TZs in the response. Moreover, the novel coupling structure (here called "Double FVC") allows for large slope parameters of the equivalent rejection resonators modeling the transmission zeros generation. As a consequence, the TZs can be placed very close to the passband, where the classical structures implementing FVC cannot arrive. The paper introduces an equivalent circuit for the double FVC and shows how it can be used in the filters’ implementation. To validate this new proposed structure, a 5-pole filter with a double FVC was fabricated and measured.

In this work, we analyze the behavior of TE201 waveguide singlets, proposing dimensioning criteria applicable in the portion of the single-mode bandwidth of the input waveguide comprised between $1.4f_{c}$ and $1.6f_{c}$ , where $f_{c}$ is the dominant mode cut-off frequency. We address the relationship between the physical features of the singlet and the equivalent circuit parameters, by proposing a method to build ad hoc charts from full-wave simulations based on mode-matching. In the framework of an extracted pole waveguide filter design procedure, the initial dimensioning of the singlets is completed quickly through the charts and the final filter optimization is extremely fast, the initial design being accurate enough. The validation of this procedure is shown with a suitable design example of a filter with zeros both above and below the passband.

In this article, we discuss the synthesis of a strictly inline filter configuration allowing the placement of up to four transmission zeros (TZs) in the frequency response. This configuration [here referred to as extracted-zero (EZ)] is often adopted in the practice, but the dimensioning generally resorts to empirical strategies and numerical optimization, being no synthesis-based approaches available till now. The topology of these filters is represented by an array of coupled resonators without cross couplings, with source and load coupled to internal resonators (instead of the first and last as in the classical all-pole filters). We show here how to compute the equivalent circuit parameters (coupling coefficients and resonating frequencies) once a suitable approximating frequency characteristic has been devised. Several synthesis examples are presented, and it is shown how filters of this type, previously empirically designed, and actually fabricated, can be obtained with the new design approach.