Coupling matrix and admittance function synthesis for mixed topology filters

In this paper, novel approaches to synthesize admittance function polynomials and canonical <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +2 coupling matrices for narrowband lossy filters are presented. The methods are simpler and more general than the ones found in the literature. The polynomial synthesis approach is fully analytical and also very useful for lossless polynomial synthesis with simpler derivations. The coupling matrix synthesis method is based on a lossy transversal network model, which can also accommodate direct source to load coupling. Unlike the lossless transversal coupling matrix, the lossy coupling matrix model requires the assumption of complex <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> -inverters and additional resistive elements in the network. The complex <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> -inverter circuit model is defined and explained in detail in this paper. The lossy transversal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> +2 matrix can be systematically rotated to obtain a number of practical realizations. Parallel-coupled pairs and folded lossy configurations are shown as examples. Moreover, the synthesis of novel networks with different return-loss levels at source and load is presented. A performance comparison with a predistorted filter is also included in this paper.

In this paper a new approach to the synthesis of coupling matrices for microwave filters is presented. The new approach represents an advance on existing direct and optimization methods for coupling matrix synthesis in that it will exhaustively discover all possible coupling matrix solutions for a network if more than one exists. This enables a selection to be made of the set of coupling values, resonator frequency offsets, parasitic coupling tolerance etc that will be best suited to the technology it is intended to realize the microwave filter with. To demonstrate the use of the method, the case of the recently – introduced ‘extended box’ (EB) coupling matrix configuration is taken. The EB represents a new class of filter configuration featuring a number of important advantages, one of which is the existence of multiple coupling matrix solutions for each prototype filtering function, eg 16 for 8th degree cases. This case is taken as an example to demonstrate the use of the synthesis method – yielding one solution suitable for dual-mode realization and one where some couplings are small enough to neglec

ABSTRACTA novel coupling matrix synthesis method for dual‐band bandpass filter is presented in this article. The output admittance poles and zeros of the single‐band filter prototype are firstly obtained and then transformed into dual‐band prototype. Then the coupling matrix with predefined topology is optimized according to these poles and zeroes directly. This method can be achieved with no need to construct the characteristic function of dual‐band filter and reconfigure the coupling matrix. Symmetric and asymmetric dual‐band bandpass filter coupling matrix synthesis has been carried out to illustrate and validate this method. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:603–606, 2016

This paper presents a comparison between two techniques of S band interdigital diplexer design with i.e. with generalized multiplexer theory and coupling matrix synthesis. The design based on GMT, doubly terminated Chebyshev low pass filter response is used. The first two resonators of each channel are modified using formulas in GMT. The design is verified though MathCAD plots. In coupling matrix synthesis design, the general coupling matrix of each filter and coupling band width for two adjacent resonators are calculated. A novel technique is used for diplexer input design. The group delays are measured at the centre frequencies of channel filters. The physical diplexer design round rod type inter digital filter is selected. Both designs are simulated in HFSS with 2100 and 2250MHz with 100MHz channel band width.

This paper presents a new analytical approach for a problem of coupling matrix (CM) synthesis. The approach is based on reformulation of well-known equations representing filter scattering parameters S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</inf> for a given coupling matrix. With the use of relation connecting inverse matrix its determinant and its adjugate matrix the system of equations is formed. The equations are reformulated in a way allowing direct comparison of polynomials coefficients for numerator and denominator of S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> and numerator of S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</inf> . This enables to form the system of polynomial equations, where unknowns are all entries of searched coupling matrix. In the proposed approach no conversion from S-parameters to Y-parameters is needed like in most of published techniques. SINGULAR software (GPL license) using Groebner basis for solution of such a system of polynomial equations was used. Two numerical experiments have been presented. First one CM synthesis for 4th order (one cross-coupling) filter. Second one is CM synthesis for 8th order (two cross-couplings) filter. Both experiments showed excellent results obtained with the proposed method. The method works for S-parameters of filters with arbitrary topologies.

A general approach for in-line filters that contain a set of frequency-variant couplings is presented in this work. By utilizing an absolute matrix transformation process, the synthesis is distinctive from all other similar literatures because no optimization is required. In result, it is shown that multiple transmission zeros can be individually generated by the frequency-variant couplings. Moreover, some unique topologies where in-line frequency-variant couplings are connected with traditional extracted-pole sections and cross-coupled structures are introduced. For validation of the proposed approach, a group of examples with practical results are demonstrated.

Although the synthesis of symmetrical dual-band bandpass filters has been studied, little seems to be known about the general asymmetrical case. In this paper, a procedure for the synthesis of general asymmetrical dual-band bandpass filters implemented with inline dual-mode cavities is proposed. The inline architecture, as well as the asymmetrical nature of the response, lead naturally to the choice of an extended box topology or generalizations of the latter. It was recently shown that these topologies possess the property of multiple solutions, meaning that the related coupling matrix synthesis problem admits several solutions. On one hand, this multiplicity offers some flexibility to the designer, but on the other hand, working with multiple solutions may lead to ambiguities during the tuning process. Our procedure takes the best of both worlds: using the list of equivalent coupling matrices, simplifications of the original topology can be obtained by canceling some particular couplings. The locations of cancelled couplings are chosen so as to preserve the electrical response and to provide some hardware simplifications. It is also shown that the resulting simplified topology no longer has the multiple solution property, therefore solving ambiguity problems. The procedure is detailed and demonstrated on two examples.

In this communication, the coupling matrix synthesis of dissipative microwave filters is analyzed and compared to the synthesis of lossless filters. A modified definition of the vector matrix product allows using the same synthesis procedure in both cases. The constraint conditions to obtain a symmetric coupling matrix are also presented in the communication. Finally, a synthesis example is presented to show how the proposed method is used.

Coupling matrix synthesis has been recognized as a widely employed and powerful tool for microwave filter modeling and design. Generally, to obtain a coupling matrix whose topology maps to the actual physical structure, the rotation matrix is used for the matrix reduction and elimination. However, it is difficult to obtain a precise simplified matrix through the rotation matrix method for the corresponding planar resonant circuit filter structure. To overcome the shortcomings of conventional rotation matrices and similar equivalent simplification methods, based on the idea of optimization, we propose a simplification of the coupling matrix using a hybrid optimization algorithm. By the proposed algorithm, a simplified matrix that accurately consistent with the physical structure can be obtained. Firstly, we use the matrix M R that after the conventional equivalent transformation of the coupling matrix as the initial value of the hybrid optimization. Secondly, in order to further obtain the mapped coupling matrix, the scattering parameters corresponding to the coupling matrix is used to calculate the optimization fitness index, and the filter topology is used as the optimization constraint. Then, a global optimization algorithm is used to obtain a matrix M G which is similar to the initial coupling matrix engineering and the matrix structure is similar to the topology of the microwave filter. Finally, use a local optimization algorithm to further iteratively optimize the M G until it converges to meet the engineering accuracy requirements. Then, the simplified matrix M D that is approximately equivalent to the initial coupling matrix and corresponds to the filter topology can be obtained.

An analytical approach for the synthesis of narrow-band lossy filters with arbitrary transmission zeros is proposed in this paper. The scattering parameters are deduced from filtering polynomials once the transmission zeros are assigned. The formulas defining the transformation from scattering matrix to admittance matrix can be used by reconstructing the non-paraconjugate transmission zeros as paraconjugate. A canonical $$N + 2$$ transversal or $$N \times N$$ coupling matrix is then identified using partial fraction expansion of the normalized admittance functions. An increased order of the final network (with respect to the order of the characteristic polynomials) is required for obtaining this result, provided there are non-paraconjugate transmission zeros. Because of its versatility, the proposed approach can also be employed for lossless networks that have a transfer function with symmetrical transmission zeros. Two typical examples are presented to validate the proposed technique.

In this paper, the multiport coupling matrix theory is adopted to represent the performance of OMT, such as return loss, isolation, cross-polarization. The initial values of the corresponding coupling matrix are synthesized according to the specified return loss and bandwidth by ignoring the weak cross couplings, and then the whole coupling matrix is optimized to achieve all the specifications including the cross-polarization and isolation. Two examples of single-band and dual-band OMTs are presented to validate our approach.

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This paper presents a filter design technique of the FM-cavity filter by using the N+2 coupling matrix synthesis. The proposed calculation can be used to predict the frequency response of filter before realizing the cavity filter. The filtering performance of the realized filter shows very low passband insertion loss and also shows good agreement results with the calculated results. The proposed filter can be used in a practical work of an FM transmitting station in order to resolve the RIM problem. The proposed FM-cavity filter can be well used in the FM broadcasting system at any FM station in Thailand.

The generalized Chebyshev (pseudoelliptical) filter functions may not be optimal for certain applications due to physical constrains. With redundancy in filter polynomials, this article breaks down the “mental barrier” in conventional synthesis and directly synthesizes the “Chebyshev-like” functions to achieve desired filter performance under physical limitations. By exploiting the redundant restrictions on exact equal-ripple response, the reflection zeros can be moved to the complex plane, thus forming the “Chebyshev-like functions.” A class of inline filters with a block of second-order dangling resonators is synthesized, which can generate a pair of symmetric transmission zeros (Tzs) but is considered unrealizable using standard Chebyshev functions. With the proposed theories, an accurate and much improved filter prototype is directly derived from the “Chebyshev-like” polynomials, avoiding additional optimization in the design process. For verification, a group of examples with synthesis results are elucidated. Eight ten-pole filters with four Tzs are synthesized and fabricated. The simulated and measured results demonstrate the effectiveness and application of the proposed theories.

This paper presents novel design procedures for a decoupling circuit, utilizing the coupling between antennas. The proposed decoupling circuit consists of, a Band-Stop Filter (BSF) based on Coupling Matrix Synthesis (CMS) theory, a pair of matching circuits, and microstrip connecting lines. By inserting a BSF into an antenna pair, high isolation can be achieved. By utilizing coupling between antennas, the proposed BSF can be designed only using 2 parallel resonators based on the CMS theory. To maintain impedance matching of patch antennas, a pair of matching circuits is inserted after the BSF for each port. Lastly, the decoupling circuit model was fabricated. The experimental results have a good agreement with the simulation result and the validity of the proposed design method is confirmed.