Complex Transmission Zeros Research Articles

Frequency-Variant Double-Zero Single-Pole Reactive Coupling Networks for Coupled-Resonator Microwave Bandpass Filters

In this work, a family of frequency-variant reactive coupling (FVRCAFVC) networks is introduced and discussed as new building blocks for the synthesis of coupled-resonator bandpass filters with real or complex transmission zeros (TZs). The FVRCAFVC is a type of nonideal frequency-dependent inverter that has nonzero elements on the diagonal of the impedance matrix, along with a nonlinear frequency-variation profile of its transimpedance parameter. The distinctive feature of these new FVRCsAFVC is that they can be modeled with a simple bridged-T network consisting of four reactive elements. Such FVRCsAFVCs can introduce one pole and up to two TZs—so that they are referred to as double-zero single-pole (DZSP) networks. DZSP networks allow the pole to be located above, below, or in-between the TZs. Depending on the choice of the elements in the bridged-T circuit, the position of the TZs and the pole can be controlled independently. The coupling matrix for filters with DZSP networks can be found by solving an inverse-structured nonlinear eigenvalue problem (ISNEVP). Examples of possible implementations of DZSP couplingAFVC networks are provided for both lumped and quasi-lumped-element circuits, as well as for transmission-line-based and waveguide technologies. The application of DZSP coupling networks to the design of microwave bandpass filters with generalized Chebyshev-type characteristics is illustrated by means of the synthesis of three microstrips and two waveguide coupled-resonator bandpass filters. The waveguide filters are verified through electromagnetic (EM) simulations and the microstrip filters are manufactured and characterized for proof-of-concept demonstration purposes, showing a fairly close agreement between EM simulations and measurements.

Novel Topology and Design for Wideband Bandpass Filter With Frequency- and Attenuation-Reconfigurable In-Band Notch

A novel topology and the design method are proposed for a wideband bandpass filter (BPF) with frequency- and attenuation-reconfigurable in-band notch by engineering the complex frequencies of transmission zeros. The proposed topology consists of a fifth-order wideband BPF and two coupled notch resonators. With the two coupled notch resonators, a pair of complex in-band transmission zeros are formed. By controlling the frequency difference between the two notch resonators, a frequency- and attenuation-reconfigurable notch can be obtained in the passband of the wideband BPF. A matrix analysis method is presented to characterize the frequency- and attenuation-tunable in-band notch precisely. The relationship between complex transmission zeros and in-band attenuation is also investigated. To demonstrate the proposed techniques, a prototype using microstrip and evanescent mode resonators is designed and fabricated. The proposed wideband BPF exhibits a reconfigurable in-band notch with frequency tuning from 1.494 to 2.004 GHz and attenuation tuning from 2 to 79 dB. The simulated and measured results are in good agreement with each other, validating the proposed design and method.

RF Multi-Functional Input-Reflectionless Dispersive-Delay Structure With Sharp-Rejection Filtering Using Channelization Techniques

A class of RF multi-functional input-reflectionless dispersive-delay structure (DDS) with linear-type in-band group-delay variation and sharp-rejection bandpass-filtering capability is reported. It exploits a two-branch-channelized/balanced-type circuit with similar low-order reflective DDS units inside its channels, which are connected through input/output 3-dB quadrature wideband couplers. The adopted DDS unit is based on a coupled-resonator network with a frequency-dependent cross-coupling. It introduces a pair of complex transmission zeros (TZs) to shape the intended in-band group-delay profile. Unequal transmission-line-based phase-shifting sections are also inserted at the outputs of both channels. In this manner, an input-absorptive behavior and selectivity enhancement with TZ generation are attained by means of transversal signal-interference techniques at the overall input and output nodes, respectively. Moreover, as the transfer-function phase term of the interference action in transmission is linear with frequency, the total group-delay pattern is defined by the DDS unit of the channels. As practical validation, a 1.5-GHz proof-of-concept microstrip prototype is constructed and tested.

Dispersive Delay Structures With Asymmetric Arbitrary Group-Delay Response Using Coupled-Resonator Networks With Frequency-Variant Couplings

This article reports the design of coupled-resonator-based microwave dispersive delay structures (DDSs) with arbitrary asymmetric-type group delay response. The design process exploits a coupling matrix representation of the DDS circuit as a network of resonators with frequency-variant couplings (FVCs). The group delay response is shaped using complex transmission zeros (TZs) created by dispersive cross-couplings. We also present an optimization-based synthesis procedure for characteristic polynomials with a prescribed group delay profile. Thus, when compared with prior-art DDS approaches, the proposed DDS solutions allow a general group delay profile to be patterned while incorporating optimization-based coupling matrix design techniques for their synthesis. The design method is validated by full-wave simulations and measurements of three built proof-of-concept prototypes of DDS devices with different shapes of group delay response in waveguide and microstrip technologies.

Techniques for the generation of multiple additional transmission zeros in H-plane waveguide filters

AbstractIn this paper, different techniques for the generation of additional transmission zeros (TZs) in planar waveguide filters are investigated. In the classical theory, TZs are generated only by destructive interference of non-adjacent cavities, limiting the available number of TZs to the filter order itself. However, more approaches for the generation of TZs are known, including bypass-coupling in oversized cavities, frequency-dependent coupling apertures as well as dispersive/resonant TZs which can be realized by the direct source to load cross-coupling. The aim of this paper is to combine several of the strategies in one physical filter set-up to increase the maximal number of TZs beyond the filter order. Different Ku-band fourth-order filter set-ups are presented, showing in total between six and eight real as well as complex TZs. Three filters are manufactured as a proof of concept and compared with the simulation, showing very good agreement.

Filter design for folded canonical topologies based on equivalent circuit segmentation

This paper presents a methodology to design filters with folded canonical topologies, which implement cross couplings between non-adjacent resonators. The technique is based on segmenting the traditional coupling matrix in a step-by-step fashion. At each step, a subset of the whole physical structure is optimized to match the response of the corresponding segment of the coupling matrix. In the context of this design technique, in this paper we propose an efficient segmentation methodology of the coupling matrix based on multiport networks. The use of multiport networks allows to generate at each step several goal functions, which are simultaneously used during the optimization of the corresponding physical segment. These multiport networks allow to efficiently monitor the different paths of the signal, present in folded canonical topologies. It is shown that this strategy leads to a fast convergence of the step-by-step segmentation technique for the design of this type of coupling topologies. We apply the proposed methodology to the design of two filters using the quartet topology. The first filter has two transmission zeros placed at the real frequency axis, and the second one has two complex transmission zeros intended for group delay equalization. The results indicate that the proposed methodology is effective for the design of this type of coupling topologies, leading to initial dimensions for the filters that typically have less than 1% of error when they are compared with those obtained from a final global optimization.

Fast Design of IIR Digital Filters With a General Chebyshev Characteristic

In this brief, a fast design technique based on a multiband mapping relation is discussed for infinite-impulse-response digital filters with a general Chebyshev characteristic, which is suitable for single- and multiband operations. Each bandwidth and the ripple in it can be accurately controlled. Without increasing the order of the filters, the out-of-band performance of the filters can be easily adjusted by appropriately placing transmission zeros wherever they are desired. In addition, complex transmission zeros can also be introduced to improve the group delay to some extent. The proposed technique is analytical and easy to implement.

A Linear Phase Filter in Quadruplet Topology With Frequency-Dependent Couplings

This letter presents a design of a linear phase microwave bandpass filter. The filter is composed of four resonators arranged in the quadruplet topology. Making the cross and one direct coupling dispersive gives additional design flexibility. The first advantage of using frequency-dependent couplings is the possibility to chose an arbitrary location of a pair of complex transmission zeros (TZs) in the s-domain. The second one is the presence of an additional imaginary transmission zero that improves the filter selectivity. We provide a proof-of-concept design of a filter using substrate integrated waveguide (SIW) technology. The frequency-dependent couplings are implemented in SIW as a composition of both: an inductive part realized in a form of an H-plane iris and a capacitive part realized as a grounded coplanar waveguide (GCPW). The measured filter characteristics prove the validity of the model.

Quantitative Analysis of Transmission Zeros in Cross-Coupled Two-Port Power Systems

In this paper, we present a practical and quantitative method for theoretical determination of the complex transmission zero locations of lumped two-port power systems. We have derived several closed-forms of transmission zero characteristic equations in order to prove an important result – that the integer pairs of complex transmission zeros originate solely from the cross-coupled portion of the system.

A New Coupling Matrix Extracting Method From the Frequency Response

Coupled resonators are widely used in many applications, especially for filters. It is necessary to know the coupling matrix of those resonators in order to further modify and/or optimize the existing design. In recent years, many efforts have been made to generate a coupling matrix. In this paper, a new method is proposed, which can be applied for both the synchronous and asynchronous coupled resonators. With this method, the eigenvalues and eigenvectors of the coupling matrix can be generated directly from the simulated frequency responses, and the coupling matrix can then be determined. Typical examples are illustrated for the cases such as a quadruplet with an image, real, or complex transmission zeros. The impact of loss is also discussed. As a matter of fact, this method has been successfully used in the design of high-temperature superconducting filters

Frequency transform synthesis method for cross-coupled resonator bandpass filters

In this letter, an improved synthesis method for equal-ripple cross-coupled resonator bandpass filter is proposed based on the frequency transform method and Atia's method. In this method, the conventional lowpass prototype method is revised by replacing the low pass prototype with the frequency transform method. The detailed element extraction procedure in z-domain is given. Also the coupling matrix reduction implemented by optimization algorithm is described. This method is powerful for filter synthesis with asymmetric frequency response and complex transmission zeros. The design examples are presented and the experimental results validate its effectiveness.

A self‐equalization band pass filter involving complex transmission zeros and its equivalent circuit in the Foster type circuit

AbstractThis paper proposes a design method for a bandpass filter with characteristics close to ideal ones in which the amplitude and group delays are simultaneously flat in the passband and selectivity is assured in the stopband by means of an attenuation pole. In the present approach, first a method of designing the network function of a low pass prototype is proposed in which the group delay and the amplitude can be made flat at the same time over the same bandwidth by means of self‐equalizationThis refers to equalization carried out by the design of only the network function without an external equalizer. using complex transmission zeros. It is shown that a circuit network with this characteristic can be synthesized by a Foster type circuit. Further, it is shown that degradation of the group delay, which is unavoidable in conventional methods, can now be suppressed if frequency transformation is carried out directly to the individual circuit elements in the Foster type circuit. By means of this frequency transformation, a Foster type equivalent circuit is derived for a bandpass filter which faithfully performs frequency shifting of the characteristic of the low pass prototype. As a design example, a bandpass filter is presented in which a ninth‐order Bessel filter is self‐equalized by a set of complex transmission zeros and a set of transmission zeros on the imaginary axis. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 88(4): 54–61, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20086

A revision of cascade synthesis theory covering cross-coupled filters

The classical zero-shifting technique is generalized to cover extraction of complex transmission zeros (TZs) in the form of fourth-order LC sections whereby the j/spl omega/- and /spl alpha/-axis TZs appear as special cases. Using this approach, bandpass filters can be synthesized in direct coupled resonator forms by pole placement instead of designing them through low-pass prototypes. By using circuit transformations, the resulting direct coupled resonator filter circuits can then be transformed into a variety of cross-coupled forms like a fully cross-coupled form or cascaded N-tuplet form. It is shown that one or more finite j/spl omega/-axis, /spl alpha/-axis, or complex TZs can be extracted as direct coupled resonator circuit blocks, which can be converted into cross-coupled triplets, quadruplets, or other N-tuplets of resonators. In particular, it is shown that a cascaded quadruplet section can be used to realize a complex TZ quadruplet S/sub i/ = /spl plusmn//spl sigma//sub i/ /spl plusmn/j/spl omega//sub i/, as well as two pairs of j/spl omega/-axis TZs, S/sub i/ = /spl plusmn/j/spl omega//sub i/, and S/sub k/ = /spl plusmn/j/spl omega//sub k/.

A CAD METHOD FOR THE DESIGN OF A DOUBLY-MATCHED BROADBAND NETWORK HAVING COMPLEX TRANSMISSION ZEROS

In this paper, it is shown that in the solution of the double matching problem given by Carlin and Yarman there does not exist a one-to-one correspondence between the output impedance Zq(s) and the transducer power gain function when the matching network contains the complex transmission zeros contributed by the common factors of the numerator and denominator of Zq(s). Also Youla’s conditions imposed on the chain parameters are extended and applied to the passive, lumped, lossless, and nonreciprocal two-port networks. Based on the above discussion, a CAD method using the chain parameters is proposed to solve the double matching problem where the equalizer may have complex transmission zeros. The result permits us to design a general doubly-matched network, the amplitude and phase of which are both required to be matched. Finally, an example is given to describe the iterative approximation process and its computations.

Synthesis of arbitrary digital transfer functions using allpass-based structures derived via LBR two-pair extraction procedure

The implementation of a digital filter transfer function with all transmission zeros on the unit circle is developed via the synthesis of an appropriate allpass function. The synthesis procedure is based on the “LBR-extraction” approach. The resulting structure is in the form of a doubly terminated cascade of lossless (LBR) two-pairs, with each two-pair realizing a single real or a pair of complex transmission zeros. The Concepts of complete and partial “1” removals, and “1” shifting are introduced and utilized during the synthesis process. The resulting structures have several properties in common with the Gray and Markel lattice filters, but do not require tap coefficients for numerator realization. The building blocks used in this paper are similar to those in certain wave-digital filters and orthogonal filters.

Generalised lattice transformation for crystal filters

Crystal lattice filters are usually based on the transformation of a lowpass Brune section to a second-order lattice section. This letter describes a generalisation, which transforms n Brune sections simultaneously into a lattice of order 2n, and which offers advantages for high-order filters, or filters with complex transmission zeros.

Synthesis of a class of lossy ladder networks

A method is described for synthesising ladder networks in which each element may be assigned arbitrary loss, within limits. The networks may be terminated in resistances at one or both ends or they may be terminated in impedances consisting of a resistance and inductance in parallel. The networks are of the Cauer ladder type in which the transfer characteristics realised are rational functions possessing complex transmission zeros.

Some recent advances in integrated crystal filters

Integrated crystal filters-monolithic, tandem monolithic, and hybrid monolithic (polylithic) quartz crystal filters-are widely used in HF, VHF, UHF, and satellite communications equipments, in both commercial and military, in telephone FDM equipment, and in a number of other applications including frequency synthesizers and airborne navigation aids. Frequencies range from 5 to 180 MHz and occasionally to 250 MHz. Maximum inductorless bandwidths are usually 0.25 to 0.35 percent of center frequency below about 30-35 MHz and less at higher frequencies where overtones must be used. In the past decade, piezoelectric resonator theory has been extended to model accurately the linear and nonlinear behavior of monolithic filter devices. While most integrated crystal filters are all-pole networks, techniques for the design of filters with real and complex frequency transmission zeros are finding increasing application. A number of examples of current production filters are presented.

Synthesis of recursive digital filters with prescribed attenuation and group-delay characteristics

A method of synthesizing recursive digital filters with pre- where scribed attenuation and group-delay characteristics is presented. The method depends on the fact that the introduction of complex transmission zeros into the transfer function of the filter network allows independent control of both attenuation and group-delay responses of the filter. An example is presented which clearly demonstrates the improvement in attenuation response obtained when complex transmission zeros are introduced into the transfer function of the filter.

The jaumann structure in wave‐digital filters

AbstractThis paper deals with an extension of the wave‐digital filter structures introduced by Fettweis.A new structure is introduced, viz, the digital translation of the Jaumann structure. The Jaumann structure is a well‐known canonical realization of analogue, symmetric, grounded lossless two‐port networks. With this structure, transfer functions with complex transmission zeros can be obtained in a wave‐digital realization, which is not possible by means of a wave‐digital ladder filter. Two examples are given, one of which has been implemented using TTL digital integrated circuits showing excellent properties.