Lossless Two-ports Research Articles

New Design Approach of “3rd - Order Dipole Antenn” Based on Direct Coupled Resonator Bandpass Filter

ABSTRACT In ultra-wideband (UWB) antennas used with the applications of wireless communication systems (WCS), the following five antenna parameters; radiation patterns, directivity, bandwidth, efficiency and antenna gain should be well optimized. A new design approach-based on coupling matrix theory of synthesis antenna has been presented. The most important parameters of this matrix are; external normalized quality factor, normalized un-loaded quality factor, radiation quality factor and coupling coefficients between the resonators. Accuracy in calculating these parameters will greatly facilitate control of the antenna bandwidth to be designed. The design approach included a BPF which was also expanded to become an antenna arrays-filter in the hope of increasing the gain and bandwidth of the antenna. Further, a matching unit is placed between the designed BPF and the antenna, to overcome the mismatching situation, and to achieve a high transmission power. The paper presented a new design approach for an active BPF at frequency “2.45 GHz” and then its integration with a 3rd-order dipole antenna [1]. This design is followed by the creation of another efficient couple-resonant filter (CRF), in which each resonant grid is represented by a radiator. Moreover, a lossless two-port dipole antenna was introduced. Here, each of the poles is integrated with an inductor, to sure that the bipolar antennas can exploit as a resonator. The scores of the simulation-sketches and the computed results were convincing. Finally, the performance efficiency of the designed filter at the resonant frequency 2.45 GHz and for both “H-plane” and “E-plan” were summarized in Table 1.

Robust Digital Filter Structures: A Direct Approach

One of the many contributions of Prof. Fettweis was the invention of wave digital filters. These filters are obtained from classical RLC filters, in particular doubly terminated lossless two-ports, by using some transformations. Namely, the voltages and currents in the circuit elements are transformed into wave-variables and then a bilinear transformation is performed. If the wave transformation is performed appropriately it results in a realizable digital filter structure which furthermore enjoys a number of robustness properties such as low passband sensitivity, low roundoff noise, and freedom from limit cycle oscillations. Prof. Fettweis and his colleagues also showed that these properties are due to the inheritence of passivity properties from the continuous-time domain into the digital filter domain. Subsequent to this landmark work, a number of researchers worked on the problem of obtaining robust digital filter structures without starting from continuoustime circuits. One of these is the structurally bounded or structurally passive class of digital filters. These structures are based on inducing structural passivity directly into the implementation and are therefore simpler, both conceptually and from a practical viewpoint. They are also more general and lead to new structures which have no natural connection to electrical circuits. This paper gives an overview of some of these developments.

Coupling Matrix Synthesis of Nonreciprocal Lossless Two-Port Networks Using Gyrators and Inverters

A coupling matrix technique is presented for the synthesis of nonreciprocal lossless two-port networks. This technique introduces complex inverters to build the nonreciprocal transversal network corresponding to the nonreciprocal coupling matrix. It subsequently transforms this matrix into canonical topologies through complex similarity transformations. The complex inverters in the final topology are transformed into real inverters and gyrators for implementation simplicity. A second-order network example and a fourth-order network example, as well as an experimental validation, are then provided to illustrate the proposed technique. Finally, other possible implementations of the nonreciprocal gyrators are discussed.

Miniaturization of Rat-Race Coupler With Dual-Band Arbitrary Power Divisions Based on Stepped-Impedance Double-Sided Parallel-Strip Line

Generalized equations are presented for the design of a rat-race coupler with a phase inverter and an arbitrary power division, where its four arms are built by symmetric reciprocal lossless two-port networks. According to these equations, uniform- and stepped-impedance rat-race couplers are analyzed and synthesized with dual-band arbitrary power divisions. The relationships between the geometries and the design specifications of proposed dual-band rat-race couplers are completely determined. Under such circumstances, the most compact configuration of the stepped-impedance rat-race coupler is achieved when the maximum allowable impedance ratio is applied for all its arms. Several prototypes are realized with double-sided parallel-strip lines (DSPSLs) and DSPSL phase inverters. As the stepped-impedance arms are not limited to simulate 90° sections and the phase inverters are implemented into our proposed dual-band couplers, the component circumferences are reduced significantly by 65%-70%, in comparison with their conventional 540° counterpart. Their good performances are demonstrated by the simulated and measured results.

Wide-Band Impedance Matching:<tex>$H^infty$</tex>Performance Bounds

This paper presents the first implementation of Helton's H/sup /spl infin// approach to wide-band impedance matching. The prototypical problem is to maximize the transducer power gain uniformly over an operating band for a load connected to a generator by a lossless two-port. The H/sup /spl infin// approach computes the maximum transducer power gain attainable by any lossless two-port uniformly over the operating band. This maximum gain is computed for Fano's classic RLC circuit and an high-frequency antenna represented by measured reflectance data.

Generalized Constraint for a Lossless Multiport Network

This paper presents the generalized constraint conditions for an arbitrary lossless multiport network in partitioned matrix forms, which involve the constraints at magnitudes, phases and determinant of the scattering matrix. The results show that some special properties of a lossless two-port network, such as quasi-reciprocity, quasi-symmetry, and π-convergence of characteristic phases, can be generalized to a lossless N-port network in partitioned matrix forms. Some examples of lossless networks are given to illustrate the application and validity of the proposed approach in this paper.

Comments on "Relationship between group delay and stored energy in microwave filters"

For original paper, see ibid., vol.49, no.1, p.192-6 (2001). In the original paper, it is shown that the time-averaged stored energy in a passive lossless reciprocal symmetrical or antimetrical two-port is proportional to the group delay. The authors point out that some of their results were previously reported in a book by Penfield et al. (1970) and apologize for claiming credit for the work.

Relationship between group delay and stored energy in microwave filters

In this paper, an expression for the time average stored energy (t.a.s.e.) in a passive lossless two-port is derived in terms of its scattering parameters. In particular, it is shown that the t.a.s.e. in a passive lossless reciprocal symmetrical or antimetrical two-port is proportional to the group delay. One implication of this result is that the t.a.s.e., which is linked to the power-handling capability in many passive filters used in practice, is proportional to the group delay of the filter. This rigorous derivation is based on a variational theorem, which has been used in the past to prove energy storage results for passive lossless one-ports and periodic two-ports.

A Real Frequency Approach to Describe Lossless Two-Ports Formed with Mixed Lumped and Distributed Elements

Summary The design of microwave filters, matching networks, amplifiers, that is the “Broadband Networks” with mixed lossless lumped and distributed elements, has been a significant concern of the circuit theoreticians of the field. Yet, there has been no complete practical solution introduced in the literature so far. In this paper, an attempt has been made to design broadband networks constructed with a cascade connection of low pass LC ladders connected with commensurate transmission lines. The new design procedure is based on the two-variable description of the Simplified Real Frequency Technique. Up to five mixed-elements explicit equations are given to describe some selected network topologies. In general, synthesis is carried out employing a decomposition technique first introduced by Alfred Fettweis. A “Double Matching Design” exampleis presented to exhibit the merits and the application of the new approach.

Transmission zeros and the two-port parameters

This paper presents relationships between the transmission zeros of an impedance and the two-port impedance parameters z ij ( s) ( i, j = 1, 2) or the chain parameters of its Darlington equivalent. The odd and even properties of the two-port parameters are investigated. It is shown that z 12( s) and z 21( s) of a lossless two-port network need not be odd functions. A general relationship between the complex-normalized scattering matrix of a two-port network with complex load impedances and the unit-normalized scattering matrix of its augmented two-port network, when the complex load impedances are represented by their Darlington equivalents, is given.

Comments on "An equivalent transformation for the mixed lumped lossless two-port and distributed transmission line"

Stimulated by previous articles by the authors of the above paper [see ibid., vol. 42, p. 272-82, 1994] Finkler and Unbehauen have done related research. In doing so, they have found additional results and synthesis applications. These are communicated here briefly. >

Power-source element and its properties

A power-source element is defined and its properties are studied. The power source describes the output characteristics of the loss-free resistor, as well as high quality rectifiers, some types of switched-mode convertors, and other loss-less two-ports. It is shown that controlled power sources are inherent in the large class of buffered power-conservative two-port networks. This approach has inspired some new realisations and applications of the loss-free resistor. A family of high frequency switched-mode convertors is shown to exhibit naturally power-source output characteristics.

Synthesis of pipelineable complex wave digital filters

A decomposition algorithm is presented for the synthesis of pipelineable, modular, cascade, complex wave (unitary) digital filters (CWDFs) with emphasis on simplicity of implementation. The main features of the algorithm are the following: (1) the extraction step obviates coefficient-form polynomial manipulations and zero-finding operations by using an alternative representation of the canonic polynomials that describe the lossless two-port; (2) first-order sections that effect pipelineability are treated like any other section (they realize a at z/sup /spl minus/1/=0, thus eliminating the need for special treatment; (3) a fully general first-order complex section is derived that can realize a transmission zero anywhere in the z-plane and is the only section required for the cascade decomposition. The algorithm can also be used to synthesize real two-port networks; equivalences are given between a cascade of two complex sections with ke/sup /spl plusmn/jw(0/) zeros and a 2nd-order real section. Also, a method is presented for investigating coefficient quantization effects directly in the z-domain. >

An equivalent transformation for the mixed lumped lossless two-port and distributed transmission line

It is shown that the circuit consisting of a cascade connection of a lumped type D section and a distributed transmission line is transformed to an equivalent circuit consisting of a cascade connection of a class of a nonuniform transmission line and a lumped type D section. Previously obtained equivalent transformations, i.e., Brune, type C, type A and type B sections, are included in the type D section transformation presented in this paper. The type D section is reduced into the Brune section and both type A and B sections are obtained as a degenerate case of the Brune section. Procedures for obtaining these transformations are given and a general theorem concerned with a mixed lumped lossless two-port and distributed transmission line transformation is established. By using these equivalent transformations, a new analytical method for nonuniform transmission lines is derived without having to solve the telegraph equations. >

A numerical method of direct search optimization for parameters of reciprocal lossless two-port network

A numerical method of direct search optimization is presented for calculating parameters of a reciprocal lossless two-port network (RLTPN). Some examples are given. It is pointed out that the results obtained by different methods agree with one another.

On the synthesis of a class of 2-D acausal lossless digital filters

Passive and lossless two-dimensional (2-D) discrete systems of the fully recursive half-plane type are reviewed as one-dimensional (1-D) filters over convolutional algebra. Necessary and sufficient conditions for 2-D transfer functions to be valid scattering as well as immittance description of such systems are obtained. An algorithm for the structurally passive (in fact, lossless) synthesis of filters having such recursive structure is then derived from these representation results as an extension of a recent 1-D Schur-type algorithm for the synthesis of discrete lossless two-ports. Comments on various aspects of design and implementation of such 2-D filters potentially useful in practical problems are also made. >

On a generalized factorization problem for structurally passive synthesis of digital filters

The problem of structurally passive synthesis of multidimensional digital filters of the quarter-plane causal type as an interconnection of more elementary building blocks directly in the discrete domain is addressed by means of the factorization of the chain matrix, the hybrid matrix and the transfer function matrix associated with a prescribed multidimensional lossless two-port. By using recent results on the discrete domain representation of such matrices, a generalized lossless two-port matrix is introduced to present all three factorizations in a unified setting. Necessary and sufficient conditions for factorability as well as an algorithm for computing these factors when they exist are obtained. In particular, it is shown that, in one dimension the factorizations can always be performed. Thus, in one dimension, a discrete domain algorithm for synthesizing previously unpublished internally passive structures and alternative methods of synthesis for more conventional structures such as the cascade structure are also obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Gyrators Application in Power Processing Circuits

The gyrator is a lossless two-port network which transforms one-port networks into its dual with respect to its gyration conductance. For example, capacitance at the gyrator output is viewed as inductance at the input and a voltage source is transformed to a current source.

On the factorization of scattering transfer matrices of multidimensional lossless two-ports

The problem of cascade decomposition of arbitrary bivariate lossless two-ports is addressed via factorization of the associated scattering transfer matrix. Necessary and sufficient conditions for the existence of solution to the factorization problem so formulated, are obtained. It is shown that the criterion for factorability can be expressed in terms of solvability of a set of linear simultaneous equations, which is overdetermined in general. Since no restrictions are imposed on the type of transmission zeros of the given scattering transfer matrix, earlier results in the literature can, in principle, be viewed as special cases of the results obtained here.

A general theory and synthesis procedure for low-sensitivity active RC filters

The fundamental requirements for low-sensitivity analog filter structures are shown to be the bounded-real (BR) property of the transfer function and its implementation by a structure that "preserves" the BR property for incremental changes in the parameters of the network. Using these properties, a low-sensitivity realization of any stable BR analog transfer function is developed. The final structure is in the form of a singly constrained analog active <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> "two-pair" implemented as a cascade of two-pairs where each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The proposed theory is shown to include the class of low sensitivity wave active <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> structures related to the doubly terminated lossless two-ports. The new theory has been verified by computer simulation.