Synthesis Of Transmission Lines Research Articles

An inverse scattering framework for several problems in signal processing

The aim of this paper is to show that a general inverse scattering formulation illuminates alternative, computationally efficient solution methods for several classes of signal processing problems. Inverse scattering problems arise in physics, transmission-line synthesis, geophysics and acoustics and in one class of formulations they require a procedure to determine the parameters of a layered wave propagation medium from measurements taken at the boundary. There exists a close relationship between the physical inverse scattering problems and some important issues in signal processing such as the design of digital filters, the development of linear prediction algorithms and their lattice filter implementations and cascade synthesis of systems with a given impulse response (realization problems). For many of these problems several efficient algorithms already exist in the literature, but the connection between the different solutions was not always clear. Recently, the push to VLSI implementations led to the realization that, in spite of their apparent similarity, the alternative algorithms possess radically different properties when, say, a parallel implementation is sought. In this paper we shall show that alternative procedures that are usually arrived at by various clever tricks, in fact correpond to two conceptually extremely simple, basic ways of solving inverse scattering problems: the so called layer-peeling and layer-adjoining methods. Examples include the Schur vs Levinson methods for determining the optimal filters for prediction of stationary stochastic processes, and the generalized Lanczos vs Berlekamp-Massey methods for the partial realization (Pade approximation) problem, and also several recent design procedures for some classes of digital filters.

Analogue-numerical approach to conformal mapping

A highly efficient engineering approach is described for the calculation of capacitance using the Schwarz—Christoffel equation but which avoids the need for complicated mathematical analysis. The method is suitable for the analysis and synthesis of transmission lines.

Cascade synthesis of transmission lines and lossless lumped networks

Considerable interest in mixed lumped/distributed networks has arisen in recent years. The use of semiconductor elements, which have essentially lumped equivalent circuits, in microwave networks is an obvious example, and the need to meet even more exacting filter specifications at ever higher frequencies has resulted in many problems which are essentially mixed lumped/distributed. In most applications, the cascade type of structure is required, and it has been claimed that the sufficient condition for a 2-variable bounded real reflection coefficient to be realised by a resistively terminated cascade of lossless transmission lines and lumped 2-ports is that the transmission zeros are the product of the transmission zeros of the basic sections. Primarily by a particular numerical example, it is shown that this result is not generally valid for a canonic cascade realisation. This result is because of the possibility of ‘dummy’ sections existing within the network without violating the bounded-real condition at the terminals. Consideration of the existence of ‘dummy’ sections leads to the conclusion that an additional n(n−1)/2 conditions are required, where n is the number of transmission matrices for both terminated and unterminated networks. Additional conditions for reciprocity etc. are given in the realisability conditions, which are entirely algebraic in nature.

An Improved Design of Waveguide Band-Rejection Filters

The usual design technique for waveguide band-rejection filters uses narrow-band approximations and thus discrepancies generally exist between the designed and measured response, particularly in the fairly wide passband. Nevertheless, this design technique has been used because of its simplicity and because the filter configurations obtained are relatively simple. Lately, a new design technique using transmission line synthesis became available which, theoretically, would yield the desired response. However, the physical realization results in a complicated configuration which leads to certain practical problems. This paper presents a modified technique which simplifies the structure without sacrificing performance. With this modification the design procedure becomes very simple and many of the practical problems can be avoided. This paper gives precise design information and convenient design formulas. Furthermore, it shows that excellent agreement between the designed and measured response can be achieved.

Least-Weighted-Square Method for Analysis and Synthesis of Transmission Lines

Analysis and synthesis of transmission lines of arbitrary geometry are not easy to realize with currently available methods. The object of this paper is to show that by introducing a new principle to be called the "least-weighted-square invariance deformation," it is possible to solve transmission line problems to desired orders of accuracy. A procedure based on this principle is given for deforming a given transmission line geometry keeping the characteristic impedance an invariant, or for synthesizing a transmission line cross-sectional geometry corresponding to the given constant parameters of the structure. The method is applied to the analysis of transmission lines having a regular polygonal outer conductor and a circular inner conductor. An application to a representative situation in synthesis is also described.

Multiplicity Line in Cascade Transmission Synthesis---Part II

The first portion of this paper related to an examination of the synthesis of cascade transmission line structures providing a polynomial insertion loss function phrased in terms of the cosine of an electrical length. Certain features of nonuniqueness of the synthesis were uncovered which, particularly in the case of couplers, lead to a flexibility in design. This portion of the paper includes a specific examination of couplers and concludes with some general comments on transmission line synthesis.

Application of Sampling Theorem to the Synthesis of Transmission Line Tapers and Antenna Radiation Patterns (Correspondence)

In this note it is demonstrated how the sampling theorem may be used to reduce the problems of transmission line taper synthesis and antenna aperture field synthesis to that of optimizing a polynomial. In both cases the problem may be stated mathematically in the following form: find the function g(x) which is zero outside the domain - /spl pi//spl les/x/spl les//spl pi/ that will yield a desired f(u) where f(u) is given by the fourier transform of g(x).