Generalized Nonuniform Transmission Lines

Berger, H.H.

doi:10.1109/tct.1966.1082528

Cited by 23 publications

(8 citation statements)

References 5 publications

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“…There are two routes from original to the equivalent line. Needless to say, Equation (12) corresponds to the route via the intermediary line in the x space, whereas Equation (15) does so via the intermediary line in the space. Note that each operation is reversible.…”

Section: Elastic Equivalent Transformationmentioning

confidence: 99%

“…Equations (14) and (15) have an advantage over Equation (12) that they do not contain both (x) and X ( ). The line generated by Equation (15) is just the generalized line of Berger's work [12] though his intention might have been restricted to exactly solvable lines. Equation (15), however, always gives an equivalent line to the original whether it is exactly solvable or not.…”

Section: General Non-uniform Linesmentioning

confidence: 99%

“…On the basis of Equation (17), an explicit formula is derived for determining (x) from a pair of fused parameters H (x) of the same of an original line and the intermediary line in the x space. Once (x) or its inverse function X ( ) is found, the distributed parameters of the equivalent line are completely determined by invoking Equation (12) or (15).…”

Section: Conditioned Equivalent Line With Speciÿed H (X)mentioning

confidence: 99%

“…Furthermore, a special example with constant distributed series impedance has been presented with respect to the generalized exponential lines. Berger [12] has shown that it is possible to obtain a new exactly solvable line by performing arbitrary change of variable on any known exactly F. KATO the equivalence condition, provides us a technique to generate a line equivalent to the original line by two steps of operations in accordance with an arbitrarily given change of spatial variable. We call the technique 'elastic equivalent transformation' and the change of variable 'elasticity function'.…”

Section: Introductionmentioning

confidence: 99%

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Considerations on the equivalence between non-uniform transmission lines

Kato

2005

Int. J. Circ. Theor. Appl.

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SUMMARYWe investigate the relation of equivalence between non-uniform lossless transmission lines (LC lines or lines, for short) with sectionally smooth distributed parameters (series inductance L(x) and shunt capacitance C(x) per unit length, x being the spatial variable). The equivalence condition is derived by heuristic and well-grounded inference. The condition provides us with the basis on which we can generate by rote a line equivalent to a ÿxed original line according to a speciÿed change of spatial variable (elasticity function). The concept of intermediary lines between a pair of equivalent lines is introduced to enhance precise understanding of the condition and the procedure to generate equivalent lines. In addition, fused parameters are deÿned as a generalization of distributed parameters, in terms of which the argument and formulas are developed in a brief and inclusive manner. It is shown to be possible, on generating equivalent lines, to preassign a fused parameter of the equivalent line or one of the associated intermediary lines instead of specifying the elasticity function. Equivalent lines thus obtained are called conditioned equivalent lines. We discuss how to get conditioned equivalent lines as well as equivalency tests of arbitrarily given pair of LC lines to present some comprehensible and promising methods involving a versatile, graphical technique. We also refer to such interesting topics as a normalization of LC lines, a kind of conservation law of fused parameters between equivalent lines and the scope of realizable characteristics by LC lines conditioned in an arbitrary way. Some formerly known equivalence conditions are located appropriately in the context of our theory. Further, the equivalence condition is shown to be not only su cient but also necessary for LC lines whose distributed parameters may have a ÿnite number of points of discontinuity by invoking a theorem for an inverse scattering problem.

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Section: Elastic Equivalent Transformationmentioning

confidence: 99%

Section: General Non-uniform Linesmentioning

confidence: 99%

Section: Conditioned Equivalent Line With Speciÿed H (X)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Considerations on the equivalence between non-uniform transmission lines

Kato

2005

Int. J. Circ. Theor. Appl.

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“…Berger (1966) [25] took a slightly different approach to the problem. He started with a nonuniform line characterized by Z=A(x) and Y= B(x) which has a known solution:…”

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confidence: 99%

Tapered radio frequency transmission lines

Matarrese¹

2000

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There are other academic disciplines at work here, however. The mathematician, for instance, will enjoy all the mathematical effort which is required to obtain the results of this paper, particularly those of the third chapter. The historian will appreciate the portrait of the early days of communication electronics shown through the references to Heaviside, Carson, Collin, and some of the other "fathers" of the industry, in the second chapter. The test and measurement engineer will take keen interest in the fourth and fifth chapters, which present an overview of design constraints for a tapered transmission line and describe the efforts to measure the performance of a sample line. The breadth of coverage of this project has made the work challenging and rewarding.Special mention must be made of the many people who contributed to this paper.First and foremost, loving thanks to my wife, Robbi, for all the support and hard work, often performing the duties of two parents while I was laboring over the project. Thanks also go to Ed Wardzala, Laudie Doubrava, Bill Schell, and many others at Tektronix for their help, and to Tony Tovar, fellow student at PSU, for his assistance with this paper.

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Very fast design formulas for microwave nonhomogeneous media filters

Bilotti

Toscano

Vegni

1999

Microw. Opt. Technol. Lett.

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In this paper, a new design method for microwave nonhomogeneous media filters is proposed. The application of this method leads to closed‐form design formulas by which physical properties of the filters can be carried out in a very fast way. The proposed formulas can be successfully used because they are less time consuming than others known in the open technical literature. Some examples of analysis and synthesis are presented. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 22: 218–221, 1999.

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Generalized Nonuniform Transmission Lines

Cited by 23 publications

References 5 publications

Considerations on the equivalence between non-uniform transmission lines

Considerations on the equivalence between non-uniform transmission lines

Tapered radio frequency transmission lines

Very fast design formulas for microwave nonhomogeneous media filters

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