Tapered Transmission Line Research Articles

Ultraspherical tapers

Tapered transmission lines for impedance matching at microwave frequencies are obtained from quarter-wave transformers using ultraspherical polynomials. It is shown that a free parameter can be suitably chosen so as to optimise energy transmission.

Low-frequency wide-band impedance matching by exponential transmission lines

It is shown that by using an exponentially tapered transmission line in Ruthroff's connection it is possible to achieve impedance matching at low frequencies over a much wider band than is possible by using a uniform line. For a given ratio of load to source resistances, there is shown to exist an optimum set of line parameters for which the bandwidth obtained is a maximum.

Design of stepped microstrip components

The analysis of the impedance step by the mode matching procedure using a waveguide model for the microstrip line yields an explicit design formula for the frequency-dependent equivalent series inductance. The single-section quarter-wavelength transformer is calculated under the assumption of interacting steps. It turns out that in regard to practical design the neighbouring steps can be considered to be decoupled so that the calculation can be done simply with the results given before. Finally the derived results for the impedance step are used to calculate the scattering matrix of an n-section tapered transmission line. Experimental data show good agreement with theory.

Transient Analysis of Systems with Exponential Transmission Lines

Two computer solutions are given for pulse propagation along exponentially tapered transmission lines with arbitrary nonlinear sending and receiving networks. The solutions allow series and shunt loss terms per unit of length of the line. The method of characteristics is shown to be computationally superior to the cubic spline method in terms of accuracy and efficiency.

Normalized Impedance Graphs for Exponential Transmission Lines (Short Papers)

Sign errors in an existing closed form solution for the reflection coefficient along an exponentially tapered transmission line have been corrected and the solution has been modified by the use of electrical line length. This allows useful graphs for the input impedance of the tapered line to be computed which are normalized with respect to frequency and system impedance. The graphs clearly demonstrate both the broad-band and narrow-band properties of the tapered line.

Distributed RC notch filters based on a circular geometry

The analysis for a distributed RC transmission line based on a circular geometry in which a plane circular resistive sheet is separated from a circular conductor by a dielectric is developed. Connections to this sheet are made using an outer circumferential electrode and an inner central circular electrode. Two types of notch filter are then analyzed, one incorporating a single discrete resistor and having a fixed notch frequency, and a second with a discrete resistor and a discrete capacitor in series combination that has a variable notch frequency. In common with notch filters based on linearly and exponentially tapered transmission lines, the filters described demonstrate improved selectivity compared with zero-tapered lines. The effect of loading that is likely to be encountered in experimental conditions is discussed.

Correction to "A Transmission Line Taper of Improved Design" (Letters)

The optimum tapered transition formulated by Klopfenstein fails to meet the end values of impedance when the transformation ratio is large. A minor correction of Klopfenstein's formula corrects the inconvenience.

Shaping Fast Rise-Time Pulses with Tapered Transmission Lines

For the purpose of checking very fast time-domain reflectometer (TDR) systems it is desirable to have a fast rise-time pulse whose parameters are known. A means for obtaining pulses meeting these requirements has been achieved by suitably tapering the inner conductor of a rigid coaxial transmission line having air dielectric, commonly referred to as an air line. The air line is driven with a pulse that has a very fast rise time compared to the rise time of the expected output pulse. A reflected pulse will be generated whose shape is dependent upon the taper of the inner conductor. A procedure is outlined for determining the proper taper to shape the leading edge of the reflected pulse to match any continuous single-valued function. Air lines that were designed and built for producing a pulse whose leading edge is a linear ramp, a truncated Gaussian function, and the integral of a truncated Gaussian function are discussed and traces of these pulses are shown. The problem of re-reflections due to the multiple discontinuities along the air line was analyzed by means of a computer. This program is described. The effect of the driving-pulse parameters on the reflected pulse is analyzed on a theoretical basis. Rise time, pulse shape, and aberrations such as overshoot and ringing of the driving pulse are considered in this analysis.

Broad-Band Properties of a Class of TEM-Mode Hybrids (Correspondence)

The analysis of a class of N-port TEM-mode hybrids, operating as equal or unequal power dividers or summers, has been extended to include the use of tapered transmission lines. The analysis indicates design limitations on the VSWR and isolation characteristics, and can be applied for arbitrary frequency bandwidth and/or power division ratios. Also included are design graphs and tables that cover some common ranges of power division/summation ratios.

Transmission Line Matching Section with Linear Variation of Characteristic Impedance

The use of a linearly tapered transmission line as a matching section is discussed and the low and high frequency behaviour of the impedance transformer is investigated.

Coupled linearly tapered transmission line directional coupler†

A coupled linearly tapered transmission line directional coupler has been analysed and an asymmetrical directional coupler is shown to possess high pass characteristics.

Comment on "Tapered transmission line computer program using Collin's derivation"

Impedance versus distance data are provided on a -8.34 dB tapered coupler suitable for use in a broad-band -3 dB magic tee, correcting data previously presented by Fuchs.

Linearly Tapered Transmission Line and Its Application in Microwaves (Correspondence)

Linearly Tapered Transmission Line and Its Application in Microwaves (Correspondence)

Tapered transmission line computer program using Collin's derivation

Collin's synthesis of the equal ripple transmission line is shown to be computationally identical with Klopfenstein's synthesis. A simple computer program for computing impedance versus length of a tapered line is given, based on Collin's work.

Realizability Conditions for the Impedance Function of the Lossless Tapered Transmission Line-A Critique

In a recent brief <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> in the B.S.T.J., Zador presents, without proof, realizability conditions for the input impedance of the lossless tapered transmission line terminated in unit resistance. Upon a careful examination of the brief, it appears that the conditions are not accurate. The following analysis clarifies this point and, incidentally, provides alternatives to Zador's necessary conditions.

Fluid Pressure Transients in a Tapered Transmission Line

Previous investigations have shown that a liquid-filled tapered tube can be used as a transformer for amplifying or reducing the magnitude of input pulses of pressure and volume flux, but the output pulse becomes distorted, depending on the geometry of the taper. The principal objective of this paper is to present and illustrate a method for the determination of the output from liquid-filled tapered tubes subjected to step, pulse, and time-dependent inputs of pressure and volume flux. Several output results are also included to illustrate the effect of the input condition and the taper function. The model considered consists of a rigid tapered tube terminated by a very long uniform line and filled with an inviscid liquid. The input is applied to the entrance of the tapered tube while the output is taken as the terminal end of the tapered section or entrance to the long uniform line.

The linearly tapered transmission line as a matching section—High- and low-frequency behavior

The linearly tapered transmission line is very attractive as a matching section because it is the simplest and easiest to fabricate. It is shown that the high- and low-frequency behavior of the reflection coefficient is strongly frequency dependent.

Realizability Conditions for the Impedance Function of the Lossless Tapered Transmission Line

In the study of tapered transmission lines or accoustical horns, an unsolved problem of great practical interest is the determination of the taper function (inductance or capacitance per unit length as a function of distance; it is assumed that the product of these quantities is unity) for the structure which will possess a prescribed driving point impedance function. For the case where the structure may be modeled by a cascade of sections of uniform transmission line segments, physical realizability conditions and a synthesis procedure have been given by B. K. Kinariwala. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> For the case of continuous taper no results of a general nature are known.

Appoximate analysis of lossless tapered transmission lines with arbitrary terminations

Appoximate analysis of lossless tapered transmission lines with arbitrary terminations

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).