Theory Of Nonuniform Transmission Lines Research Articles

Scattering from Spheres: A New Look into an Old Problem.

In this work, we introduce a theoretical framework to describe the scattering from spheres. In our proposed framework, the total field in the outer medium is decomposed in terms of inward and outward electromagnetic fields, rather than in terms of incident and scattered fields, as in the classical Lorenz–Mie formulation. The fields are expressed as series of spherical harmonics, whose combination weights can be interpreted as reflection and transmission coefficients, which provides an intuitive understanding of the propagation and scattering phenomena. Our formulation extends the previously proposed theory of non-uniform transmission lines by introducing an expression for impedance transfer, which yields a closed-form solution for the fields inside and outside the sphere. The power transmitted in and scattered by the sphere can be also evaluated with a simple closed-form expression and related with the modulus of the reflection coefficient. We showed that our method is fully consistent with the classical Mie scattering theory. We also showed that our method can provide an intuitive physical interpretation of electromagnetic scattering in terms of impedance matching and resonances, and that it is especially useful for the case of inward traveling spherical waves generated by sources surrounding the scatterer.

The Research on the Establishment and Simulation of Intelligent Drill String Cables Based on Nonuniform Transmission Line Theory

The cable transmission line has more obvious advantages in long-distance information transmission, and is suitable for the transmission of various MWD signals during drilling. The research on the information transmission pattern of the cable transmission line will be the focus of intelligent drill string. According to the characters of the intelligent drill string, combing with the nonuniform transmission line theory, and considering the effect of temperature variation on the impedance of the smart drill string, the distribution parameters of the cable transmission line has been analyzed. On the basis of the two port network system, the transfer function and the transport matrix of the nonuniform transmission line have been obtained, and the model of nonuniform transmission line impedance of the intelligent drill string cable has been established. In order to verify the feasibility of the established model, the communication channel model has been built utilizing the MATLAB/Simulink software. Through experiment simulation and result analysis, the error rate curves under different parameters have been obtained, the transmission rate and transmission distance of different signals have been explored, and the influence of modulation and demodulation on data transmission quality has been studied, which provides a certain reference for the information transmission pattern of the intelligent drill string.

Close electric fields and lightning-induced voltages predicted by a return-stroke model including corona and nonlinear channel resistance

In this paper, a return-stroke model based on nonuniform transmission line theory that includes nonlinear losses and corona is used for calculating close electric fields and lightning-induced voltages on an overhead line. A study is performed to identify the influence of return-stroke corona on close electric fields and line overvoltages considering different model assumptions. It is shown that the consideration of corona affects the attenuation and distortion of the return-stroke current. Close vertical electric fields predicted by the model present waveforms, peak values, and decay with distance that are in agreement with measured data. A simpler case in which the return-stroke speed is artificially set to a prescribed value by controlling the inductance and capacitance of the channel is shown to lead to results that are in agreement with the complete return-stroke model considering nonlinear losses and corona. Similar conclusions apply to popular engineering return-stroke models typically used in lightning-induced voltage calculations provided the return-stroke speed is suitably adjusted. It is also shown that lightning-induced voltages calculated with the considered model are in good agreement with experimental data.

Three-Dimensional FEM Approach to Model Twisted Wire Pair Cables

A study to model an unshielded twisted wire pair (TWP) cable above-ground plane is presented. The TWP line is discretized into small sections of line which are analyzed by the 3-D finite-element method in order to extract the equivalent multiport network suitable for circuit analysis. The method is compared with the theory of nonuniform transmission lines and with the method of moments. A set of experimental results is finally carried out in order to validate the calculations

Full‐wave FDTD design and analysis of wideband microstrip‐to‐waveguide transitions

AbstractWideband transitions are designed and analysed by using two different approaches of the finite‐difference time‐domain (FDTD) method, in combination with the theory of nonuniform transmission lines. These transitions consist of a ridged waveguide‐based taper between a shielded microstrip and a standard X‐band rectangular waveguide. In the first step, a full‐wave 2D‐FDTD scheme is used to calculate the dispersion characteristics, as well as the geometry dependence of the impedance in the double ridged waveguide. Once these design curves have been obtained, the stepped transmission line transformer theory is used to design the tapers. In a former step, the nonuniform 3D‐FDTD technique is applied, the transitions are simulated and the method is validated. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 317–320, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11048

Tapered stripline embedded in inhomogeneous media as microwave matching line

A novel design method for a stripline microwave matching line is developed in this paper. Striplines considered have a tapered inner conductor embedded in an inhomogeneous dielectric material with continuous spatial variation of the relative permittivity. The employment of this kind of waveguide, as it is shown in this paper, ensures good matching properties in a wide frequency range. These matching properties can be controlled by means of two different factors: the taper of the stripline inner conductor and the relative permittivity spatial variation of the dielectric material filling the stripline. Starting from the nonuniform transmission-line theory, a novel closed analytical form for the input reflection coefficient of such lines is derived, and design formulas for the matching line are carried out. Finally, several applications that show the capability, flexibility, and fastness of the developed synthesis method are presented.

A New Stripline High Pass Filter Layout

A new kind of stripline microwave high pass filter is proposed in this paper. Striplines here used have a tapered inner conductor and are filled by inhomogeneous dielectric materials with continuous spatial variation of the refraction index. Thus, filtering properties of such components can be controlled by means of two different keys: the inner conductor taper and the refraction index spatial variation of the dielectric material filling the stripline. A design method for such a filter is carried out starting from the generalized nonuniform transmission line theory by which a novel closed analytical form for the input reflection coefficient is derived. This closed form allows to obtain straightforwardly the design formulas for the high pass filters. Finally, some applications that show the capability of the new filter here proposed and the fastness of the developed synthesis method are presented.

On the formal theory of nonuniform transmission lines

Some results are given in the formal theory of nonuniform transmission lines whose constitutive parameters are bounded measurable functions of the geometric abscissa <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</tex> and holomorphic functions of the complex variable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> in some region <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> of the complex plane.

Electromagnetic scattering from a radially inhomogeneous sphere

The generalization of the Lorenz-Mie theory for scattering from a homogeneous sphere to a radially inhomogeneous sphere is given. In this case, the scatterer consists of a spherical body with any number of concentric homogeneous regions. The treatment makes use of the analogy with non-uniform transmission line theory.

The Nonuniform Transmission Line as a Broadband Termination

The problem of obtaining a broadband microwave termination is considered from the point of view of nonuniform transmission line theory. Attention is restricted to lines in which only the distributed shunt admittance may be varied. An optimization argument is presented which leads to the consideration of a line in which the fractional increase in admittance per wavelength in the line is constant. The nonuniform transmission line equations are solved exactly for this case, and the results are expressed in terms of readily interpretable elementary functions. It is shown that a fixed geometrical length of line can lead to an arbitrarily large effective length without destroying the match at the input. The introduction of a small loss term makes the line almost totally absorbing regardless of its termination. The line has a long-wavelength cutoff given by 4Π times the actual length of the line. If the line is short-circuited at its far end, a return loss of greater than 11.4 db is obtained at all frequencies above twice the cutoff frequency. The effect of certain practical limitations on the performance of this line is also discussed.

Outline of a theory of non-uniform transmission lines

Complex differential equations relating to non-uniform transmission lines are studied, and the corresponding two-parameter families of solution curves are investigated with the aim of establishing some important properties, e.g. the relationship which exists between the singular points of the differential equation for the normalized impedance and the non-reflective impedances of the corresponding non-uniform line. Because of this relationship it is possible to determine the non-reflective impedances of an arbitrary tapered line by purely algebraical method and to construct the tangents to the impedance loci at a given point of the impedance plane. Moreover, reflection and transmission coefficients are uniquely determined by the singularities, and differential equations can be readily deduced for these coefficients. Methods of synthesis of non-uniform lines are also indicated.