An efficient dynamic analysis of non-uniform microstrip transmission lines

This paper presents a novel time-domain integration method for transient analysis of nonuniform multiconductor transmission lines (MTLs). It can solve the time response of various kinds of transmission lines with arbitrary coupling status. The spatial discretization in this method is the same as the finite-difference time-domain (FDTD) algorithm. However, in order to eliminate the Courant-Friedrich-Levy condition constraint, a precise time-step integration method is utilized in time-domain calculation. It gives an analytical solution in the time domain for the spatial discretized Telegrapher's equations with linear boundary conditions. Large time steps can be adopted in the integration process to achieve accurate results efficiently. In the analysis of transmission lines with frequency-dependent parameters, a passive equivalent model is introduced, which leads to the similar semidiscrete model as that for the frequency-independent case. In addition, a rigorous proof of the passivity of the model is provided. Numerical examples are presented to demonstrate the accuracy and stability of the proposed method.

The nonuniform transmission line is traditionally modeled and analyzed in the frequency domain. However, it is difficult to characterize and simulate nonuniform lossy transmission lines accurately in the time domain. A highly accurate and general approach for time domain analysis of lossy inhomogeneous transmission lines is described. The propagator method presented is an exact solution to the lossy telegrapher's equations based on the modal matrix technique. Simpson's rule is applied to produce a remarkably accurate numerically compatible result. An exponentially tapered transmission line example shows that this method is not only simple and efficient, but also an accurate technique for analyzing lossy nonuniform transmission lines with minimal numerical dispersion. Multiple sectioned transmission lines can be handled by a straightforward application of the presented equations.

The vast majority of nonuniform transmission lines are no analytical solution except for a few special forms of transmission line. Dividing nonuniform transmission line into several equal parts, then each part can be regarded as uniform transmission line approximately. Using the theory of uniform transmission line to analyze nonuniform transmission line's transient response is the commonly used method. Composite Simpson's rule for transient analysis of nonuniform transmission lines is proposed in this paper. The exponential transmission matrix of nonuniform transmission line's equation is transformed into a general algebraic equation, which greatly simplifies the analysis on transient response for nonuniform transmission line. The simulation results illustrate the accuracy of the presented approach with examples.

Based on the reciprocity theorem, a simple method for the analysis of the radiated electromagnetic fields from a arbitrary nonuniform lossless transmission line with a linear termination is presented. The radiation problem is solved using the known solution of the coupling problem. The method of the solution for the coupling problem in nonuniform transmission lines is based on the steplines approximation of the nonuniform transmission line and quasi-TEM assumptions. An example of nonuniform transmission line is then solved to show the capabilities of the present method.

Transient analysis of nonuniform lossy transmission lines with frequency dependent parameters

In this paper, a discrete time-domain method to analyze multiple coupled nonuniform lossless transmission lines has been presented. The solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation, the system of coupled nonuniform transmission lines is decomposed into a large number of coupled steplines with different characteristics. Then, using modal decomposition method, the system of coupled partial differential equations for each step is decomposed to a set of uncoupled ordinary wave equation. Using time-domain approach and invoking the boundary condition at the discontinuities of the adjacent steps, each step is modeled as continuous time linear filter characterized by a time-domain transfer matrix. Finally, this continuous time linear filter (for band limited input signal), is modeled as a discrete time-domain linear filter with constant matrix coefficients using sampling theorem. The method proposed here can be implemented using general purpose software packages like MATLAB.

Nonuniform transmission lines are encountered in high-speed VLSI circuits due to complex interconnect geometries and nonuniform electromagnetic coupling. Analysis of arbitrary nonuniform coupling advocates the need for a general and efficient numerical technique. This paper presents the analysis of coupled multiconductor lossy nonuniform transmission lines, using the highly efficient Asymptotic Waveform Evaluation technique.

In this work a simplified model for the simulation of electromagnetic transients on non-uniform multiconductor transmission lines is presented. The proposed model is based on the method of characteristics of partial differential equations theory. Using the method of characteristics to rigorously model nonuniform multiconductor transmission lines requires calculating the space derivatives of the modal transformation matrices. Since such derivatives are calculated numerically, the method can become prone to numerical oscillations. The new procedure presented here does not require the space derivatives, therefore is less prone to numerical oscillations and leads to computing time savings. Results obtained with the proposed model are compared with those from the numerical Laplace transform method.

A Meshless Time Domain Method is proposed to solve the telegrapher's equation for the Nonuniform Transmission Line. The approach is based on a combination of the Point Interpolation Method PIM and the Leapfrog algorithm. The accuracy of the proposed method is confronted with both the conventional FDTD and a wavelet expansion method. The strong stability of the computing scheme is set in evidence from the computational results for a linear tapered planar line.

The author presents an effective method for computation of the transient response of multiple nonuniform transmission lines. This time-domain analysis technique can predict reflections and crosstalk. The proposed spectral technique is used to transform partial differential equations describing a system of transmission lines into a set of linear ordinary differential equations, which can be solved with one of the many well-developed integration techniques. Numerical experiments performed with the prototype program showed that the method can solve specific problems (lossless, uniform lines) just as fast as less general methods based on modal analysis exploiting the particular properties of lines.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Matching Impedance (MI) design method using Non-Uniform Transmission Line (N.U.T.L.) is a design method that offers more advantages over the 1/4 transformer method, the 1/4 multisection method, and the stub method. In this study, the Matching Impedance system is designed to match the WLAN antenna load with a line impedance of 50 Ohm at the 2.4 GHz. The Matching Impedance system is designed using a transmission line with a Characteristic Impedance (Zo) value that is triangular (Triangular Taper) distributed. This study also examines the effect of the number of cutting sections on a transmission line if the line with the Triangle distribution is implemented on a Microtsrip. From the test results, it is found that the number of sections used to form the Non Uniform transmission line has a significant effect on the bandwidth of the system working frequency for the required value of the Reflection Coefficient.

The nonuniform nonlinear transmission line (NLTL) is presented. The NLTL is based on parallel-plate ferroelectric (FE) capacitors. Figure of merit defined as the relative change of the reciprocal steepness of the wave front at NLTL input and output is suggested to characterize the NLTL efficiency. Formulas allowing the calculation of figure of merit for nonuniform ferroelectric-based NLTL are derived. The designed NLTL demonstrates three times increasing of front steepness for input rectangular video pulse of 1.5 ns front duration and 40 V amplitude.

In this work a simplified model for the simulation of electromagnetic transients on non-uniform multiconductor transmission lines is presented. The proposed model is based on the method of characteristics of partial differential equations theory. Rigorous modeling of Nonuniform Multiconductor Transmission Lines requires calculating the space derivatives of the modal transformation matrices. Since such derivatives are calculated numerically, the method can become prone to numerical oscillations. The new procedure presented here does not require the space derivatives, therefore is less prone to numerical oscillations and leads to computing time savings. Results obtained with the proposed model are compared with those from the Numerical Laplace Transform method.

An iteration method is introduced to analyze arbitrary nonuniform transmission lines (NTLs). In this method, the equations of NTLs are converted to the integral equations. Then the integral equations are solved using an iteration approach. This method is applicable to all arbitrary lossy and dispersive NTLs especially at low frequencies. The validity of the method is verified using some comprehensive examples.

A compact ring Branch‐Line Coupler (BLC) with size reduction of about 50%(in circuit area) of conventional BLCs at frequency 2 GHz is introduced. The coupler is designed by using nonuniform transmission lines (NTL) instead of Uniform Transmission Lines in each arm. The normalized width w (z)/h function of the NTLs is expanded in a truncated Fourier series. The reduced size couplers are potential building blocks for the growing wireless communication markets. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2679–2682, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24703