Transient analysis of nonuniform transmission lines using asymptotic waveform evaluation

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.

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.

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 general asymptotic waveform evaluation (GAWE) is proposed for computing the radar cross section (RCS) of an arbitrarily shaped three-dimensional perfect electric conductor (PEC). In the novel technique, the solution of a matrix equation is approximated by the fraction expression with a numerator of vector summation and a denominator of vector summation. The comparison of the GAWE and the traditional asymptotic waveform evaluation (AWE) is also given. Finally, the RCS for different PEC objects such as a square plate, an angular-plate and a cube are computed. The results prove that the extrapolation frequency range in GAWE is wider than that in AWE under the same order derivative. Meanwhile, the computed speed in GAWE is hardly different with that in AWE.

The asymptotic waveform evaluation (AWE) technique is utilized to deal with broadband electromagnetic problems of surface–wire junction geometries in this paper. To ensure the current continuity, triangles-to-segments junction model is used and the Rao–Wilton–Glisson (RWG) and triangular basis functions are used to solve the distributions of current on perfect electric conductor and wire, respectively. Then, the current on surface conductor, wire, and junctions are expanded in a rational function via Padé approximation. The AWE technique needs to store the high-order derivatives of the self-impedance and mutual-impedance matrices of surface–wire, which increase the memory requirements. Thus, the adaptive integral method is employed to reduce memory requirements and to accelerate the matrix-vector multiplications in an iterative solver. Finally, some numerical examples are shown to demonstrate the efficiency and accuracy of the proposed method

A novel methodology for designing a microwave filter has been implemented. The designed filter is a wideband dual-band bandpass filter which has been constructed in digital domain utilizing the chain-scattering parameters for low-pass parallel coupled lines (LP-PCL), serial transmission lines and shunt connected short as well as open circuited stubs. Nature inspired metaheuristic algorithms have been utilized to approximate the magnitude response of the desired transfer function in reference to the magnitude response of ideal transfer function. The dual-band bandpass filter designs are proposed for the 2.1 and 5.2 GHz band. The configuration obtained is to be then simulated in the ADS environment utilizing RT Duroid 5880 substrate. The proposed microstrip structure is capable of covering various microwave applications, most important and common being, the WLAN operating range. KeywordsDual-band bandpass filterMetaheuristic optimizationMicrostripTransmission line elements

Coupled-mode analysis provides a conceptually simple technique for the analysis of nonuniform transmission lines and nonuniform coupled systems. The variable series and shunt elements couple backward and forward traveling waves. Reflection coefficients are derived for an exponential and linear taper by this technique.

With a view to accurate and fast time domain analysis of nonuniform transmission lines, a method is presented for applying the FDTD method to a finite length nonuniform transmission line. A step response analysis is carried out for a parabolic line as one of the nonuniform transmission lines. Effectiveness of this approach is confirmed by comparison with analytical solutions and other methods. An equation for the voltage at the initial rising duration of the step response of a nonuniform transmission line is derived. It is shown that if the nonuniform transmission line has the characteristic impedance with a continuous distribution the initial arriving voltage can be determined by the characteristic impedance at both ends of the transmission line. As an application, a method is described for approximating the step response waveform of a parabolic line to a step wave. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(2): 22–31, 2002

The Tickhonov based well condition asymptotic waveform evaluation (TWCAWE) is presented here to study the non-Fourier heat conduction problems with various boundary conditions. In this paper, a novel TWCAWE method is proposed to overwhelm ill-conditioning of the asymptotic waveform evaluation (AWE) technique for thermal analysis and also presented for time-reliant problems. The TWCAWE method is capable to evade the instability of AWE and also efficaciously approximates the initial high frequency and delay similar as well-established numerical method, such as Runge-Kutta (R-K). Furthermore, TWCAWE method is found 1.2 times faster than the AWE and also 4 times faster than the traditional R-K method.

A method is described for the transient analysis of lossy coupled transmission line networks with nonlinear elements. The method combines the asymptotic waveform evaluation technique with a piecewise decomposition algorithm. Two to three orders of magnitude speedup can be achieved relative to previously published methods with comparable accuracy. The method is useful for delay and crosstalk simulation of high speed VLSI interconnects.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The objective of this paper is to present a moment method numerical technique based on a combined approach of using a ”quasi-dynamic”, a “dynamic” and an asymptotic approach for the analysis of non-uniform microstrip transmission lines and discontinuities using the grounded dielectric slab Green’s Functions. To validate the approach, the regions of validity the quasi-dynamic and asymptotic approximations have been determined in terms of the microstrip physical parameters. Finally, numerical examples have been solved and checked with available data.

An efficient finite element algorithm based on the asymptotic waveform evaluation method and nested matrix decomposition is presented for broadband electromagnetic simulation. The original finite element model is reduced to be a much smaller model for the fast frequency sweeping by using a well-conditioned asymptotic waveform evaluation method. A nested matrix decomposition algorithm is introduced for the model reduction, which reduces the computational complexity to be logarithmic-linear. Broadband analysis of a substrate integrated waveguide is shown as an example to demonstrate the effectiveness of the proposed method.

An optimal pole selection process is introduced to deal with the problem of the sensitivity of the asymptotic waveform evaluation (AWE) technique to output choice. A selection criterion is developed which provides a measure of the relative accuracy of an approximating set of poles and residues. Subsequently, an algorithm in which several sets of approximating poles and residues are generated and an optimal set is chosen based on the derived selection criterion is introduced. The algorithm results in visibly improved accuracy in both transient and frequency analysis as compared to the conventional AWE method. Several examples are presented which demonstrate the accuracy of the proposed technique as compared to previously published methods. >

The electromagnetic field simulation of the target detection by high-resolution radar is performed by incorporating the asymptotic waveform evaluation (AWE) technique and the compression technique of a chirp signal. The electromagnetic field simulation is very helpful for revealing the multi-scattering mechanism of wide-band radar signal between targets or within a target. Our current simulation involves three major steps, in the first step, AWE technique is used to calculate the scattering far field over a wideband at which a radar is operated; in the second step, the frequency response of scattering field is multiplied by the spectrum of the chirp signal transmitted by radar to get the frequency response of radar system; in the third step, the system response is multiplied by the conjugate of the spectrum of the chirp signal and then transformed into time domain by inverse FFT. In this way the target detection by chirp radar can be accurately simulated using electromagnetic field. Numerical examples are presented.

An efficient algorithm is presented to quickly evaluate the frequency-domain response of a patch antenna. The method is based on the combination of the higher order vector finite element method (FEM) and the asymptotic waveform evaluation (AWE) technique for efficiently computing the frequency-domain response. The effect of moments in the power series is discussed. Numerical results for input impedance given below show that the algorithm can achieve very good approximations in the desired frequency band.