Analysis of Planar Circuits Having Arbitrary Shapes

In the preceding chapters, only the analysis of planar circuits has been considered. As pointed out in Sect. 1.2.3, however, an important significance of the planar circuit concept lies in that, if the design technique for an arbitrarily shaped planar circuit is established in the future, it will offer an exact and efficient design tool for the microwave integrated circuit (IMC).

In this paper, a 3D alternating-direction implicit finite-difference time-domain (ADI-FDTD) algorithm is used to analyze planar circuits. The source excitation in ADI-FDTD is described and two kinds of absorbing boundary conditions (ABCs) are jointly employed for ADI-FDTD algorithm: the Gedney's uniaxial PML scheme is applied in the propagation direction, and Mur's 1st-order absorbing boundary condition (ABC) is set on the other outer surfaces. Both time-domain waveforms and S-parameters are presented. The numerical simulations of several examples show that the number of iterations with this ADI-FDTD algorithm can be six times less than that with the conventional FDTD without a large loss of accuracy. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 175–179, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20936

The work presented here introduces lumped elements to an iterative method based on the wave concept combined with the two-dimentional fast Fourrier transformation algorithm known as fast modal transformation (FMT). We extend this method to the analysis of microwave-distributed circuits containing passive or active, linear or nonlinear lumped elements which are characterized by their surface impedance as defined in this article. Simulation results of varactor-tuned filter and phase-shifter circuit examples are compared with the measurement results. Good agreement between simulated and experimental results validates the use of the iterative method for the analysis of planar circuits, including lumped elements. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 269–275, 2003.

In this paper, we propose a novel approach for the analysis of shielded microstrip circuits, composed of a number of thin metallic areas with arbitrary shapes and finite conductivity, embedded in a multilayered lossy medium. The analysis is based on the solution of an Integral Equation (IE) obtained by enforcing the proper boundary condition to the electric field on the metallic areas. The solution of the IE is obtained by the Method of Moments (MoM) with entire domain basis functions, which are numerically determined by the Boundary Integral-Resonant Mode Expansion (BI-RME) method. The use of the BI-RME method allows for the efficient calculation of entire domain basis functions in the case of metallic areas with arbitrary shapes, thus permitting the analysis of a wide class of circuits. Two examples demonstrate the accuracy, rapidity, and flexibility of the proposed method.

The mixed-potential integral-equation approach, using spatial-domain closed-form Green's functions, and discretized with the method-of-moments, is a state-of-the-art method for the analysis of planar microstrip circuits. One of its most time-demanding tasks is the evaluation of the impedance matrix terms, which typically requires the numerical computation of two-dimensional integrals. A method based on suitable changes of coordinates and domains is introduced in this paper in order to reduce such integrals to a quasi-one-dimensional numerical integration, with a substantial enhancement in the efficiency of the analysis, without affecting the accuracy of the approach. Results are given demonstrating, for practical accuracy values, an improvement of typically one order of magnitude in simulation times.

A novel algorithm based on generalized transmission line equations (GTL) and on the method of lines (MoL) for the analysis of planar waveguide circuits with anisotropic layers is proposed and substantiated. The algorithm uses discretization lines in the propagation direction of the waves. As in the case of multiconductor transmission lines two modal matrices are determined. Impedance/admittance transformation equations are determined on the basis of the GTL equations. Using these equations numerically stable and accurate impedance transformations and field calculations can be performed.

This paper presents two powerful pedagogical approaches for finding Thevenin and Norton equivalent circuits for d.c. linear electric circuits. These approaches are based solely on mesh analysis (for planar circuits) and on nodal analysis (for planar or nonplanar circuits) and simultaneously provide all equivalent circuit parameters from one circuit.

It is shown that the description of absorbing boundary condition algorithms (ABCs) in terms of single incident plane waves does not provide sufficient information for choosing the best ABC for planar waveguide termination. A technique for optimizing the ABCs that results in a return loss from a wideband pulse less than -50 dB is demonstrated. This technique reduces the risk of loss of accuracy due to mode conversion at the boundary. The use of these optimized ABCs considerably improves analysis results for an important category of microstrip components. For boundaries transverse to the direction of propagation, it is shown that inaccuracy and late time instability can result if the boundary is placed in regions of high field strength.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fast direct planar full-wave electromagnetic analysis of microstrip structures embedded in multilayered medium is demonstrated. The impedance matrix of the Moment Method is stored in compressed format of a hierarchical matrix. The matrix equation is subsequently solved using hierarchical LU decomposition. Accuracy of analysis in a broad range of frequencies is demonstrated. Compression rate and accuracy of the computed reflection loss for a microstrip structure situated in multilayered media are presented as a function of tolerance in SVD of rank-deficient blocks of the hierarchical matrix.

The Transmission Line Matrix (TLM) method [1] is applied to the analysis of planar circuits for monolithic microwave integrated circuits (MMICs). The high-density packaging of these circuits demands full-wave analysis. Recently, efforts have been made to improve the accuracy and efficiency of the TLM schemes based on symmetrical condensed nodes [2]. The modeling of planar circuits containing thin metallic boundaries and three-dimensional discontinuities require TLM meshes with large numbers of nodes. In order to cover the simulation in reasonable computing time additional models have to be incorporated into a general purpose TLM field solver. We investigate several coplanar structures emphasizing the advantages of TLM method.

This paper deals with the computation of planar circuits embedded in layered media by a spectral domain approach using a very flexible nonuniform mesh strategy in connection with different kinds of expansion functions. Besides the widely used rooftop or piecewise sinusoidal current expansion functions allowing piecewise constant distributions normal to the current direction, we use expansion functions allowing linear cross distributions. The focal point of this contribution is to present a spectral domain approach which can support a large class of expansion functions. Computational efficiency is achieved, on the one hand, by analytical and numerical integration schemes to improve the convergence and accuracy of the spectral domain integrals, and on the other hand, by a matrix fill technique which is based on the efficient detection of identities in the coupling matrix to avoid redundant computations. Typical applications are shown in order to demonstrate some of the advantages of the presented approach. © 1997 John Wiley & Sons, Inc. Int J Microwave Millimeter-Wave CAE 7: 455–467, 1997.

Wavelets are well-known to accelerate the simulation of planar microwave circuits. In this paper computational savings in both CPU time and memory are discussed that can be achieved by properly implementing a wavelet base for the analysis of complex microstrip circuits. The choice of a suitable grid is discussed for two examples.

A numerical method has been developed for the analysis of microwave devices made with superconducting materials or/and normal (perfect or imperfect) metal conductors and lossy dielectrics. This method, based on 2D and 3D Finite Element Method (F.E.M.) is applied here to evaluate the propagation characteristics of microstrip lines, coplanar waveguides, and the scattering parameters of planar circuits (resonators,. . .). The results given by F.E.M. are compared with those obtained by using other theoretical analysis or/and with experimental data.

A method of Galerkin analysis of polygonal planar circuits embedded in a multilayered medium is presented. The circuit is gridded up using rectangular and triangular cells. Rooftop basis functions are used. An efficient calculation scheme for the cell-cell interactions is discussed. A microstrip low-pass filter is investigated, and comparisons are made with measured and other simulated data. Grid accuracy and convergency are discussed. >

Double-bouquet cells in the monkey and human cerebral cortex with special reference to areas 17 and 18