Multiple Coupled Microstrip Lines Research Articles

A New High-Efficient Spectral-Domain Analysis of Single and Multiple Coupled Microstrip Lines in Planarly Layered Media

The analysis of propagation of bound and leaky modes in single and multiple coupled microstrip lines in planarly layered media by means of Galerkin's method applied to an electric field integral-equation formulation in the spectral domain with Chebyshev polynomials basis functions weighted with the edge behavior of the unknown surface current densities on the metallic strips leads to the evaluation of improper integrals of oscillating functions with a slow asymptotic decay. In this paper, a new analytical technique for drastically speeding up the computation of such integrals is presented. First, suitable half-space contributions are pulled out of the kernels, which makes the integrands exponentially decaying functions. The integrals of the extracted contributions are then expressed as combinations of proper integrals and fast converging improper integrals by means of appropriate integration procedures in the complex plane.

An Efficient Analysis of Shielded Single and Multiple Coupled Microstrip Lines With the Nonuniform Fast Fourier Transform (NUFFT) Technique

A nonuniform fast Fourier transform (NUFFT) technique is incorporated into the spectral-domain approach for the analysis of shielded single and multiple coupled microstrip lines. Each of the spectral-domain Green's functions is decomposed into an asymptotic part and a remaining part. At the interface of layered dielectrics with conducting strips, the product of a basis function and an associated Green's function constitutes an expansion E-field. The inverse Fourier transform (IFT) of the expansion E-field is its spatial distribution all over the interface. We take this advantage to match the final boundary conditions on all the conducting strips simultaneously. As a result, if all the strips are at one interface, the number of operations required in this method is proportional to N/sub /spl lscr//, but not to N/sub /spl lscr///sup 2/, where N/sub /spl lscr// is the number of the strips. The IFT of the asymptotic part of each expansion E-field can be obtained analytically, and that of the remaining part can be quickly processed by the NUFFT. The Gauss-Chebyshev quadrature is used to accelerate the computations of the integrals resulted from the Galerkin's procedure. The proposed method is also applied to investigate the dispersion characteristics of coupled lines with finite metallization thickness and of coupled lines at different levels. A convergence analysis of the results is presented and a comparison of used CPU time is discussed.

Coupled-Mode Analysis of Line Parameters of Coupled Microstrip Lines - Abstract

An approximate method to obtain the line parameters of multiple coupled microstrip lines based on the full-wave analysis is presented. The technique uses the coupled-mode equations for the amplitudes of currents on each line. The coupling matrix in the equations, expressed by overlap integrals between the eigenmode fields of each isolated single line, characterizes the electromagnetic natures of the coupled lines. The eigenvalues and eigenvectors of the matrix yield the propagation constants, the ratios of line currents, and the characteristic impedances of the coupled modes. The proposed method is applied to two nonidentical coupled lines and three nonidentical coupled lines in a single plane, and two identical coupled lines in dual planes. The numerical results for the mode propagation constants and characteristic mode impedances are compared with those obtained by the direct numerical solution method for the coupled lines. Both results show a good agreement.

Hybrid-mode computation of propagation and attenuation characteristics of parallel coupled microstrips with finite metallization thickness

The hybrid-mode mixed spectral domain approach (MSDA) is formulated to investigate the dispersion nature of multiple coupled microstrip lines with arbitrary metallization thickness. Incorporated into the solution procedure, a new set of basis functions with /spl delta//sup -1/3/ field singularity near conductor edges is found to be effective in calculating both the phase and attenuation constants. The computation of conductor loss is based on the perturbation procedure. Over a broad band of frequency spectrum, excellent agreement is obtained between the calculated results and existing experiment data for the metallic losses of a single microstrip and effective dielectric constants of coupled lines. The influence of finite metallization thickness on the frequency dependent modal propagation and attenuation characteristics is presented for both a three-line and four-line structure.

Riccati matrix differential equation formulation for the analysis of nonuniform multiple coupled microstrip lines

A Riccati matrix differential equation (RMDE) is formulated for analyzing nonuniform coupled microstrip lines (NCML's) in the frequency domain. The formulation is based on a reciprocity-related definition in the theory of multiconductor transmission lines under quasi-TEM assumption. The hybrid-mode nature of modal phase velocities and strip characteristic impedances for multiconductor microstrip structure is included. The nonlinear RMDE is first transformed into a first-order linear differential matrix equation which can be efficiently solved using method of moments. A convergence study is performed to investigate the sufficient number of basis functions used in the method. The voltage-scattering parameters of a tapered microstrip and two three-line structures are presented. The frequency responses of a pair of nonuniform coupled lines are measured and compared with calculated results.

Accurate quasi-TEM spectral domain analysis of single and multiple coupled microstrip lines of arbitrary metallization thickness

The quasi-TEM spectral domain approach (SDA) is extended to rigorously and efficiently analyze single and multiple coupled microstrip lines of arbitrary metallization thickness. The charge distributions on both the horizontal and vertical conductor surfaces are modeled by global basis functions. This results in a relatively small matrix for accurate determination of the line parameters of coupled thick microstrips. A convergence study is performed for the results of a pair of coupled lines with crucial structural parameters to explore the conditions for obtaining reliable solutions using the technique. Results for thick microstrips are validated through comparison with those from available measurements and another theoretical technique. The soundness of the technique is further demonstrated by looking into the trend of the results obtained by a simplified model in which the structural parameters are pushed, step by step, to the numerical extremities. Variations of circuit parameters of a four-line coupled microstrip structure due to the change of finite metallization thickness are presented and discussed. >

Full-wave iterative variational formulation for multiple coupled microstrip lines

A novel variational formulation in terms of two formally decoupled potentials is derived for the full wave propagation constants of multiple coupled microstrip lines. At very low frequency limits, the present formulation is reduced directly to the conventional quasi-static formulation. The quasi-static solutions are then used as an initial guess to solve the high-frequency problem for each coupled mode by a generalized Newton-Raphson iterative scheme. Numerical results are presented for two and three coupled microstrip lines of identical or nonidentical widths with various spacings and frequencies. >

Comments, with reply, on "Spectral domain computation of characteristic impedances and multiport parameters of multiple coupled microstrip lines" by V.K. Tripathi and H. Lee

The commenter argues the question of whether it is possible to normalize currents and voltages simultaneously, as implied by a relationship used in the above-titled paper (see ibid., vol.37, no.1, p.215-222, 1989). In their reply, the authors identify two main issues raised in the comments, one dealing with the definition and meaning of characteristic impedance for general multiconductor systems and the other dealing with the computation of the elements of the line mode impedance matrices. They attempt to clarify both issues.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>