The equivalent circuit of a microstrip crossover in a dielectricsubstrate

A quasi-static analysis is carried out to examine the capacitive coupling between two nonintersecting orthogonal microstrip lines above a ground plane and in a dielectric substrate. The charge density along the width of each strip is described using a prescribed charge distribution. A pair of coupled integral equations is derived and solved by the method of moments to obtain the excess charge densities. The lumped excess capacitances are computed and compared to those obtained using wire lines with radii equal to the equivalent radii of the strips     

Static analysis of microstrip discontinuities using the excesscharge density in the spectral domain

Galerkin's method in the spectral domain is applied to solve for the excess charge density existing on the strips of open-end and symmetric gap discontinuities in multilayered anisotropic substrates. The excess charge density is used to determine the capacitance components of the equivalent circuits, of these discontinuities. Numerical results are provided and a comparison with previous results is carried out     

Hybrid Mode Analysis of Microstrip Lines on Anisotropic Substrates

A rigorous hybrid mode analysis is applied to microstrip lines on anisotropic substrates to determine its high-frequency performance. The analysis is based on a general formulation of the problem of planar transmission lines on multilayered substrates with uniaxial anisotropy, of which the microstrip line is a special case. Exact solution is obtained using a functional equation technique which was previously developed and applied to microstrip and bilateral finlines. The results were used to check the validity of the concept of equivalent isotropic substrate, suggested by some authors to simplify the calculation of the parameters of these lines. Certain approximations are introduced to allow the efficient calculation of the characteristics of microstrips on anisotropic substrates at relatively high frequencies or for wide strips. Numerical results are given for some values of the parameters of microstrip lines on sapphire and include the regions of excitation of higher modes.     

Comparison between theoretical and measured microstrip gapparameters involving anisotropic substrates

In this paper, experimental results are presented for microstrip symmetrical-gap discontinuities. The experimental technique is based on the measurement of the resonant frequencies of several gap-coupled rectangular microstrip resonators. In particular, gap discontinuities on anisotropic dielectric and two-layer composite substrates have been investigated. Reasonably good agreement has been found in most cases between theoretical data [obtained by means of the excess charge technique in the spectral domain (EC-SDA)] and experimental data, even though the theoretical results have been obtained by using a quasi-static approach     

Equivalent circuits for multiconductor microstrip benddiscontinuities

The T-equivalent circuit previously used for single-line microstrip bends is extended to the variable-angle, multiconductor microstrip bend. A brief overview is given of the excess-charge and current approaches which are employed to obtain the capacitance and inductance matrices for the equivalent circuit. These techniques effectively avoid the majority of the numerical difficulties that occur in accounting for the infinite extent of the microstrip lines making up bends with arbitrary bend angles. In addition, to accurately accommodate the oblique bend angles without requiring many unknowns, the charge and current distributions are modeled with a combination of rectangular and triangular patches. Comparisons with previously published results from the technical literature and with experimental data are used to validate the excess capacitance and inductance computations. The excess capacitance and inductance matrices of several three-line bends are presented, and the three-line bend model is used in a simulation of a high-speed digital circuit to demonstrate the effect of the bend on digital pulse waveforms     

Effect of substrate dielectric anisotropy on the frequency behaviorof microstrip circuits

In this paper, we carry out a full-wave analysis of shielded two-port microstrip circuits, in which the metallizations are embedded in a multilayered substrate that may contain isotropic dielectrics and/or anisotropic dielectrics. The Galerkin's method in the spectral domain is applied for determining the current density on the metallizations of the circuits when their feeding lines are excited by means of delta-gap generators, and the matrix pencil technique is subsequently used for deembedding the scattering parameters from the computed current densities. Results are presented for the scattering parameters of some microstrip discontinuities and filters printed on both isotropic dielectric substrates and anisotropic dielectric substrates. These results show that when substrate dielectric anisotropy is ignored, errors arise when computing the scattering parameters of microstrip discontinuities and when predicting the operating frequency band of microstrip filters     

Generalized Analysis of Microstrip-Like Transmission Lines and Coplanar Strips with Anisotropic Substrates for MIC, Electrooptic Modulator, and SAW Application

A unified variational expression is presented for the line capacitance of a general, multilayer anisotropic structure. The propagation characteristics of a variety of striplines, microstriplines, and coplanar strips, in isolated and coupled configurations, with anisotropic substrates having optical axis aligned along the axis of the substrate, are computed. The characteristics of these structures with anisotropic substrates having tilted optical axis are also studied. Using the formulas presented, the study of structures with anisotropic substrates having aligned or tilted optical axis, for various applications including MIC, electrooptic modulator, and SAW IDT, reduces to the determination of a single admittance parameter. This parameter can be obtained from the transmission-line equivalent circuit of the structure almost by inspection.     

Toward a Generalized Algorithm for the Modeling of the Dispersive Properties of Integrated Circuit Structures on Anisotropic Substrates

A variety of substrate materials used in practice exhibit anisotropic behavior which is either inherent to the material or may be acquired during the manufacturing process. The development of highly accurate models for the propagation properties of integrated circuit structures necessitates careful accounting of substrate anisotropy. In this paper, an algorithm is developed which models structures such as microstrip, inverted microstrip, slotlines, and coplanar waveguides on anisotropic substrates. The model includes cases where the circuit has a cover or is enclosed in a rectangular shield.     

Equivalent isotropic relative permittivity of microstrip on multilayer anisotropic substrate

A closed-form model to obtain the equivalent isotropic relative permittivity of the multilayer microstrip line on the anisotropic substrate for 0 w/h ≤ 10, anisotropic ratio 0.5 ≤ n ≤ 3 for both low and high permittivity substrates is reported. The model has accuracy 0.5% against the full-wave method. It computes effective relative permittivity and characteristic impedance of microstrip on composite anisotropic substrates with deviations 5.3% and 1.78%, respectively against the EM-software Empire. It is used to obtain dispersion in multilayer anisotropic substrate microstrip up to millimetre wave range with high accuracy against the results of HFSS.     

Lumped capacitance and open end effects of striplike structures inmultilayered and anisotropic substrates

An accurate calculation of the lumped capacitance of a rectangular microstrip patch and the edge capacitance of an open-circuit microstrip or stripline is carried out. Variational expressions in the spectral domain are developed to analyze these conductors when they are embedded in a multilayered anisotropic substrate. A recurrence algorithm, easy to compute, is proposed to determine the three-dimensional spectral Green's function characterizing the sort of substrates employed. The method makes it possible to study biaxial substrates in the case of the rectangular patch and uniaxial substrates with tilted optical axis in the transverse plane in the case of open-circuit striplike transmission lines. A detailed study of trial functions to approximate the charge density on the conductors is carried out, taking into account the physical features of each problem. The results obtained are compared with those appearing in the literature. Original design graphs are presented, with special emphasis on the use of inhomogeneous and anisotropic substrates     

Propagation Characteristics of a Microstrip Line Printed on a General Anisotropic Substrate

An analysis is presented for determining the propagation modes in a microstrip line printed on a substrate having both electric- and magnetic-type general anisotropies. An integral equation is derived for the unknown current distribution on the microstrip line. The kernel of this equation is a complicated 2x2 matrix function of the substrate anisotropy and of the substrate thickness. In order to determine the dispersion relations for the propagating waves, this integral equation is reduced into a finite system of linear equations by employing Galerkin's technique. Numerical results are given for several cases, and the effect of rotating the anisotropy axis in anisotropic substrates is investigated. The proposed method can be employed to compute the propagation characteristics of microstrip lines printed on anisotropic substrates.     

Accurate CAD-Model Analysis of Multilayer Microstrip Line on Anisotropic Substrate

Computationally efficient equivalent isotropic relative permittivity of the multilayer microstrip line on the uniaxial anisotropic substrate for 0 < w/h ≤ 10, anisotropic ratio0.5 ≤ n ≤ 3.0. Model has accuracy 0.5% against the full-wave method. It computes effective relative permittivity and characteristic impedance of microstrip on composite anisotropic substrates with deviation 4.5% respectively against the EM- software HFSS. Dispersion in multilayer anisotropic substrate microstrip up to mm wave range with high accuracy against the results of HFSS. The proposed models could be incorporated in the computer aided design for development of the components on the uniaxial anisotropic substrates.     

A new development of an equivalent circuit model for magnetostaticforward volume wave transducers

A three-port equivalent circuit model of microstrip transducers used for the generation and detection of magnetostatic forward volume waves (MSFVW) is derived from fundamental physical considerations. In this circuit model, each microstrip MSFVW transducer is modeled as a three-port circuit incorporating a frequency-dependent series reactance, a frequency-dependent lossless transformer, and a lossy transmission line. Circuit parameters are determined in closed form by the use of solutions of pertinent boundary-value problems. The effects of parasitics, for example, capacities of bonding pads, are easily taken into account. Some typical transducer configurations are analyzed numerically. The three-port model developed is in excellent agreement with experiments. The model can be applied directly to nonuniform arrays of microstrips weighted by varying the separation between strip centers and the widths of successive strips or reversing the current direction of some groups of strips     

各向异性衬底上的高温超导(HTS)微带天线

分析了各向异性衬底上的高温超导微带天线特性.选取两种典型的高温超导各向异性介质--GaNdAlO3和SrLaAlO4作为高温超导微带天线的衬底,采用各向异性媒质中的谱域矩量法,对微带天线的输入阻抗和辐射效率进行了计算.计算和分析结果表明,高温超导衬底的各向异性特性会影响高温超导微带天线的性能,而且这种影响因衬底而异,同时,衬底特性随温度的变化也将影响天线的性能.     

Multiple microstrip lines on a multilayered cylindrical dielectricsubstrate on perfectly conducting wedge

The quasi-TEM characteristics of a class of cylindrical microstrip lines are rigorously determined. The class of microstrip lines considered consists of multiple infinitesimally thin strips on a multilayered dielectric substrate on a perfectly conducting wedge. Expressions for the potential distribution inside and outside the dielectric substrate, charge distribution on the strips, and capacitance matrix of the microstrip lines are derived. The problems of a microstrip line on a cylindrically capped wedge and on a cylindrical dielectric substrate on perfectly conducting core are also considered as special cases. Sample numerical results based on the derived expressions are given and discussed     

The dispersion characteristics of shielded microstrip lines on magnetized ferrite and anisotropic dielectric substrates

The dispersion characteristics of the dominant mode in shielded microstrip lines on magnetized ferrite and anisotropic dielectric substrates have been obtained. The solution is obtained by applying the transverse equivalent transmission line in the spectral domain and Galerkin's method. Numerical results for the frequency-dependent propagation constants are presented which could be used in designing directional couplers and isolators.     

Quasi-TEM analysis of multilayered, multiconductor coplanarstructures with dielectric and magnetic anisotropy including substratelosses

A quasi-TEM (transverse electromagnetic) analysis of multiconductor planar lines embedded in a layered structure involving lossy iso/anisotropic electric and/or magnetic materials is achieved. Conditions under which a quasi-TEM assumption is valid are theoretically determined. An efficient spectral-domain analysis is used to determine the complex capacitance and inductance matrices characterizing the transmission system. computation of the inductance matrix is reduced to the computation of an equivalent capacitance matrix when media characterized for a fully general permeability tensor are present. It is also shown that most actual monolithic microwave integrated circuit (MMIC) microstrip-type structures (where semiconductor substrates are present) and possible future applications including lossy magnetic materials can be analyzed by using the simple quasi-TEM model. The validity of the results has been verified by comparison with full-wave theoretical and experimental data on microstrip lines on magnetic substrates and slow-wave structures     

Quasi-static analysis of a microstrip via through a hole in aground plane

The equivalent circuit of a via connecting two semi-infinitely long transmission lines through a circular hole in a ground plane is found. The π-type equivalent circuit consists of two excess capacitances and an excess inductance. These are quasistatic quantities and thus are computed statically by the method of moments from integral equations. The integral equations are established by introducing a sheet of magnetic current in the electrostatic case and a layer of magnetic charge in the magnetostatic case. Parametric plots of the excess capacitances, the excess inductance, and the characteristic admittance of the via are given     

Characteristics of broadside-coupled microstrip lines with iso/anisotropic substrates

A quasistatic analysis of broadside-coupled microstrip lines using a series form expression of Green's function and the method of moments is described. Characteristic impedances, effective permittivities and ratios between phase velocities for the even and odd modes were obtained for various values of strip widths, W/b, spacings between strips, s/b, and for isotropic and anisotropic substrates.     

Wide bandwidth microstrip antennas for circuit integration

Novel multilayer concepts for the formation of efficient micro-strip antennas on alumina substrates that allow simple antenna/circuit integration to be achieved are described. Experimental results show that, by using these techniques, bandwidth in excess of 16 times those of alumina microstrip antennas can be obtained, at the expense of an increase in the overall antenna height.