Strip Line with Rectangular Outer Conductor and Three Dielectric Layers
TL;DR: In this paper, a general method for analyzing the transmission line characteristics of strip lines with rectangular outer conductor and multidielectric layers within a TEM wave approximation is proposed, and numerical results are found consistent with other theories and experiments.
Abstract: A general method is proposed for analyzing the transmission line characteristics of strip lines with rectangular outer conductor and multidielectric layers within a TEM wave approximation. This method uses Green's function for formulating the problem and a variational principle for obtaining practical solutions. The case of the microstrip line is first discussed, and numerical results are found to be consistent with other theories and experiments. The case of strip lines with a rectangular outer conductor and three dielectric layers is examined for various combinations of dielectric materials. Other applications of Green's function and the theoretical limitation of this method are also described.
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12 Jul 2000TL;DR: Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems using a variety of available numerical methods.
Abstract: Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems. It gives them the ability to expand their problem-solving skills using a variety of available numerical methods. Topics covered include fundamental concepts in EM; numerical methods; finite difference methods; variational methods, including moment methods and finite element methods; transmission-line matrix or modeling (TLM); and Monte Carlo methods. The simplicity of presentation of topics throughout the book makes this an ideal text for teaching or self-study by senior undergraduates, graduate students, and practicing engineers.
662 citations
TL;DR: In this paper, the capacitance matrix and inductance matrix for a multiconductor transmission line in a multilayered dielectric region is presented, where the conductors are either above a single ground plane or between two parallel ground planes.
Abstract: A method for computing the capacitance matrix and inductance matrix for a multiconductor transmission line in a multilayered dielectric region is presented. The number of conductors and the number of dielectric layers are arbitrary. Some of the conductors may be of finite cross section and others may be infinitesimally thin. The conductors are either above a single ground plane or between two parallel ground planes. The formulation is obtained by rising a free-space Green's function in conjunction with total charge on the conductor-to-dielectric interfaces and polarization charge on the dielectric-to-dielectric interfaces. The solution is effected by the method of moments using pulses for expansion and point matching for testing. Computed results are given for some cases where all conducting lines are of finite cross section and other cases where they are infinitesimally thin.
445 citations
TL;DR: In this article, an accurate and efficient method was developed for computing the resonant frequencies of microstrip resonators, which was carried out rigorously using the full-wave analysis rather than the quasi-static approximation.
Abstract: An accurate and efficient method was developed for computing the resonant frequencies of microstrip resonators. The formulation of the problem was carried out rigorously using the full-wave analysis rather than the quasi-static approximation. The characteristic equation was derived using Galerkin's method applied in the Fourier transform domain. The accuracy of the method has been proven by comparing the numerical results with the experimental data. Numerical data have been provided for the microstrip resonators with different structural parameters. Finally, the results for microstrip resonators have been used for predicting the end effect at the open end of microstrip structures.
176 citations
TL;DR: In this paper, a conformal mapping method is used to obtain simple analytical relations for the filling factors and the effective permittivity of two fundamental types of three-layer microstrips.
Abstract: Multilayer microstrip transmission lines are investigated. The conformal mapping method is used to obtain simple analytical relations for the filling factors and the effective permittivity of two fundamental types of three-layer microstrips. Numerical results obtained by the present method are compared with available data from other authors. >
163 citations
TL;DR: In this paper, an analytical method and numerical results for a gap capacitance in the microstrip transmission line are described, and the equivalent circuit parameters are formulated with three-dimensional Green's functions, based on a variational principle.
Abstract: Although microstrip transmission lines have been widely used in microwave integrated circuits, the discontinuity structures in the microstrip transmission lines such as a gap, an abruptly ended strip conductor, and so on, have hardly been analyzed. An analytical method and numerical results for a gap capacitance in the microstrip transmission line are described. The equivalent circuit parameters are formulated with three-dimensional Green's functions, based on a variational principle. The numerical results are in good agreement with the published experimental data. The fringing effect of an abruptly ended strip conductor is also investigated.
142 citations
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TL;DR: In this article, the shape ratio and the effective filling fraction of a sheet of dielectric material are computed in terms of exponential and hyperbolic functions, respectively, for a transmission line made of a symmetrical pair of strip conductors.
Abstract: A transmission line is made of a symmetrical pair of strip conductors, or a single strip and a ground plane, on opposite faces of a sheet of dielectric material. There is computed, to a close approximation, the relations among the dielectric constant of the sheet, the effective dielectric constant of the sheet and the empty space, the shape ratio, and the wave resistance, for the entire range of possible values. These relations are summarized in a graphical chart covering the range of practical interest. The computation is based on conformal mapping of the dielectric boundary on coordinates such that its effect can be most closely evaluated by simple principles. All relations are approximated in terms of ordinary functions (exponential and hyperbolic). Of particular interest is the effective filling fraction of the dielectric material, which depends mainly on the shape ratio and only slightly on the dielectric constant. Explicit formulas are given for analysis or synthesis.
837 citations
"Strip Line with Rectangular Outer C..." refers methods in this paper
...The characteristic impedance based on the above formula agrees well with that based on conformal mapping [ 1 ]....
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...mierostrip line has been analyzed by various methods based on a TEM wave approximation [ 1 ]-[4]....
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TL;DR: In this paper, expressions for the conductor loss in microstrip transmission lines are derived for rutile and alumina substrates, taking into account the finite thickness of the strip conductor and apply to the mixed dielectric system.
Abstract: Expressions are derived for the conductor loss in microstrip transmission lines. The formulas take into account the finite thickness of the strip conductor and apply to the mixed dielectric system. Good agreement with experimental data is obtained for rutile and alumina substrates.
543 citations
TL;DR: In this paper, a theoretical analysis of a shielded double-layer microstrip line is presented based on a variational calculation of the capacitance in the Fourier-transformed domain and on the charge density distribution as a trial function.
Abstract: A theoretical method is presented by which microstrip-like transmission lines can be analyzed. These transmission lines are characterized by conducting strips, large ground planes, multi-dielectric-layer insulation, and planar geometry. The method is essentially based on a variational calculation of the line capacitance in the Fourier-transformed domain and on the charge density distribution as a trial function. A shielded double-layer microstrip line is analyzed by this method. Derived formulas for this structure are also applicable to simpler structures: a double-layer microstrip line, a shielded microstrip line, and a microstrip line. The calculated values of the line capacitance and the guide wavelength are compared with the measured values where possible. Oxide-layer effects on a silicon microstrip line and shielding effects on a sapphire microstrip line are also discussed based on this theory. The limitations and possible applications of this method are described.
220 citations
"Strip Line with Rectangular Outer C..." refers methods in this paper
...Z, the energy propagation velocity v, and the guide wavelength k, are given by [ 3 ]...
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01 Jan 1968
TL;DR: In this article, the wave propagation properties of microstrip transmission lines can be determined accurately if an exact electrostatic field solution can be found for a pair of charged conductors separated by a dielectric sheet.
Abstract: Wave-propagation properties of microstrip transmission lines can be determined accurately if an exact electrostatic-field solution can be found for a pair of charged conductors separated by a dielectric sheet. The latter problem is framed as an integral equation for whose solution simple numerical methods are available. To determine the kernel function of this integral equation, the classical method of images is generalised to include, multiple partial images; the kernel function is then given by well convergent infinite series. Wave impedances calculated using this theory yield very good agreement with experiment. Detailed results are given for the propagation velocity in microstrip lines with very thin strip conductors, and the method used to solve thick-strip problems is described.
193 citations
TL;DR: In this article, the authors considered the use of multiple microwave devices in a single package and offered the possibility of improved performance of the microwave components by eliminating packaging of each individual element and the ability to place the package interface in a more advantageous position in the circuit.
Abstract: As a result of both a larger number of microwave functions performed by semiconductor devices and a larger number of functions required in modern systems, it has become highly desirable from both the system and the device standpoint to fabricate multiple microwave semiconductor devices on a common substrate. The use of multiple devices in a single package has system and reliability advantages, but there is also offered the possibility of improved performance of the microwave components. This results from the elimination of packaging of each individual element and the ability to place the package interface in a more advantageous position in the circuit. To effect such an improvement, an efficient means of microwave interconnection must be available. The interconnections must have not only low dissipative losses through the microwave region, but be capable of providing the impedances necessary for transformations by the various microwave functions and for circuit resonating elements. The range of impedance commonly required is of the order of 20 /spl Omega/ to 80/spl Omega/. To be compatible with semiconductor materials and processing, the choice of dielectric material was limited to film dielectrics, possibly SiO/sub 2/, or the use of the semiconductor material itself as a dielectric. For both semi-insulating gallium arsenide and silicon of resistivity greater than 1000 /spl Omega/-cm, the loss is sufficiently low to perform efficient interconnection of devices on a common substrate and is considered even suitable for other components such as directional couplers and hybrids where extremely high Q is not required.
101 citations