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Showing papers in "IEEE Transactions on Microwave Theory and Techniques in 1971"


Journal Article•DOI•
TL;DR: In this article, the dielectric constant of saline water was represented by an equation of the Debye form and the parameters for the parameters were given as functions of the water temperature and salinity.
Abstract: The dielectric constant of saline water may be represented by an equation of the Debye form. Equations for the parameters in the Debye expression are given as functions of the water temperature and salinity.

715 citations


Journal Article•DOI•
TL;DR: In this article, a parallel-plate waveguide model for the microstrip line formed on the Si-SiO/sub 2/ system is analyzed theoretically and the results are compared with the experiment.
Abstract: A parallel-plate waveguide model for the microstrip line formed on the Si-SiO/sub 2/ system is analyzed theoretically and the results are compared with the experiment. The experiment has been performed over wide ranges of frequency, substrate resistivity, and strip width. Existence of three types of fundamental modes is concluded and the condition for the appearance of each mode is clarified. In particular, the slow-wave mode is found to propagate within the resistivity-frequency range suited to the monolithic circuit technology, and its propagation mechanism is discussed. Approximate analysis of the fringing effect is also made for the slow-wave mode.

516 citations


Journal Article•DOI•
Arthur W. Guy1•
TL;DR: In this paper, the authors used a thermograph camera to record temperature disitributions produced by energy absorption in phantom models of the tissue structures, which are composed of materials with dielectric and geometric properties identical to the tissue structure which they represent.
Abstract: One of the most vexing problems in studies involving the interaction of electromagnetic fields and living biological systems and tissues is the quantification of the fields induced in the tissues by nearby sources. This paper describes a method for rapid evaluation of these fields in tissues of arbitrary shape and characteristics when they are exposed to various sources including plane wave, aperture, slot, and dipole sources. The method, valid for both far- and near-zone fields, involves the use of a thermograph camera for recording temperature disitributions produced by energy absorption in phantom models of the tissue structures. The magnitude of the electric field may then be obtained anywhere on the model as a function of the square root of the magnitude of the calculated heating pattern. The phantoms are composed of materials with dielectric and geometric properties identical to the tissue structures which they represent. The validity of the technique is verified by comparing the results of the experimental approach with the theoretical results obtained for the case of plane layers of tissue exposed to a rectangular aperture source and cylindrical layers of tissue exposed to a plane-wave source. This technique has been used successfully by the author for improving microwave applicators.

484 citations


Journal Article•DOI•
TL;DR: In this paper, an approximate analysis is presented together with a physical description of the modes of propagation in stripline and microstrip devices of significant width, using ferrite slabs as dielectric material, magnetized perpendicular to the ground plane.
Abstract: An approximate analysis is presented together with a physical description of the modes of propagation in stripline and microstrip devices of significant width, using ferrite slabs as dielectric material, magnetized perpendicular to the ground plane. The dominant mode resembles TEM propagation, except that there is a strong transverse field displacement, causing wave energy to be concentrated along one edge of the line. Nonreciprocal behavior is obtainable by asymmetrically loading the edges. Approximate analytical techniques are given for isolators and phase shifters, with examples of numerical computations and experimental results.

234 citations


Journal Article•DOI•
TL;DR: In this paper, the induced EMF method has been extended and applied to derive the driving-point impedance of a common waveguide structure used for mounting small microwave devices, and an equivalent circuit is developed and discussed in detail.
Abstract: The induced EMF method has been extended and applied to derive the driving-point impedance of a common waveguide structure used for mounting small microwave devices. An equivalent circuit is developed and discussed in detail. Theoretical impedance curves are presented demonstrating the circuit characteristics for various configurations of the mount. The driving-point impedance of this mount has also been considered experimentally. A novel measurement technique is used based upon the use of subminiature coaxial line to gain electrical access to the terminal pair located inside the waveguide. A model of the measurement circuit, which enhances the accuracy of the results, providing excellent agreement between the theoretical and measured values, is developed. The multilateral nature of the circuit allows consideration of the mount in the waveguide as an obstacle to any incident propagating mode. Some related measurements have been made using standard techniques for the H/sub 10/ mode. It is anticipated that this formulation will permit accurate design of many components which previously required empirical methods based on limited experimental data.

219 citations


Journal Article•DOI•
TL;DR: Theoretical and experimental results of open microstrip propagation on both a pure dielectric and a demagnetized ferrite substrate are presented in this article, where a Fourier transform method is used to obtain the frequency dependence of phase velocity and characteristic impedance, and also the electromagnetic field quantities around the microstrip line.
Abstract: Theoretical and experimental results of "open" microstrip propagation on both a pure dielectric and a demagnetized ferrite substrate are presented. The theory enables one to obtain the frequency dependence of phase velocity and characteristic impedance, and also to obtain the electromagnetic field quantities around the microstrip line. It utilizes a Fourier transform method in which the hybrid-mode solutions for a "fictitious" surface current at the substrate-air interface are summed in such a way as to represent the fields caused by a current distribution that is finite only over the region occupied by the conducting strip and is assumed equal to that for the quasi-static case.

202 citations


Journal Article•DOI•
TL;DR: In this paper, a design theory for evanescent dominant mode waveguide filters is presented, where the cutoff guide is represented by its equivalent /spl pi/section network, the elements of which closely approximate lumped inductances.
Abstract: A design theory for evanescent dominant mode waveguide filters is presented. The cutoff guide is represented by its equivalent /spl pi/-section network, the elements of which closely approximate lumped inductances. Resonators may be formed by introducing appropriate capacitive obstacles at suitable intervals along the guide. The filter that results is a microwave analog of lumped inductance filters with series inductance coupling, the magnitude of the series "inductance" being controlled by the separation between capacitive obstacles. The theory derives the equivalent ladder network from the low-pass prototype and is accurate up to at least 20 percent band-widths. Filters may be designed to couple into other cutoff waveguide components using the same basic principles, a propagating guide, and coaxial terminations. The filters are normally constructed in standard production waveguide and are simple and cheap to manufacture. A considerable size and weight reduction, compared with orthodox waveguide filters, is possible at the cost of a small increase in insertion loss.

186 citations


Journal Article•DOI•
TL;DR: In this paper, the complete solution of the ridged waveguide eigenvalue problem is presented by the formulation of an integral eigen value equation which is subsequently solved numerically by application of the Ritz-Galerkin method.
Abstract: The complete solution of the ridged waveguide eigen-value problem is presented. The solution is obtained by the formulation of an integral eigenvalue equation which is subsequently solved numerically by application of the Ritz-Galerkin method. The significance of the eigenvalue spectrum is discussed and the modes are classified as either hybrid or trough modes. Equations are given for the electric and magnetic fields and a brief discussion of the edge singularity is presented. The theory is illustrated by computing the dominant eigenvalues and characteristic impedances of various unsymmetrical ridged waveguides.

177 citations


Journal Article•DOI•
TL;DR: In this article, the induced fields and the static heating patterns within a multilayered spherical model that approximates the primate cranial structure irradiated by plane waves in the microwave spectrum are calculated.
Abstract: The induced fields and the static heating patterns within a multilayered spherical model that approximates the primate cranial structure irradiated by plane waves in the microwave spectrum are calculated. The relation of the model to the biological structure and the sensitivity of the results to the uncertainties in the dimensions and electrical properties of biological material are investigated. A method of solution for both the scattered and the interior fields for a sphere with an arbitrary number of electrically different concentric layers is developed in a form readily amenable to machine computation. It is shown that the semi-infinite slab model is inappropriate for calculating the microwave radiation dosage for the human head and similar structures.

158 citations


Journal Article•DOI•
TL;DR: In this article, the convergence of numerical solutions of several iris-type discontinuity problems in waveguides and periodic structures is investigated, and it is shown that the numerical solution of a set of equations obtained from a mode-matching procedure (which corresponds to an integral equation formulation of the problem generally known as the moment method) may converge to an incorrect value if an improper ratio is chosen between the number of modal terms in the aperture and the number number of terms retained in the kernel of the integral equation.
Abstract: The convergence of numerical solutions of several iris-type discontinuity problems in waveguides and periodic structures is investigated. It is demonstrated that the numerical solution of a set of equations obtained from a mode-matching procedure (which corresponds to an integral equation formulation of the problem generally known as the moment method) may converge to an incorrect value if an improper ratio is chosen between the number of modal terms in the aperture and the number of terms retained in the kernel of the integral equation. Guidelines for efficient numerical computations are indicated.

146 citations


Journal Article•DOI•
Arthur W. Guy1•
TL;DR: In this article, the authors derived and evaluated expressions for the electromagnetic fields and associated relative heating patterns in two-Iayered biological tissue media exposed to a direct-contact rectangular aperture source.
Abstract: Expressions are derived and evaluated for the electro-magnetic fields and associated relative heating patterns in two-Iayered biological tissue media exposed to a direct-contact rectangular aperture source. The source consists of a linearly polarized electric field distribution specified in the plane of the aperture. The results may be used for many biomedical applications ranging from the design of diathermy applicators to the establishment of standardized electromagnetic field intensities in connection with research on electromagnetic effects in living biological media.

Journal Article•DOI•
TL;DR: In this paper, the reflection and transmission of a plane wave incident on a thin perfectly conducting screen perforated periodically with circular holes are considered, where the spacings between holes may be comparable to or less than the wavelength.
Abstract: The reflection and transmission of a plane wave incident on a thin perfectly conducting screen perforated periodically with circular holes are considered. The spacings between holes may be comparable to or less than the wavelength. The metal screen is assumed to be either backed by a flat dielectric sheet, or sandwiched between two or more dielectric sheets that are used to match the susceptsnce of the screen. The techniques of transmission line analysis and the method of moments are employed to obtain a solution for this general class of boundary-value problems. Numerical results for several cases of interest in both X and Ku bands were obtained and shown to be in good agreement with experimental measurements.

Journal Article•DOI•
TL;DR: In this paper, a numerical analysis in terms of finite elements of hybrid-mode propagation in closed microstrip is presented, and two modes with zero frequency cutoff are described; one is a quasi-TEM mode and the other a surface mode.
Abstract: A numerical analysis is presented in terms of finite elements of hybrid-mode propagation in closed microstrip. Two modes with zero frequency cutoff are described; one is a quasi-TEM mode and the other a surface mode. Also investigated is a third mode which corresponds to the lowest order waveguide mode in the absence of the strip.

Journal Article•DOI•
TL;DR: In this article, the output power from 12 IMPATT diodes has been combined in a single-cavity multiple-device oscillator and the condition for stable operation, the noise performance, and the locking behavior of the oscillator are discussed.
Abstract: The output power from 12 IMPATT diodes has been combined in a single-cavity multiple-device oscillator. The oscillator is free from the well-known moding problem of multiple-device oscillators. The objective of this paper is to present the oscillator-circuit theory, which clearly indicates why this particular circuit configuration can give a stable operation free from moding problems. To handle the formidable equations necessary for the analysis, the eigenfunction approach is extensively used. The condition for stable operation, the noise performance, and the locking behavior of the oscillator are all discussed. The noise performance is similar and the locking behavior identical to those of single-device oscillators.

Journal Article•DOI•
H.P. Schwan1•
TL;DR: A survey of thermal and non-thermal effects is presented in this paper with some recommendations for future work and a guideline for future standard work in complex fields is proposed It is based on the concept of a tolerance current density, which is stated to be near 3 mA/cm/sup 2/ between 1 and 1000 MHz.
Abstract: A survey of thermal and nonthermal effects is presented with some recommendations for future work A basis of all biophysical considerations are the electrical properties including dielectric constants and conductivities for nearly all body tissues Equations are presented which summarize previous experimental work and state dielectric constant and conductivity for tissues of high water content as functions of macromolecular content and frequency No evidence is available supporting resonance behavior Previous thermal work includes determination of depth of penetration values and the relative absorption cross section of man and was the basis for present standards Nonthermal principles which explain many previous observations are largely due to field-induced forces Such effects occur in the human body only at field-strength levels which are thermally dangerous Several important conclusions are made 1) Field-force effects cannot be enhanced by use of pulsed fields 2) It is not possible to directly stimulate nerve membranes by microwave fields 3) It is fluids and tissues Finally, a guideline for future standard work in complex fields is proposed It is based on the concept of a tolerance current density, which is stated to be near 3 mA/cm/sup 2/ between 1 and 1000 MHz The biophysical principles which pertain to the interaction of nonionizing electromagnetic radiations with biological systems are not discussed This was done in the past on several occasions The field will be summarized only briefly and attention will be given to problems not already delt with satisfactorily We intend to concentrate on some topics that are presently of particular interest

Journal Article•DOI•
TL;DR: In this article, a new method of synthesizing matched broad-band TEM-mode three-ports is presented, which consist of n sections in cascade with each section composed of two coupled lossless transmission lines of electrical length /spl theta/ and an intermediate resistor.
Abstract: A new method of synthesizing matched broad-band TEM-mode three-ports is presented. The three-ports consist of n sections in cascade with each section composed of two coupled lossless transmission lines of electrical length /spl theta/ and an intermediate resistor. The main object is to analyze and design broad-band unsymmetrical structures with the symmetrical three-port as a special and important case. The analysis of the three-port is performed by means of a more convenient four-port analysis. An even-odd-mode method is used and a new definition of the odd mode is introduced. This new definition considerably simplfies the treatment of unsymmetrical three-and four-ports with one half of the network identical to the other apart from an impedance scaling factor. The analysis yields two uncoupled two-ports in each mode. The even-mode networks are identical with cascaded quarter-wave impedance transformers while the odd-mode networks contain all the resistors. A new technique for their design is presented and a computer program for complete synthesis of hybrid three-ports has been worked out. Several experimental stripline three-ports were built. A three-section unsymmetrical (k=1.7) matched three-port showed a measured isolation better than 20 dB and a maximum VSWR of 1.3 from 5 to 12 GHz. The total loss of a four-section equal-power divider was 0.2dB, maximum VSWR 1.25, and minimum isolation 23 dB over the frequency range 2.5-12.0 GHz.

Journal Article•DOI•
TL;DR: In this article, synthesis procedures for commensurate linelength combline and capacitively loaded interdigital filters are presented, where a simple modification for using lumped capacitors is given and is found to yield excellent results for any practical bandwidth.
Abstract: Synthesis procedures are presented for commensurate linelength combline and capacitively loaded interdigital filters. A simple modification for using lumped capacitors is given and is found to yield excellent results for any practical bandwidth. The synthesis procedures for both filter types follow directly from the classical bandpass filter design approach using a transformed frequency variable. Two design examples are given to illustrate the design procedures and experimental results are presented for a 40 percent bandwidth combline filter. The problems of network sensitivity, use of network equivalents, and extension to other filter types are also discussed.

Journal Article•DOI•
TL;DR: FormuIas are derived for the direct calculation of the scattering parameters of a linear two-port, using measurements made on a test set having residual, tracking, and mistermination errors.
Abstract: FormuIas are derived for the direct calculation of the scattering parameters of a linear two-port, using measurements made on a test set having residual, tracking, and mistermination errors. The problem is formulated by representing the measuring system in terms of scattering parameters. Solutions using this formulation have previously been obtained only in an implicit manner using an iterative approach. The associated calibration procedure is included.

Journal Article•DOI•
TL;DR: In this article, the effects of 10-GHZ CW radiation on a poikilothermic invertebrate animal, Tenebrio molitor, were investigated in a waveguide and irradiated at waveguide powers of either 20 or 30 min or at 20 mW for 120 min.
Abstract: Several investigators have reported experiments in which microwave radiation caused biological damage at tissue temperatures which were not harmful when brought about by means other than microwaves. To study the effects of 10-GHZ CW radiation on a poikilothermic invertebrate animal, we irradiated early pupae of the mealworm beetle, Tenebrio molitor. Each pupa was inserted in a waveguide and irradiated therein at waveguide powers of 80 mW for either 20 or 30 min or at 20 mW for 120 min, after which their subsequent development was observed. In control groups similarly treated, except that no microwave power was applied, 90 percent metamorphosed to become normal adult beetles. In the irradiated groups only 24 percent developed normally; 25 percent died and 51 percent developed abnormally. In half of the abnormal animals, the front half had undergone metamorphosis to form a normal beetle head and thorax but the hind part remained in the pupal state. Temperature increases within pupae were recorded during irradiation. When these thermal conditions were duplicated by means of radiant heating, subsequent development of pupae was normal in 80 percent of the experiments. We therefore concluded that the abnormalities induced by microwave radiation were not a thermal effect.

Journal Article•DOI•
TL;DR: In this article, the authors investigated microwave heating of phantom models of human limbs by aperture sources, which consist of triple-layered circular lossy dielectric cylinders, and the resulting temperature patterns in the phantom models were detected by the use of a thermograph camera.
Abstract: Microwave heating of phantom models of human limbs by aperture sources is investigated theoretically and experimentally. These phantom models consist of triple-layered circular lossy dielectric cylinders. The three layers of dielectric materials simulate human tissues of fat, muscle, and bone. In the theoretical investigation, apertures operating in the frequency range of 433 to 2450 MHz are used as microwave sources for heating the dielectric materials. The theoretical investigation makes use of the technique of summation of cylindrical waves. A high-speed computer is used to calculate the numerical results. For the experimental investigation, an aperture is designed and built to operate at the frequency of 918 MHz. The resulting temperature patterns in the phantom models are detected by the use of a thermograph camera. The theoretical results are shown to be in agreement with the experimental results. The technique and results of this investigation may be applied towards the design of applicators for therapeutic heating of human tissues.

Journal Article•DOI•
TL;DR: In this paper, an active transversal filter concept for microwave frequencies is proposed, where silicon metal semiconductor field effect transistors (MESFETs) with high impedances are used as active coupling elements.
Abstract: An active transversal filter concept for microwave frequencies is proposed. Silicon metal semiconductor field-effect transistors (MESFETs) with high impedances are used as active coupling elements. A hardware implementation yields a minimum interval between equalized pulses of 1.5 ns. Simulations with improved MESFETs predict equalization for smaller pulse intervals than 400 ps.

Journal Article•DOI•
TL;DR: The sparse data generated in the western hemisphere on low-power-density modulated RF energy are considered, the reasons for their sparseness are noted, and the hypotheses on mechanisms that may provide an explanation for the observed effects and other possible effects are sketched.
Abstract: In recent years it has been recognized that low-power-density modulated RF energy can affect the functioning of higher living organisms. In this paper the sparse data generated in the western hemisphere on this subject are considered, the reasons for their sparseness are noted, and the hypotheses on mechanisms that may provide an explanation for the observed effects and other possible effects are sketched. Possible conclusions with regard to hazards to personnel are then considered.

Journal Article•DOI•
TL;DR: The use of lumped elements in microwave integrated circuits (MICS) is discussed in this article, where the design, fabrication, and performance of networks used in both active and passive circuits are described.
Abstract: The use of lumped elements in microwave integrated circuits (MICS) is discussed. The design, fabrication, and performance of networks used in both active and passive circuits are described. Studies on amplifier impedance matching and transforming networks have resulted in the achievement of a 35-dB-gain 6-W-CW 26-percent-efficient amplifier at 2.25 GHz using only lumped elements. Construction of lumped-element low-pass filters and 3-dB quadrature hybrids at S band have produced circuits much smaller than, but with performance comparable to, microstrip distributed circuits. At C band a large-impedance transformer operating as a filter had less than 0.4-dB loss for an impedance transformation close to 20:1. The performance of lumped-element circuits through X band is compared with that of distributed circuits from the standpoint of size, economy, and technological applications. Lumped-element circuits are competitive with distributed circuits through 6 GHz and are practical through 12 GHz.

Journal Article•DOI•
TL;DR: In this article, the capacitance coefficients for a system of irregular finite conductors on a dielectric sheet are considered, and an integral representation of the Green's functions for the desired mathematical model is presented.
Abstract: The capacitance coefficients for a system of irregular finite conductors on a dielectric sheet are considered. There are two parts to the Green's function-integral equation approach considered herein: the first deals with a derivation of Green's functions for a desired mathematical model; the second solves the integral equation by a discretization procedure in which a solution for a large number of unknowns is required-a significant limitation. This approach, however, allows treatment of rather complex finite geometric configurations that are useful in the design of modern thin-film circuits. An integral representation of the Green's functions for the desired mathematical model is presented in which ground planes are assumed at finite distances from the dielectric sheet. However, in this paper, final results are obtained only for the case in which ground planes are at infinity. Numerical results are presented for some typical multiconductor systems. For the case of a two-dimensional parallel strip problem, the result of the present analysis compares well with that available in the literature.

Journal Article•DOI•
TL;DR: In this article, the propagation of guided waves in a rectangular geometry having impedance boundary conditions is investigated and an impedance compatibility relation is derived that must be satisfied in order that a separable modal solution exists for a given impedance configuration.
Abstract: The propagation of guided waves in a rectangular geometry having impedance boundary conditions is investigated. An impedance compatibility relation is derived that must be satisfied in order that a separable modal solution exists for a given impedance configuration. Several new rectangular waveguides are developed; among them are 1) a tall rectangular waveguide operating in a dominant H/sub 10/ mode with no H/sub 0N/ modes; 2) a rectangular waveguide with two parallel anisotropic impedance surfaces; 3) a rectangular waveguide with two parallel walls having isotropic impedance surfaces, the other two walls being anisotropic; 4) a rectangular waveguide supporting only E modes; and 5) rectangular coaxial systems containing impedance surfaces. The modal structure of rectangular waveguides with impedance boundary conditions offers advantages over the conventional waveguide. The potential of oversizing for low-loss and high-power applications is enhanced because of the additional modal control provided by the impedance surfaces. Other applications are suggested.

Journal Article•DOI•
TL;DR: In this paper, the design of bandpass filters for microwave integrated circuits (MICS) utilizing dielectric resonators is discussed, and synthesis methods for both Tschebycheff and Butterworth responses are derived.
Abstract: Design of bandpass filters for microwave integrated circuits (MICS) utilizing dielectric resonators is discussed. Synthesis methods for both Tschebycheff and Butterworth responses are derived. Experimental results with S- and X-band filters are presented, and the agreement between theory and experiments is shown to be fairly good. Limitations on this technique due to poor temperature stability are also discussed.

Journal Article•DOI•
TL;DR: In this article, a new type of elliptic filter was proposed for narrow-band low-loss applications at VHF and UHF, particularly suitable for narrowband lowloss applications.
Abstract: The design of a new type of elliptic filter, particularly suitable for narrow-band low-loss applications at VHF and UHF, is presented. The filter is derived from a lumped-element bandpass prototype by replacing the lumped inductors, which are normally the main contributory factors to the loss, by a comparatively low-loss distributed network. The latter consists of an n-wire digital line short-circuited at one end, the length of which is i/8 or less. An experimental elliptic filter of fifth order was constructed at 136.6 MHz with a pass bandwidth of 5 MHz, having 60-dB points at /spl plusmn/ 7 MHz from midband. The measured insertion loss of 1.1 dB is lower than that of a comparable lumped-element filter by a factor of at least 3,5:1. It compares favorably also with a comb-line filter, both in terms of loss and physical size.

Journal Article•DOI•
TL;DR: In this article, a method of determining the microwave dielectric constant of microwave integrated circuit substrates is described, which is especially suitable to substrates being prepared for MICs since they are, in general, regular, rectangular, and, therefore, simple resonators.
Abstract: A method of determining the microwave dielectric constant of microwave integrated circuit substrates is described. The technique is especially suitable to substrates being prepared for MICs since they are, in general, regular, rectangular, and, therefore, simple resonators. The dielectric constant using this technique has been determined in the 2- to 12-GHz range for GaAs (/spl epsiv/R = 12.46), sapphire (/spl epsiv/R =9.37), polyguide (/spl epsiv/ =2.33), and Alsimag 772 (/spl epsiv/R = 10.08).

Journal Article•DOI•
TL;DR: In this paper, the authors derived the continuous modes for a circular dielectric rod, which are identified with the fields due to the scattering of a plane wave at oblique incidence from a rod, thus providing insight into their behavior.
Abstract: The continuous modes for a circular dielectric rod are derived. These modes are identified with the fields due to the scattering of a plane wave at oblique incidence from a dielectric rod, thus providing insight into their behavior. This identification suggests that the modes be classified as incident transverse magnetic (ITM) modes when the incident plane-wave portion of H/sub z/ is zero and as incident transverse electric (ITE) modes when the incident plane-wave portion of E/sub z/ is zero. The transition region from discrete to continuous modes is analyzed in detail. Very simple approximate modes are derived for use in optical waveguide studies.

Journal Article•DOI•
TL;DR: In this article, the method of moments is applied to three-dimensional microstrip problems to calculate lumped (or excess) capacitance, which can be used to compute the lumped capacitance of any microstrip discontinuity.
Abstract: The method of moments is applied to three-dimensional microstrip problems to calculate lumped (or excess) capacitance. As examples, the capacitance of open-circuited microstrip lines and the capacitance of rectangular microstrip sections are computed. The open-circuit data are basic to any three-dimensional problem. The method is a general one and can be used to compute the lumped capacitance of any microstrip discontinuity, such as bends and T junctions.