On the electromagnetic field in a cavity fed by a tangentialelectric field in an aperture in its wall

Heretofore, the electromagnetic field produced by a specified tangential electric field in an aperture in the wall of an arbitrarily shaped cavity has most often been expanded in terms of cavity modes. An alternative approach, that of the electric field integral equation is presented. In this approach, the cavity field is expressed as the field of a surface density of tangential electric current, or a surface density of tangential magnetic current, or a combination of surface densities of tangential electric and magnetic currents on the boundary of the cavity. Each surface density is characterized by a single tangential vector function which is determined by the integral equation requiring that the part of the electric field tangent to the boundary of the cavity must reduce to the specified tangential electric field in the aperture and zero elsewhere on the boundary of the cavity. The electric field integral equation method is specialized to more easily determine the field inside an arbitrary cylindrical cavity excited by a tangential electric field in an aperture in its lateral wall. The method is further specialized to a circular cavity     

Galerkin solution for the thin circular iris in aTE11-mode circular waveguide

An integral equation for the transverse electric (TE) field in the aperture of a concentric circular iris in a transverse plane of a circular waveguide is approximately solved using Galerkin's method. The aperture field is represented by a finite sum of normal TE and TM (transverse magnetic) circular waveguide modes that fit the circular aperture. The numerical convergence of the Galerkin solution is demonstrated using the resultant aperture field distributions and equivalent shunt susceptance for the case of dominant TE₁₁-mode excitation. The resultant aperture electric field distribution closely resembles that of the TE₁₁ aperture mode alone, except for edge contribution behavior at the edge of the iris. A resonant or capacitive iris is possible over a restricted range of frequencies     

Analysis of pyramidal horn antennas using moment methods

A hybrid numerical technique is developed for electrically large pyramidal horn antennas radiating in free space. A stepped-waveguide method is used to analyze the interior surfaces of the horn transition. The electric field integral equation (EFIE) is employed on the outer surfaces of the pyramidal horn including the radiating aperture. Meanwhile, the magnetic field integral equation (MFIE) is used on the aperture to relate the aperture fields and those in the horn transition The resultant hybrid field integral equation (HFIE) is solved numerically by the method of moments. This formulation is both accurate and numerically stable so that high-gain microwave pyramidal horns can be analyzed rigorously. Far-field radiation patterns, both computed and measured, are presented for three electrically-large X-band horn antennas. The comparisons demonstrate that this method is accurate enough to predict the fine pattern structure at wide angles and in the back region. Computed far-field patterns and aperture field distributions of two smaller X-band horns are also presented along with a discussion on the validity of the approximate aperture field distributions routinely used in the analysis and design of pyramidal horns     

A field iterative method for computing the scattered electricfields at the apertures of large perfectly conducting cavities

An iterative method is developed for computing the scattered electric fields at the apertures of large perfectly conducting cavities. The field iterative method (FIM) uses Kirchhoff's approximation to initiate a two stage iterative process (i.e., the method of successive approximations), involving both the magnetic field integral equation and the electric field integral equation, to calculate the electric currents on the internal cavity walls and the electric fields across the aperture of the cavity. The technique combines the flexibility of the boundary-integral method with the speed necessary to efficiently analyze large scale cavity problems. The paper presents the general theory, and applies the technique to the problem of TE scattering from two-dimensional perfectly conducting cavities     

Diffraction of an H-polarized electromagnetic wave by a circular cylinder with an infinite axial slot

A comparison of three methods of solution for the problem of scattering and diffraction of a transverse electric (TE) polarized plane wave by an infinite circular cylinder having an infinite axial slot is presented. In one method of solution, the aperture field integral equation (AFIE) method, the fields in and around the cylinder are found from the apertureE-field and the Green's functions for the interior and exterior of a cylinder. In the other two methods, the fields are determined from the surface current, which is obtained by solution of theH-field integral equation (HFIE) or theE-field integral equation (EFIE). The field in the aperture of the cylinder is found from the three methods, and the advantages and disadvantages of each method of solution are discussed. In addition, it is also shown that for shell thickness less than 1/20 of a wavelength, the aperture fields do not differ signifcantly from those of an infinitely thin shell cylinder.     

Scattering and coupling properties of a slotted elliptic cylinder

Near-field analysis and coupling of a perfectly conducting slotted elliptic cylinder excited by an electric line source placed inside or outside the cylinder is considered. The solution can be easily extended to account for a z-polarized incident plane wave excitation. The separation of variables technique is used to express external and internal fields in terms of Mathieu and modified Mathieu functions with unknown expansion coefficients. The problem is then reduced to an integral equation in terms of the aperture field. The solution of the integral equation is carried out by expressing the aperture field in terms of a Fourier series expansion with unknown coefficients. Then Galerkin's technique is introduced to solve for the unknown aperture field coefficients. Results for the penetrated and near fields are given in terms of different parameters such as location and type of the excitation, aperture width, cylindrical axial ratio, and the loading of the cylinder     

The annular aperture antenna with a hemispherical center conductor extension

An annular aperture antenna mounted on an infinite ground plane and containing a hemispherical center conductor extension above the ground plane is investigated. A Green's function for the region above the ground plane is derived so as to be compatible with numerical solution techniques. A magnetic field integral equation is obtained in terms of the unknown tangential aperture electric field and is solved by the method of moments. A comparison between flush mounted and hemispherically extended annular aperture antennas is presented for the tangential aperture electric field, the coaxial line apparent input admittance, and the far radiated field.     

Radiation from a dielectric coated hemispherical conductor fed by acoaxial transmission line

A dielectric-coated hemispherical conductor mounted on an infinite perfectly conducting ground plane and fed by a coaxial transmission line is investigated. Green's functions for the region above the ground line are derived with separated homogeneous and particular solution parts so as to be compatible with numerical analysis techniques. A magnetic field integral equation is constructed in terms of the unknown annular aperture tangential electric field and is solved by the method of moments. A comparison of the characteristics of the dielectric-coated hemispherical conductor and a flush-mounted coaxial line to an infinite homogeneous region above the ground plane is presented with respected to the tangential aperture electric field, with respect to the tangential aperture electric field, the coaxial line apparent input impedance, and the far radiated field     

On combined source solutions for bodies with impedance boundary conditions

Numerical solutions to the impedance boundary condition (IBC) combined source integral equation (CSIE) for scattering from impedance spheres are presented. The CSIE formulation is a well-posed alternative to the IBC electric and magnetic field integral equations which can be contaminated by spurious resonant modes. Compared with the IBC combined field integral equation (CFIE), CSIE solutions have the same accuracy when the combined source coupling admittance is chosen to be the same value as the combined field coupling admittance. However, the CSIE formulation is better suited than the CFIE for creating a general purpose computer code capable of handling aperture radiation problems and/or a scatterer which has a spatially varying surface impedance.     

An approximate solution for coupling to a coaxial waveguide whichterminates at a conducting wedge

An integral equation is derived to approximate the aperture electric field for a coaxial waveguide that terminates at a conducting wedge. The integral equation is derived by retaining the standard kernel for the infinite-flange case and adapting the solution for the two-dimensional conducting wedge for use as the excitation term. The solution of this equation gives rise to an approximation to the TEM open-circuit voltage. Because only the excitation term is modified, the equation is useful for connectors that are greater than about one wavelength away from the corner. Theoretical and experimental results for the power transmitted down the coax are presented     

Experimentally based modeling of field sources forthree-dimensional computation of SAR in electromagnetic hyperthermia andtreatment planning

Presents field source-modeling, for applications to hyperthermia, by utilizing experimental data from the paraxial region of a liquid muscle-like phantom irradiated by an aperture antenna. The data are used in an optimization algorithm, applied to a Gaussian beam model (GBM), to determine the source parameters for GBM-computations of specific absorption rates everywhere, accurate to within 1% (relative to the global maximum) of the experimental results. This paper also shows how the aperture and incident fields may be determined accurately by the GBM and links them to the electric-field integral equation (EFIE), as an example, to improve the accuracy of numerical computations of the electric or magnetic fields associated with the EFIE, the magnetic-field integral equation, or any other field formulations. It is further demonstrated that models of plane waves, or approximate source fields, predict power levels with significant, unacceptable errors. Finally, it is concluded that the GBM is a viable tool for characterizing aperture antennas used in hyperthermia for cancer therapy     

Input admittance and aperture field of flanged coaxial line radiating into layered half-space

The problem of a semi-infinite coaxial line opening into a layered half-space with arbitrary number of layers is investigated. An integral equation for the radial component of the aperture electric field is formulated and solved numerically using the Galerkin method. Numerical computations were performed for two layer half-space in a numerical example taken from a biomedical engineering application in the irradiation of composite biological tissues with a radio frequency wave. Results for the input admittance as well as the aperture field distribution are presented and comparison with existing literature is made.     

Analysis of a cylindrical antenna containing an aperture coupledload

In this paper we present the basis for the analysis of shielded tuning networks coupled to wire antenna elements. The structure analyzed comprises three conducting cylindrical tubes that form an aperture-fed circular coaxial waveguide. Two methods are presented for formulating and solving integral equations for the structure. The first method is based on the mixed potential electric field integral equation enforced on the three cylindrical tubes, and the second is based on aperture theory. An end correction capacitance is used to adjust the reflection coefficient in the eigenmode expressions of the aperture method. The data obtained by the two methods are in close agreement. Differences in actual currents and equivalent currents obtained from solutions are discussed and reconciled     

The analysis of arbitrarily shaped aperture-coupled patch antennasvia a mixed-potential integral equation

A mixed-potential integral equation (MPIE) is formulated for the electric and magnetic currents on a multilayered aperture-coupled patch antenna. The integral equation is solved via the method of moments (MoM) using subsectional basis functions that allow the analysis of nonrectangular aperture and patch shapes. The input impedance and radiation efficiency of various aperture-coupled elements are calculated using the proposed technique and compared to measured results. The advantages and disadvantages of several aperture and patch configurations are discussed, and six methods of numerically de-embedding the element's input impedance are compared     

Transmission through dielectric-filled slots in a conductingcylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory     

Near-zone gain of open-ended rectangular waveguides

Full-wave solutions to the problem of radiation by open-ended rectangular waveguides (OEG) are presented. The radiation problem is formulated in terms of an electric field integral equation (EFIE). The EFIE is solved using the method of moments for three OEG antennas covering the frequency range from 200 to 750 MHz. Results for the near-zone gains as a function of both frequency and distance from the OEG aperture are presented. Estimates for uncertainties in the calculated gain are also given     

Improvement of prompt response from impulse radiating antennas by aperture trimming

Reflector impulse radiating antennas (IRA) traditionally have been constructed by terminating a self-reciprocal, transverse electromagnetic (TEM) transmission-line feed structure into a paraboloidal reflector. The section of the paraboloid used is usually circular in cross-section, with the outer boundary coinciding with the circle of symmetry of the TEM feed. The reflector converts the spherical TEM mode on the feed line into an approximate plane wave in the near field by geometric optics. The prompt radiated electric field in the direction of focus is given in the physical optics approximation in terms of the integral of the electric field of the TEM mode over the aperture plane inside the reflector boundary. Balanced feed structures have TEM modes that provide both positive and negative contributions to this integral in the aperture plane. Determination of the contour where the principal component of the electric field in the TEM mode is zero identifies portions of the aperture that contribute destructively to the integral. These portions are removed, thereby increasing the prompt radiated field without altering the feed structure or the applied voltage waveform. Furthermore, decreasing the size of the TEM feed relative to the aperture size, followed by appropriate aperture trimming, allows an even greater increase in radiated field. Results are presented that predict an increase in prompt radiated fields for all electrode configurations. Improvements are largest for electrode angles that are large (with respect to the vertical). The trends predicted by the numerical results are verified by an experiment conducted on a time-domain antenna range.     

Near-zone gain of 500 MHz to 2.6 GHz rectangular standard pyramidalhorns

Full-wave solutions to the problem of radiation by rectangular standard pyramidal horn antennas are presented. The radiation problem is formulated in terms of an electric field integral equation (EFIE), which is solved using the method of moments (MoM) for four rectangular standard pyramidal horns covering the frequency range from 500 MHz to 2.6 GHz. Results for the near-zone gains as a function distance from the aperture of the horn antenna are presented. A comparison is made with the analytical formula for the fields and near-zone gains     

Electromagnetic diffraction from a dielectric-filled slit-cylinderenclosing a cylinder of arbitrary cross section: TM case

A simple moment solution to the problem of the diffraction of a TM plane wave from an infinite, perfectly conducting slotted cylinder of an arbitrary cross section is summarized. The slit cylinder encloses a smaller perfectly conducting cylinder of an arbitrary cross section, and the space between the cylinders is filled with a dielectric material. The equivalence principle is used to obtain a set of coupled integral equations for the induced/equivalent surface currents on the cylinders, and the method of moments is used to solve numerically the integral equations. The electric field integral equation formulation is used. The advantages and the limitations of the method are discussed. Sample results for the induced current, aperture field, internal field, and scattering cross sections are given. These are in good agreement with some of the available published data     

Waveguide excited microstrip patch antenna-theory and experiment

An arbitrarily shaped microstrip patch antenna excited through an arbitrarily shaped aperture in the mouth of a rectangular waveguide is investigated theoretically and experimentally. The metallic patch resides on a dielectric substrate grounded by the waveguide flange and may be covered by a dielectric superstrate. The substrate (and superstrate, if present) consists of one or more planar, homogeneous layers, which may exhibit uniaxial anisotropy. The analysis is based on the space domain integral equation approach. More specifically, the Green's functions for the layered medium and the waveguide are used to formulate a coupled set of integral equations for the patch current and the aperture electric field. The layered medium Green's function is expressed in terms of Sommerfeld-type integrals and the waveguide Green's function in terms of Floquet series, which are both accelerated to reduce the computational effort. The coupled integral equations are solved by the method of moments using vector basis functions defined over triangular subdomains. The dominant mode reflection coefficient in the waveguide and the far-field radiation patterns are then found from the computed aperture field and patch current distributions. The radar cross section (RCS) of a plane-wave excited structure is obtained in a like manner. Sample numerical results are presented and are found to be in good agreement with measurements and with published data