A compact recursive trans-impedance Green's function for the inhomogeneous ferrite microwave circulator

A detailed analytical investigation of the circular ferrite circulator is provided in this paper. The ferrite is assumed to be radially inhomogeneous as a result of an azimuthally invariant demagnetization field. The cavity model of Bosma and the stratified ferrite model of Krowne and Neidert are used to construct a compact recursive Green's function in terms of wave impedances and azimuthal modes. The Green's function logarithmic singularity is treated separately and extracted to improve the convergence characteristics of the modal series. The impedance parameters of the circulator are obtained via an integration of the Green's function and its singular term; to obtain the scattering parameters, various matrix manipulations of the impedance parameters are invoked. Data are provided and compared with independent sources to demonstrate the veracity of the Green's function approach. Finally, a circulator design is offered using the Green's function method and scattering-parameter data associated with that design are compared with data from a three-dimensional finite-element electromagnetic simulation of a microstrip circulator. The correlation between both data sets further supports the validity of the inhomogeneous cavity model and the Green's function approach.     

An asymptotic closed-form microstrip surface Green's function forthe efficient moment method analysis of mutual coupling in microstripantennas

A relatively simple closed-form asymptotic representation for the single-layer microstrip dyadic surface Green's function is developed. The large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air-dielectric interface. This asymptotic solution remains surprisingly accurate even for very small (a few tenths of a free-space wavelength) lateral separation of the source and field points. Thus, using the present asymptotic approximation of the Green's function can lead to a very efficient moment method (MM) solution for the currents on an array of microstrip antenna patches and feed lines. Numerical results based on the efficient MM analysis using the present closed-form asymptotic approximation to the microstrip surface Green's function are given for the mutual coupling between a pair of printed dipoles on a single-layer grounded dielectric slab. The accuracy of the latter calculation is confirmed by comparison with numerical results based on a MM analysis which employs an exact integral representation for the microstrip Green's function     

Wide-Band Operation of Microstrip Circulators

Octave bandwidth operation of Y-junction stripline and microstrip circulators is predicted using Bosma's Green's function analysis. The width of the coupling transmission lines is found to be a significant design parameter. Theoretical and experimental results are presented which show that wide lines and a smaller than usual disk radius can be used to obtain wide-band operation. A microstrip circulator is reported which operates from 7-15 GHz. Also presented are an analysis of the input impedance and an approximate equivalent circuit for the Y-junction circulator which shows the relationship between Bosma's equivalent circuit and that of Fay and Comstock.     

An asymptotic closed-form representation for the groundeddouble-layer surface Green's function

An efficient closed-form asymptotic representation for the grounded double-layer (substrate-superstrate) Green's function is presented. The formulation is valid for both source (a horizontal electric dipole) and observation points anywhere inside the superstate or at the interfaces. The asymptotic expressions are developed via a steepest descent evaluation of the original Sommerfeld-type integral representation of the Green's function, and the large parameter in this asymptotic development is proportional to the lateral separation between source and observation points. The asymptotic solution is shown to agree with the exact Green's function for lateral distances even as small as a few tenths of the free-space wavelengths, thus constituting a very efficient tool for analyzing printed circuits/antennas. Since the asymptotic approximation gives separate contributions pertaining to the different wave phenomena, it provides physical insight into the field behavior, as shown by examples     

Theory and numerical calculations for radially inhomogeneouscircular ferrite circulators

This paper presents a new theory for the operation of microstrip and stripline circulators, specially set up to permit radial variation of all the magnetic parameters. A computer code, taking only a few seconds per calculated point on a modest computer, was developed from the theory, and calculated results are given. In the theory we develop a two-dimensional (2-D) recursive Green's function G suitable for determining the electric field E_x anywhere within a microstrip or stripline circulator. The recursive nature of G is a reflection of the inhomogeneous region being broken up into one inner disk containing a singularity and N annuli. G has the correct properties to allow matching to the external ports, thereby enabling s-parameters to be found for a three-port ferrite circulator. Because of the general nature of the problem construction, the ports may be located at arbitrary azimuthal angle φ and possess arbitrary line widths. Inhomogeneities may occur in the applied magnetic field H_app, magnetization 4πM_s, and demagnetization factor N_d . All magnetic inhomogeneity effects can be put into the frequency dependent tensor elements of the anisotropic permeability tensor. Numerical results are presented for the simpler but immensely practical case of symmetrically disposed ports of equal widths taking into account these radial inhomogeneities. Studies of breaking up the area into 1, 2, and 5 annuli are undertaken to treat specific inhomogeneous problems. The computer code which evaluates the recursive Green's function is very efficient and has no convergence problems     

Excess Loss of the Coupling System to Double-Function Optical Circulators Utilizing Lens Twice and Two-Fiber Tips

1 Introduction An optical circulatoris useful in advanced optical fibercommunication systems such as full duplex transmissionsystems[1 ~10]. With the development of fiber opticalcommunication,there is anincreasing demand for opti-cal circulators that are suitable for use with fiber opticsystems .Incomplexfiber optic systems ,there may be amultiplicity of fibers ,each requiring a si milar function.A conventional optical circulator cannot provide suchfunctions[11]. In addition,the circulator re…     

Rigorous image-series expansions of quasi-static Green's functions for regions with planar stratification

A novel image-series expansion scheme for quasi-static Green's function in n+1 layered media is obtained by expanding the frequency-dependent Hertz potential in finite expansions and remainder terms. The expansions utilize a unique recursive representation for Green's function, which is a generic characteristic of the stratification, and are explicitly constructed for n/spl les/3. While results for 0/spl les/n/spl les/2 are given for reference only, the expansion scheme for a double-slab configuration, n=3, is quite general and outlines the procedure for n>3, without any increase in the complexity. The expansion-remainder terms can be made negligibly small for sufficiently large summation indices in the quasi-static limit, leading to rigorous image-series expansion. The image-series convergence is accelerated by including a collective image term, representing a closed-form asymptotic evaluation of the series-remainder integral. Thus, the proposed computational procedure can be used as a simple tool for producing analytical data for testing numerical subroutines applied to direct problems such as electrical simulation of muscles in the biomedical field and inverse problems, such as electromagnetic imaging.     

A Generalized Spectral-Domain Green's Function for Multilayer Dielectric Substrates with Application to Multilayer Transmission Lines

A generalized full-wave Green's function completely defining the field inside a multilayer dielectric structure due to a current element arbitrarily placed between any two layers is derived in two-dimensional spectral-domain form. It is derived by solving a "standard" form containing the current element with two substrates on either side of it, and using an iterative algorithm to take care of additional layers. Another iterative algorithm is then used to find the field in any layer in terms of the field expressions in the two layers of the "standard" form. The locations of the poles of the Green's function are predicted, and an asymptotic form is derived along with the asymptotic limit, by use of which the multilayer Green's function can be used in numerical methods as efficiently as the single-layer grounded-dielectric-substrate Green's function. This Green's function is then applied to a few multilayer transmission lines for which data are not found in the literature to date.     

Application of successive approximation method to the computationof the Green's function in axisymmetric inhomogeneous media

The successive approximation method (SAM) is applied to the computation of the Green's function in axisymmetric inhomogeneous media, SAM is implemented by using an iterative procedure that produces a series, and the series is proven to be a Taylor series. The condition of the convergence is derived from the theory of functions of several complex variables. In each iteration, the Fourier-Hankel transform and its inverse are applied to the approximation of some order of the Green's function and the result is the approximation one order higher than the original. Fast Fourier-Hankel transform (FFHT) is employed to speed up the computation, and thereby, an algorithm SAM-FFHT is formulated     

On the Smith Chart (Letters)

In a recent paper, Konig et al. report the design of a wide-band Y-junction stripline circulator for the 18-26.5-GHz frequency band. In this paper, among the design constraints and assumptions, it is stated, "Adjust the ground plane spacing such that the first transformer step physically subtends an angle at the edge of the ferrite resonator equal to the coupling angle psi."     

印刷螺线天线的分析计算

本文运用全波分析法对印刷螺旋天线进行了算法分析,根据Helmholtz方程在边界处满足的边界条件系统推导了单层印刷螺旋天线在自由空间和媒质中赫兹矢量位形式的并矢格林函数。在其计算中采用了离散复镜像理论,适当提取渐近项,以加快积分的收敛速度,并避免了数值计算中非常麻烦的极点处理问题。通过矢理法推导了阻抗矩阵的激励矩阵。并对一由绝缘材料支撑的印刷螺旋天线进行了计算,为工程设计提供了理论依据。     

Electromagnetic conductivity imaging with an iterative Borninversion

A technique which uses low frequency electromagnetic fields to image the Earth's conductivity structure between two boreholes is developed. The scheme employs the Born approximation to linearize the integral equation formulation, and a regularized least squares method to invert the data for an initial estimate of the conductivity. A second Born approximation is then applied in a iterative manner to achieve better estimates of the structure. Numerical experiments show that this iterative method improves resolution when compared to normal Born inversion due to the fact that coupling between scattering currents is accounted for. The image quality is shown to be dependent on the operating frequency with the optimal frequency corresponding to the peak of a sensitivity function the authors have termed the Born kernel, which is the product of the primary electric field and the Green's function     

Anomalous mutual coupling between microstrip antennas

An asymptotic expansion of the microstrip Green's function is used to facilitate a study of mutual coupling between two printed antennas, and coupling versus element separation is presented for substrate parameters of practical interest. For certain substrate parameters, it is found that the magnitude of mutual coupling does not decay monotonically with increasing element separation. Instead, the magnitude exhibits a quasi-periodic oscillation which can be attributed to the interference of surface and space waves. The presentation and discussion of this anomalous behavior is the purpose of the paper. The asymptotic representation of the Green's function, which differentiates space wave terms from surface wave terms when source and observation points are largely separated, is used to characterize the behavior of mutual coupling in the principal planes     

Evaluation of edge effects in slot arrays using the geometricaltheory of diffraction

The geometric theory of diffraction (GTD) is applied to evaluate efficiently the coupling coefficient associated with the design of a waveguide-fed longitudinal shunt slot arrays. The coupling coefficient is proportional to the reaction integral between the field of a slot and the equivalent current distribution of another slot. Using an approximate form of the Green's function for the wedge, it is shown that the edge-diffraction field due to each slot is practically equal to the field of a suitable `mirror image' of such slot. In this way the actual coupling coefficient can be decomposed into a sum of coupling coefficients between slots on an infinite ground plane. The latter can be evaluated very efficiently so that inclusion of edge effects does not slow down the design procedure. The same approach also allows the computation of the relation between the self-admittance with and without the edge. Some test cases are provided which show that the overall error of this approximation can be neglected since it is comparable with the error due to mechanical tolerances     

Implicit 3-D dyadic Green's function using self-adjoint operatorsfor inhomogeneous planar ferrite circulator with vertically layeredexternal material employing mode-matching

Self-adjoint operators are found for the differential equations describing the z-dependent field variation in the medium external to the ferrite microstrip circulator puck. The external medium is, in general, inhomogeneously layered, consisting of media with permittivity properties, magnetic properties, or both. Eigenvalue equations characterizing the radially sectioned medium outside the puck are found, as are the eigenvectors. When the z-dependent parts are multiplied with the radial and azimuthal dependences, the complete three-dimensional (3-D) field expressions are determined. Source-constraint equations (representing microstrip lines) driving the circulator are then combined with the mode-matching technique to obtain in direct space, implicit dyadic Green's function elements. Mode orthogonality is employed to encourage sparsity in matrix system development where appropriate or convenient. The implicit Green's function is particularly useful because field information and s-parameters may be found in real space, completely avoiding typical inverse transformations     

Efficient analysis of planar microstrip geometries using aclosed-form asymptotic representation of the grounded dielectric slabGreen's function

A newly developed closed-form asymptotic representation of the grounded dielectric slab Green's function is used in a moment-method formulation to calculate the propagation constant of an infinite microstrip transmission line and the input impedance of a finite-length, center-fed printed dipole. In these problems, source and field points are laterally rather than vertically separated with respect to the substrate. The conventional Sommerfeld integral and the plane wave spectral integral (PWS) representations of the microstrip Green's function converge very slowly in this case. However, the asymptotic closed-form representation of the Green's function does not have this limitation, and it remains accurate even for very small lateral separation between source and observation points. A modified form of the Sommerfeld integral representation is used only for observation points in the immediate vicinity of the source, while the asymptotic form is used elsewhere. Some numerical results based on this approach are presented and are shown to compare very well with previous results based on the corresponding exact-integral or PWS forms of the Green's function     

A uniform asymptotic expansion for the Green's functions used in microstrip calculations

A uniform asymptotic approximation is developed in the limit of small substrate thickness for the Green's functions used in microstrip-type problems. The author develops an approximation which is uniformly valid for all distances from the source in the limit where the substrate region is thin, which is typically the case of interest for microstrip problems. The approximation is valid for a single-layer substrate. The expansions agree with previously published near and far-field results. The approximation is compared with numerical evaluations of the exact integral solution available for the problem.<>     

Use of Asymptotic Waveform Evaluation Technique in the Analysis of Multilayer Structures With Doubly Periodic Dielectric Gratings

The reflection and dispersion characteristics of multilayer structures that involve periodically implanted material blocks are obtained by using the MoM solution of the volume integral equation. The asymptotic waveform evaluation (AWE) technique is utilized to obtain a Pade approximation of the solution in terms of a parameter such as frequency or incident angle. The use of AWE technique enables a fast sweep with respect to the approximation parameter. Moreover, a robust method for extracting the dispersion characteristics of periodic structures via Pade approximation is proposed. The AWE procedure requires the calculation of high order derivatives of the complicated kernel function that consists of Green's functions for stratified medium. These derivatives are calculated by employing the automatic differentiation theory. The reflection coefficient, propagation constant and band diagram of the structure are obtained both via point-by-point simulations and through the use of AWE technique. It is observed that AWE technique increases the computational efficiency without losing accuracy.     

Analytical Solution to the n -nth Moment Equation of Wave Propagation in Continuous Random Media

Higher order symmetrical moments play an important role in wave propagation and scattering in random media, however it remains to be solved under strong fluctuations. In this paper, a modified Gaussian solution method is proposed for analytically solving the n-nth moment. After propagating through a random medium in the fully saturated regime, the higher order symmetrical moment of the received wave is the sum of products of the second moments, i.e., the Gaussian solution. In strong scattering regimes, the higher order symmetrical moment can be considered as a sum of the Gaussian solution and a non-Gaussian correction term, where the key issue is how to solve the derived equation of the correction term. Two methods are proposed, i.e., Green's function method and the Rytov approximation approach. Green's function method leads to a rigorous solution form, but it is complicated due to an integral equation. The approach using the Rytov approximation is found to be reasonable, as the correction is relatively small     

Nonlinear intermodulation coupling in ferrite circulator junctions

We have solved the nonlinear intermodulation coupling problem of a planar ferrite junction containing 3N ports. The coupling is represented as driving currents within the junction, and the induced fields can be solved by using the radiation and the boundary-value Green's functions. Maximum coupling of intermodulations occur if the excitation frequencies at the ports are close to the circulation frequency of the circulator. Also, we find that the static demagnetizing field can effectively increase the intermodulation output power