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.     

Broad-band circulator models for active microwave circuit analysis

A general method is presented for determining a broad-band equivalent circuit of a lossy, nonideal circulator from the scattering parameters over the frequency range of interest. The equivalent circuit has application to the design and analysis of circulator-coupled circuits such as amplifiers and oscillators. The method is applied to two different circulator forms, in coaxial line and waveguide, to show the close agreement to measured performance that can be attained by the method in practice.     

Green's function calculations on circular microstrip patch antennas

Green's function calculations have been applied to solve the radiation problem of circular microstrip patch antennas. The patch is fed by either a microstrip line or a coax line to be approximated as delta-function-like sources. The resultant Galerkin elements involve only one-fold Sommerfeld-type integrals. The resonant frequency, impedance, and far-field pattern have thus been calculated, which compared nicely with measurements     

Input impedance of a circulator with an inphase eigen-excitation resonator

The input impedance of a circulator with an inphase eigen excitation resonator can be expressed by that of a 2-stage bandpass filter. The external Q factor of an inphase eigenexcitation resonator should be three-quarters that of rotational-phase eigen-excitation resonators to obtain a maximally fiat performance.     

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     

Two-dimensional Green's function for a wedge with impedance faces

The solution for the two-dimensional (2-D) Green's function for a wedge with impedance faces is presented. The important feature of this Green's function is that there are no restrictions on the locations for the source and observation points-they can be anywhere. Its development proceeds along two separate lines: one for when the source or observation point is far from the wedge vertex and another one for when it is close. Much of the effort that has been expended in these formulations has been in obtaining forms for the Green's function which are efficient to evaluate numerically. This involved deforming the various contours of integration so that they are rapidly convergent and separating the contributions from the numerous singularities that occur in the integrands and evaluating them in closed form. The formulations that are employed here allow for the individual field components such as the diffracted, geometrical optics, and surface wave components to be identified and studied individually so that a physical understanding for the various scattering mechanisms for the impedance wedge can be appreciated     

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     

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     

A UTD based asymptotic solution for the surface magnetic field on a source excited circular cylinder with an impedance boundary condition

An asymptotic solution based on the uniform geometrical theory of diffraction (UTD) is proposed for the canonical problem of surface field excitation on a circular cylinder with an impedance boundary condition (IBC). The radius of the cylinder and the length of the geodesic path between source and field points, both of which are located on the surface of the cylinder, are assumed to be large compared to a wavelength. Unlike the UTD based solution pertaining to a perfect electrically conducting (PEC) circular cylinder, some higher order terms and derivatives of Fock type integrals are found to be significantly important and included in the proposed solution. The solution is of practical interest in the prediction of electromagnetic compatibility (EMC) and electromagnetic interference (EMI) between conformal slot antennas on a PEC cylindrical structure with a thin material coating on which boundary conditions can be approximated by an IBC. The cylindrical structure could locally model a portion of the fuselage of an aircraft or a spacecraft, or a missile. Validity and accuracy of the numerical results obtained by this solution are demonstrated in comparison with those of an exact eigenfunction solution.     

An asymptotic solution for the surface magnetic field within the paraxial region of a circular cylinder with an impedance boundary condition

It is well-known that the high-frequency asymptotic evaluation of surface fields by the conventional geometrical theory of diffraction (GTD) usually becomes less accurate within the paraxial (close to axial) region of a source excited electrically large circular cylinder. Uniform versions of the GTD based solution for the surface field on a source excited perfect electrically conducting (PEC) circular cylinder were published earlier to yield better accuracy within the paraxial region of the cylinder. However, efficient and sufficiently accurate solutions are needed for the surface field within the paraxial region of a source excited circular cylinder with an impedance boundary condition (IBC). In this work, an alternative approximate asymptotic closed form solution is proposed for the accurate representation of the tangential surface magnetic field within the paraxial region of a tangential magnetic current excited circular cylinder with an IBC. Similar to the treatment for the PEC case, Hankel functions are asymptotically approximated by a two-term Debye expansion within the spectral integral representation of the relevant Green's function pertaining to the IBC case. Although one of the two integrals within the spectral representation is evaluated in an exact fashion, the other integral for which an exact analytical evaluation does not appear to be possible is evaluated asymptotically, unlike the PEC case in which both integrals were evaluated analytically in an exact fashion. Validity of the proposed asymptotic solution is investigated by comparison with the exact eigenfunction solution for the surface magnetic field.     

Green's functions and Brewster condition for a halfspace bounded by an anisotropic impedance plane

Dyadic Green's functions are obtained for a halfspace bounded by an anisotropic impedance plane. Using the Fresnel reflection coefficients, these functions are derived in planewave spectral forms. The Brewster condition is also obtained.     

Green's function for an unbounded biaxial medium in cylindricalcoordinates

The dyadic Green's function for an unbounded biaxial medium is treated analytically in the Fourier domain. The Green's function is initially expressed as a triple Fourier integral, which is next reduced to a double one by performing the integration over the longitudinal Fourier variable. A delta-type source term is extracted, which is dependent on the particular coordinate system     

A unified Green's function analysis of complicated DFB lasers

An efficient full-wave analysis technique for one-dimensional optical domains, known as the recursive Green's function method (RGFM), is presented for evaluation of distributed feedback (DFB) laser cavities with arbitrary material profiles. The method first constructs the Green's function of an inhomogeneous domain and subsequently uses Green's theorem to determine the laser optical field, lasing wavelength, and threshold gain. The technique is applied to investigate the performance of three DFB laser structures: a chirped-grating configuration, a modulated stripe width design, and a reduced duty cycle complex-coupled device. These structures are evaluated in terms of their single-mode lasing behavior and the uniformity of the optical field within the cavity     

Design of an ultra compact electronically tunable microwave impedance transformer

A novel ultra compact microwave tuneable impedance transformer topology is proposed. It consists of a classical /spl pi/ CLC network where an equivalent tuneable inductance is realised with a high impedance transmission line in series with fixed inductance and a diode's varactors. The realised hybrid prototype at 900 MHz operating frequency is only 0.06/spl lambda/-long. Impedance loads from 16.5 to 280 /spl Omega/ can be matched with a return loss better than -20 dB, and the relative bandwidth equals /spl plusmn/36% for a fixed 50 /spl Omega/ load.     

Properties of the dyadic Green's function for an unboundedanisotropic medium

Radiation in an unbounded anisotropic medium is treated analytically by studying the dyadic Green's function of the problem, initially expressed as a triple Fourier integral which is next reduced to a double one. Under certain conditions, the existence of incoming waves is verified. It is also found that exponentially decaying waves are possible in such media. Finally, the existence of branch points in the remaining integrand function is investigated, and appropriate branch cuts are proposed     

易集成的S波段小型化环行器的研制

采用半集总参数设计思路,利用高场工作模式和双Y中心结内导体形式,研制出了一种S波段电性能优良、体积十分小巧且易于集成的小型化环行器。环行器测试结果：在3．2GHz附近9％带宽范围,插损≤0．35dB,隔离≥20dB,驻波≤1．2,能在-55℃～＋85℃的宽温范围工作。     

The time domain Green's function and propagator for Maxwell's equations

The free space time domain propagator and corresponding dyadic Green's function for Maxwell's differential equations are derived in one-, two-, and three-dimensions using the propagator method. The propagator method reveals terms that contribute in the source region, which to our knowledge have not been previously reported in the literature. It is shown that these terms are necessary to satisfy the initial condition, that the convolution of the Green's function with the field must identically approach the initial field as the time interval approaches zero. It is also shown that without these terms, Huygen's principle cannot be satisfied. To illustrate the value of this Green's function two analytical examples are presented, that of a propagating plane wave and of a radiating point source. An accurate propagator is the key element in the time domain path integral formulation for the electromagnetic field.     

A hybrid representation of the Green's function in an overmodedrectangular cavity

A hybrid ray-mode representation of the Green's function in a rectangular cavity is developed using the finite Poisson summation formula. To obtain a numerically efficient scheme for computing the field generated by a point source in a large rectangular cavity, the conventional modal representation of the Green's function is modified in such a way that all the modes near resonance are retained while the truncated remainder of the mode series is expressed in terms of a weighted contribution of rays. For an electrically large cavity, the contribution of rays from distant images becomes small; therefore, the ray sum can be approximated by one or two dominant terms without a loss of numerical accuracy. To illustrate the accuracy and the computational simplification of this ray-mode representation, numerical examples are included with the conventional mode series (summed at the expense of long computation time) serving as a reference