Continuous potential Maxwell solutions on nodal-based finiteelements

A nodal-based finite-element approach for computing electric fields in heterogeneous media is presented. The primary calculation is formulated in terms of continuous potentials, so that no special care is required on element assembly at dielectric interfaces. The resulting Galerkin weak-form matrices exhibit the special Helmholtz structure, which guarantees the absence of parasitic solutions in driven problems with physically well-posed boundary conditions. The enhanced sparsity of the Helmholtz form mitigates the extra coupling effort associated with introduction of a fourth degree of freedom relative to direct E solution. E can be extracted from the computed potentials as a postprocessing step either at nodal positions or element centroids. Solutions obtained with this approach for several benchmark and practical problems are shown to be parasite-free and essentially indistinguishable from previously reported direct E computations     

A variational analysis of anisotropic, inhomogeneous dielectricwaveguides

The authors derive a variational formulation for anisotropic, dielectric waveguides using only the (E_x, E _y) or (H_x, H_y) components of the electromagnetic field. They show that the (E _x, E_y) formulation is completely equivalent to the (H_x, H_y) formulation. In fact, they are the transpose problems of each other. Given the variational formulation, one can derive the finite-element solution quite easily. The authors also show how to derive a variational expression where the natural boundary conditions are incorporated as an optimal solution of the variational expression. The theory is illustrated with a simple implementation of a finite-element solution. The solutions agree with previous results, and there is no occurrence of spurious modes     

Finite element analysis of electromagnetic scattering frominhomogeneous cylinders at oblique incidence

The method of weighted residuals is used for the derivation of a convenient weak statement that is utilized for a finite-element solution of the boundary value problem for the time-harmonic electromagnetic scattering from linear, isotropic, composite cylinders at oblique incidence. The weighted-residual statement of the problem involves the z components of the electric and magnetic field and is such that the continuity of the tangential electric and magnetic fields at media interfaces is directly enforced. The finite-element solution is carried out using the bymoment method. Numerical results for echo widths and field distributions within cylinders of various shapes and compositions are presented. Comparisons of some of the results with those obtained from exact eigenfunction expansion and integral equation solutions demonstrate the validity of the method and the associated computer program     

Diffraction by an arbitrary-angled dielectric wedge. I. Physicaloptics approximation

A complete form is presented of the physical optics solution to diffraction by an arbitrary dielectric wedge angle with any relative dielectric constant in cases of both E- and H-polarized plane waves incident on one side of two dielectric interfaces. The solution, which is obtained by performing the physical optics (PO) approximation to the dual integral equation formulated in the spatial frequency domain, is constructed by the geometrical optics terms, including multiple reflection inside the wedge and the edge diffracted field. The diffraction coefficients of the edge diffracted field are represented in a simple form as two finite series of cotangent functions weighted by the Fresnel reflection coefficients. Far-field patterns of the PO solutions for a wedge angle of 45°, relative dielectric constants 2, 10, and 100, and an E-polarized incident angle of 150° are plotted in figures, revealing abrupt discontinuities at dielectric interfaces     

Field theoretical treatment of E-plane waveguide junctionswith anisotropic medium

E-plane waveguide junctions containing an anisotropic medium are analyzed. The analysis is based on the equivalence principle and on cavity field expansions. Using the equivalence principle, magnetic surface currents are introduced at the imaginary boundaries chosen between the central region of the junction and the waveguides. The electric displacement D in the junction is expressed in terms of a solenoidal set and an irrotational set. Matching the tangential magnetic field at the imaginary boundaries leads to a matrix equation, the unknown of which are the amplitudes of the scattered waveguide modes. Using this method, the performance of E-plane waveguide junctions with full-height and partial-height ferrite post is analyzed. The influence of the completeness terms G_oq on the numerical results of an empty E-plane Y-junction is shown. The numerical results are compared with previously published experimental and theoretical results     

Diffusion and noise in GaAs material and devices

The variation of the diffusion coefficient D(E) versus the electric field strength E is determined at 300 K in n-type GaAs (N_D=3×10^-17 cm^-3 ), using pulsed high-frequency noise measurements. D(E) is found to increase slightly at low field, then to decrease down to one tenth of its ohmic value near the threshold field. Long (⩾4 μm) real n⁺-n-n⁺ Gunn diodes, with an arbitrary doping profile, can be modeled. Comparisons are made, and excellent agreement is found, between experimental and theoretical characteristics of two real diodes, with notch and with gradual doping profiles. The doping profile N_D(x ) is shown to have a considerable influence on the diode behavior, in regard to the electric field profile as well as the noise characteristics. Using the impedance field method, the noise current is modeled and found to by very sensitive in the D(E) variation law, in particular in the range of 2.5-4 kV/cm. The agreement between the experimental noise and the computed noise of real diodes is quite satisfactory when using the D(E) determined     

Silicon oxynitride and silicon oxynitride-silicon interface: aphotoemission study

A study of silicon-oxynitride materials and their interfaces with amorphous silicon using synchrotron radiation photoemission is discussed. The effect of the hydrogen atoms as an intralayer at the silicon-oxynitride-a-Si interface is also analyzed. The data relative to the bulk silicon oxynitride show that the valence band edge gradually shifts toward a higher binding energy as the [O]/[N] ratio (A) is increased. For the silicon-oxynitride-a-Si heterojunctions, the valence band discontinuities ΔE_v ranged from 1.1±0.15 eV in the case of A=0.08 up to 4.6±0.15 eV in the case of A=2.02. The effect of the hydrogen intralayer was to reduce the ΔE_v by 0.5±0.15 eV. The observed intralayer-induced effect is attributed to modification of the interface dipoles. A simple model calculation, based on electronegativity arguments, gives a reduction of 0.4 eV for A=0 and 0.46 for A corresponding to pure silicon dioxide (SiO₂)     

A generalized recursive algorithm for wave-scattering solutions intwo dimensions

A generalized recursive algorithm valid for both the E _z and H_z wave scattering of densely packed scatterers in two dimensions is derived. This is unlike previously derived recursive algorithms which have been found to be valid only for E_z polarized waves. In this generalized recursive algorithm, a scatterer is first divided into N subscatterers. The n-subscatterer solution is then used to solve the (n+n')-subscatterer solution. The computational complexity of such an algorithm is found to be of O (N²) in two dimensions while providing a solution valid for all angles of incidence. This is better than the method of moments with Gaussian elimination, which has an O(N³) complexity     

Robustness of mean E{X} and R charts

The effect of nonnormality on E{X} and R charts is reported. The effect of departure from normality can be examined by comparing the probabilities that E{X} and R lie outside their three-standard-deviation and two-standard-deviation control limits. Tukey's λ-family of symmetric distributions is used because it contains a wide spectrum of distributions with a variety of tail areas. The constants required to construct E{X} and R charts for the λ-family are computed. Control charts based on the assumption of normality give inaccurate results when the tails of the underlying distribution are thin or thick. The validity of the normality assumption is examined by using a numerical example     

Effect of hot-electron injection of high-frequency characteristicsof abrupt In0.52(Ga1-xAlx)0.48As/InGaAs HBT's

The effect of hot-electron injection energy (E_i) into the base on the high-frequency characteristics of In_0/52(Ga_1-xAl_x)_0.48 As/InGaAs abrupt heterojunction bipolar transistors (HBTs) is investigated by changing the composition of the emitter. There exists an optimum E_i at which a maximum current gain cutoff frequency (ft) is obtained. Analysis of hot-electron transport in the base and collector by Monte Carlo simulation is carried out to understand the above phenomenon. The collector transit time (τ_c ) increases with E_i, because electrons with higher energy transfer from the Γ valley into the upper L and X valleys. At first, the base transit time (τ_b ) decreases with E_i at the low E_i region. However, τ_b does not decrease monotically with E_i, because of the nonparabolicity in the energy-band structure of InGaAs. Consequently, there exists a minimum in the sum of τ_b and τ_c , in other words a maximum f_t, at an intermediate value of E_i     

Modeling of on-state MOSFET operation and derivation of maximumchannel field

A novel approach to modeling MOSFET operation in the threshold region is proposed. A two-dimensional Poisson equation is solved analytically and the current continuity equation is solved iteratively in a self-consistent feedback scheme. The I-V characteristics and the profiles of channel field and mobile charge sheet are found over the entire region of device operation. The boundary between linear and saturation regions of device operation is inherently nonexistent in the model. The physical mechanism underlying the high values of maximum channel field E_L beyond channel pinch-off is highlighted. A simple analytical E_L model is derived. A comparison of this E_L model with previous models is made in the context of the experimental data     

Asymptotic performance of M-ary orthogonal signals inworst case partial-band interference and Rayleigh fading

It is shown that for worst-case partial-band jamming, the error probability performance (for fixed E_b/N_I) becomes worse with increasing M for (M>16). The asymptotic probability-of-error is not zero for any E_b/N _I(>ln 2), but decreases inverse linearly with respect to it. In the fading case, the error-probability performance (for fixed E_b/N₀) improves with M for noncoherent detection, but worsens with M for coherent detection. For large E_b/N₀ the performance of the Rayleigh fading channel asymptotically approaches the same limit as the worst case partial-band jammed channel. However, for values of M at least up to 4096, the partial-band jammed channel does better. While it is unlikely that an M-ary orthogonal signal set with M>1024 will be used in a practical situation, these results suggest an important theoretical problem; namely, what signal set achieves reliable communication     

Periodic chiral structures

The electromagnetic properties of a structure that is both chiral and periodic are investigated using coupled-mode equations. The chirality is characterized by the constitutive relations D=εE+iξ_cB and H=iξ_cE+B/μ, where ξ_c is the chiral admittance. The periodicity is described by a sinusoidal perturbation of the permittivity, permeability, and chiral admittance. The coupled-mode equations are derived from physical considerations and used to examine bandgap structure and reflected and transmitted fields. Chirality is observed predominantly in transmission, whereas periodicity is present in both reflection and transmission     

Asymptotic performance of M-ary orthogonal modulation ingeneralized fading channels

The asymptotic (M→∞) probability of symbol error P_e,_m for M-ary orthogonal modulation in a Nakagami-m fading channel is given by the incomplete gamma function P(m, mx) where x=In 2/(E_b/N₀) and E_b is the average energy per bit. For large signal-to-noise ratio this leads to a channel where the probability of symbol error varies as the inverse mth power of E_b/N₀. These channels exist for all m⩾1/2. The special case of m=1 corresponds to Rayleigh fading, an inverse linear channel     

Error performance of a digitally processed binary ESK frequencyhopping receiver in the presence of large Doppler

Analysis is made of the effects of Doppler on the error rate performance of a low data rate binary FSK frequency hopping receiver, employing a discrete Fourier transform (DFT) technique for baseband detection. Bit detection decision is made by locating the maximum of the DFT outputs which, in the frequency domain, are assumed to be separated by 1/T where T is the bit period. Both the worst case and average error performances are obtained and presented as a function of E_b/N₀ for various values of M where E_b/N₀ is the signal bit energy-to-noise density ratio and M is the degree of freedom associated with the Doppler uncertainty window. The E _b/N₀ degradation as a function of M is also presented     

A complete E-plane analysis of waveguide junctions usingthe finite element method

A complete finite-element analysis of inhomogeneous E-plane waveguide junctions is presented. It is shown that at least two field components are needed for the analysis. This method solves for the three components of the magnetic field in two dimensions and calculates the scattering parameters of the junction. Precalculated matrices are used for fast matrix assembly. Results for a metallic post agree very well with earlier published values. A dielectric post was also analyzed     

Counting the number of minimum cuts in undirected multigraphs

The problem of counting the number of cuts with the minimum cardinality in an undirected multigraph arises in various applications, such as testing the super-λ-ness of a graph, as described by F.T. Boesch (1986), and calculating upper and lower bounds on the probabilistic connectedness of a stochastic graph G in which edges are subject to failure. It is shown that the number |C( G)| of cuts with the minimum cardinality λ(G) in a multiple graph G=(V,E) can be computed in O(|E|+λ(G)|V|² +λ(G)|C(G)||V|) time     

Modal S-matrix design of metal finned waveguide componentsand its application to transformers and filters

Optimized all-metal E-plane finned waveguide components are designed with the rigorous method of modal field expansion into the ridged eigenmodes, which includes both the higher order mode interaction between the step discontinuities and the finite thickness of the fins. The design, which combines the advantage of constant fin thickness with that of the optimum matching potential of different waveguide inner cross-section dimensions and fin heights, achieves very broadband transformers and evanescent-mode filters with improved performance. Computer optimized data demonstrate the efficiency of the method by typical design examples: compact transformers for WR112, WR42, WR15, and WR12 input waveguides to E-plane finned waveguides, corrugated lowpass filters designed for a cutoff frequency in the waveguide Ku and U bands, and an evanescent-mode bandpass filter with unequal fin heights. The theory is verified by available measurements     

Implementation and application of resistive sheet boundarycondition in the finite-difference time-domain method [EM scattering]

Use of a resistive sheet boundary condition in the finite-difference-time-domain (FDTD) analysis of scattering problems involving a resistively coated dielectric object is described. An algorithm is introduced through an analysis of E-polarized scattering from a thin resistive strip. For a given resistance, numerical experiments indicate that algorithm stability is ensured for time sampling intervals chosen according to a specific criterion. Validity of the resultant FDTD method is verified in a comparison of computed E-polarized scattering data for several resistive strips with existing data. Results on the E-polarized scattering behaviour of a resistively coated dielectric strip as a function of surface resistances and angle of incidence are also presented. Extension to the H-polarized case and application of the present method to pulsed problems are briefly discussed