Realization of 2-D linear-phase FIR filters by using thesingular-value decomposition

The singular-value decomposition (SVD) technique is investigated for the realization of a general two-dimensional (2-D) linear-phase FIR filter with an arbitrary magnitude response. A parallel realization structure consisting of a number of one-dimensional (1-D) FIR subfilters is obtained by applying the SVD to the impulse response of a 2-D filter. It is shown that by using the symmetry property of the 2-D impulse response and by developing an appropriate unitary transformation, an SVD yielding linear-phase constituent 1-D filters can always be obtained so that the efficient structures of the 1-D linear-phase filters can be exploited for 2-D realization. It is shown that when the 2-D filter to be realized has some specified symmetry in its magnitude response, the proposed SVD realization would yield a magnitude characteristic with the same symmetry. An analysis is carried out to obtain tight upper bounds for the errors in the impulse response as well as in the frequency response of the realized filter. It is shown that the number of parallel sections can be reduced significantly without introducing large errors, even in the case of 2-D filters with nonsymmetric magnitude response     

Efficient Systolic Designs for 1- and 2-Dimensional DFT of General Transform-Lengths for High-Speed Wireless Communication Applications

In wireless communication, multiple receive-antennas are used with orthogonal frequency division multiplexing (OFDM) to improve the system capacity and performance. The discrete Fourier transform (DFT) plays an important part in such a system since the DFTs are required to be performed for the output of all those antennas separately. This paper presents area-time efficient systolic structures for one-dimensional (1-D) and two-dimensional (2-D) DFTs of general lengths. A low-complexity recursive algorithm based on Clenshaw’s recurrence relation is formulated for the computation of 1-D DFT. The proposed algorithm is used further to derive a linear systolic array for the DFT. The concurrency of computation has been enhanced and complexity is minimized by the proposed algorithm where an N −point DFT is computed via four inner-products of real-valued data of length ≈ (N/2). The proposed 1-D structure offers significantly lower latency, twice the throughput, and involves nearly the same area-time complexity of the corresponding existing structures. The proposed algorithm for 1-D DFT is extended further to obtain a 2-D systolic structure for the 2-D DFT without involving any transposition operation.     

Light output enhancement for nitride-based light emitting diodes via imprinting lithography using spin-on glass

The production of micrometric imprinted structures made of spin-on glass (SOG) is demonstrated in this paper. Two different mold materials, sapphire and silicon, are fabricated by dry and wet etching for both 1-D and 2-D patterns. The imprinting pressure, the imprinting temperature, and anti-adhesive films are also discussed. Finally, the imprinted structures are integrated with the chip process of the light emitting diodes (LEDs) in order to understand how the output optical efficiency is affected by those embossed SOG structures. In our study, both the 1-D and 2-D surface structures proved to be useful in enhancing the light extraction efficiency. The output intensity of the 2-D micro-cylinder structure on LEDs increased to 26.2% compared with that of conventional LEDs. In addition, the forward voltage is almost kept identical under a 20 mA injection.     

One- and two-dimensional constant geometry fast cosine transformalgorithms and architectures

This paper presents general radix one- and two-dimensional (1-D and 2-D) constant geometry fast cosine transform algorithms and architectures suitable for VLSI, owing to their regular structures. A constant geometry algorithm is obtained by shuffling the rows and columns of each decomposed DCT matrix that corresponds to a butterfly stage. The 1-D algorithm is derived, and then, it is extended to the 2-D case. Based on the derived algorithms, the architectures with a flexible degree of parallelism are discussed     

A fast and accurate design method for broad omnidirectional bandgaps of one dimensional photonic crystals

A fast and accurate novel design method is proposed for the design of broad omnidirectional bandgaps of one dimensional (1-D) photonic crystals (PCs). Presented method is verified with various numerical examples for 1-D photonic crystals which consist of a cascade of two quasi-periodic stacks and broad omnidirectional bandgaps are achieved. Furthermore, computation time requirement of the presented method is considerably less than that required for purely numerical approaches. The proposed algorithm is quite flexible and can easily be modified to address problems involving 1-D PCs consisting of three and more cascaded stacks and specific 2D PC structures.     

Spatial integration of direct band-to-band tunneling currents ingeneral device structures

A simplified integration technique for direct band-to-band tunneling current calculation in semiconductor devices of 1- or 2-D general device structures is described. The integration, along part of the depletion region, is of a tunneling generation function which depends on the local electric field. The simplified integration scheme relies on Kane's parabolic shaped gap barrier which accurately applies to such narrow-bandgap semiconductors as InSb and Hg_1-xCd_xTe. Tunneling current and zero bias resistance calculations in 1-D Hg_1-xCd_xTe p-n junctions using the proposed technique are presented. The extension of the technique to 2-D potential structures is demonstrated by modeling peripheral surface tunneling currents. The results compare well with measured reverse breakdown currents of InSb gate-controlled diodes     

Modeling and measurement of contact resistances

This paper presents a generalized model of ohmic contacts and a unified approach for the accurate extraction of specific contact resistivity (ρc) for ohmic contacts from measured contact resistance using the cross bridge Kelvin resistor, the contact end resistor, and the tranmsission line tap resistor test structures. A general three-dimensional (3-D) model of the contacts has been developed from the first principles and has been reduced to 2-D, 1-D, and 0-D (one lump) models with the necessary approximations. It is shown that the conventional I-D models overestimate the value of ρcbecause of the parasitic resistance due to 2-D current flow around the periphery of the contact window. Using 2-D simulations, we have accurately modeled the current crowding effects and have extracted accurate values of ρcindependent of contact size and the test structure type. A theory of scaling of contacts has been developed and is applied to commonly used structures. A universal set of curves has been derived for each particular contact resistance test structure and, given the geometry of the structure, these allow accurate determination of ρc, Without the actual use of the 2-D simulator. Experimental and theoretical accuracy of the three test structures has been compared. Accurate values of ρcfor various contact materials to n⁺and ρ⁺Si have been determined. The data confirm that in the past researchers have overestimated ρc, and that ρcwill not limit device performance even with submicrometer design rules.     

Realization of 2-D denominator-separable digital filter transfer functions using complex arithmetic

In this paper the problem of realizing 2-D denominator-separable digital filter transfer functions is considered for processing of real sequences. The approach is based on expressing the given 2-D transfer function as a sum of two reduced-order rational transfer functions with complex coefficients. New structures are obtained for equivalent reduced-order, complex-coefficient, 2-D transfer functions. All the realizations are basically parallelform structures with minimum-norm, low round-off noise and freedom from overflow limit cycles. A comparison of the different structures is also made.     

Study and design of step-index channel waveguide bends withlarge-angle and low-loss characteristics

By using micro-prisms, improved three-dimensional (3-D) bends of the embedded and buried waveguides of step-index profile are proposed. A simple phase compensation rule for the optimal design of the micro-prism is also presented. Through the simulation of 3-D semivectorial finite-difference beam propagation method, the transmission characteristics of the improved bends are shown to have been enhanced dramatically as compared with those of the conventional ones. Even for a bend angle of as large as 10°, the normalized transmitted power can still be greater than 95%. These results of 3-D bends are then compared with those of the two-dimensional (2-D) ones which are simplified from 3-D structures by the effective index method, and physical explanation of the discrepancy between the 3-D and 2-D results is introduced. The influences of waveguide structures and prism parameters on the transmission characteristics are discussed in detail. Some criteria for the design of large-angle low-loss 3-D improved bends are also accessed     

Two-dimensional orthogonal lattice structures for autoregressivemodeling of random fields

Two-dimensional orthogonal lattice filters are developed as a natural extension of the 1-D lattice parameter theory. The method offers a complete solution for the Levinson-type algorithm to compute the prediction error filter coefficients using lattice parameters from the given 2-D augmented normal equations. The proposed theory can be used for the quarter-plane and asymmetric half-plane models. Depending on the indexing scheme in the prediction region, it is shown that the final order backward prediction error may correspond to different quarter-plane models. In addition to developing the basic theory, the article includes several properties of this lattice model. Conditions for lattice model stability and an efficient method for factoring the 2-D correlation matrix are given. It is shown that the unended forward and backward prediction errors form orthogonal bases. A simple procedure for reduced complexity 2-D orthogonal lattice filters is presented. The proposed 2-D lattice method is compared with other alternative structures both in terms of conceptual background and complexity. Examples are considered for the given covariance case     

Direct recursive structures for computing radix-r two-dimensional DCT/IDCT/DST/IDST

In this paper, new recursive structures for computing radix-r two-dimensional (2-D) discrete cosine transform (DCT) and 2-D inverse DCT (IDCT) are proposed. The 2-D DCT/IDCT are first decomposed into cosine-cosine and sine-sine transforms. Based on indexes of transform bases, the regular pre-addition preprocess is established and the recursive structures for 2-D DCT/IDCT, which can be realized in a second-order infinite-impulse response (IIR) filter, are derived without involving any transposition procedure. For computation of 2-D DCT/IDCT, the recursive loops of the proposed structures are less than that of one-dimensional DCT/IDCT recursive structures, which require data transposition to achieve the so-called row-column approach. With advantages of fewer recursive loops and no transposition, the proposed recursive structures achieve more accurate results and less power consumption than the existed methods. The regular and modular properties are suitable for very large-scale integration (VLSI) implementation. By using similar procedures, the recursive structures for 2-D DST and 2-D IDST are also proposed.     

Full-wave analysis of guiding structures using a 2-D array of 3-DTLM nodes

A TLM approach to the full-wave analysis of guided wave structures is introduced. Instead of real pulses as in the conventional TLM method, complex pulses are used. Therefore a nonreciprocal phase shift in the z-direction can be introduced and used to connect the z arms in a 3-D node directly. As a result, the 3-D array of 3-D nodes, normally required in the TLM method to calculate the propagation and attenuation constant, is reduced to only one mesh unit in the z direction (a 2-D array of 3-D nodes). The propagation constant is determined by choosing a value and then calculating the frequency at which this value is valid from the Fourier transform of the impulse response. Losses are found by computing the exponential decay of time harmonic solutions at the eigenfrequencies of the structure     

Relations between the reflectance and band structure of 2-D metallodielectric electromagnetic crystals

In this paper, we present two different approaches to the problem of wave propagation in two-dimensional (2-D) periodic structures; one is the search of dispersion roots of which the real and imaginary parts represent the phase and decay constants of an unbound 2-D periodic medium, respectively, and the other is the investigation of the scattering characteristics of a finite 2-D periodic structure that is treated as a stack of 1-D periodic layers. Specifically, the rigorous mode-matching method is employed for both approaches, and the class of 2-D periodic structures with metal rods of rectangular cross-section is considered explicitly for mathematical formulation and quantitative analysis of associated physical phenomena. The mutual verifications of the results by the two different approaches facilitate the understanding of band structure of the 2-D periodic medium. In addition to the stopbands that can be easily identified to be due to the individual periodicity in either x or y direction, particular attention is directed to the combined effect of both periodicities, which results in the extra stopbands that are slanted at an angle on the Brillouin diagram. This provides the physical basis for the explanation of the unusually strong reflection of an incident plane wave in certain range of frequency or incident angle.     

Implementation of 2-D denominator-separable digital filters using first-order all-pass sections

It is established that denominator-separable transfer functions which characterize an important subclass of 2-D filters can be expressed as a linear combination of first-order (1-D or 2-D separable) all-pass transfer functions with real or complex coefficients. This type of expansion is referred to as all-pass expansion of the corresponding transfer function. Based on this all-pass expansion, we derive some efficient structures for the realization of 2-D denominator-separable filters using all-pass sections.On leave from S.V. University College of Engineering. Tirupati-517502, India.     

Regularization of Mixed-Potential Layered-Media Green's Functions for Efficient Interpolation Procedures in Planar Periodic Structures

The problem of improving the computational efficiency in the numerical analysis of planar periodic structures is investigated here using the mixed-potential integral-equation (MPIE) approach. A new regularization of the periodic Green's functions (PGFs) that are involved in the analysis of multilayered structures is introduced, based on the effective-medium concept. This regularization involves extracting the singularities of the PGFs up to second-order terms. The resulting regularized PGF is very smooth and amenable to interpolation. Thus, optimized interpolation procedures for the PGFs can be applied, resulting in a considerable reduction of computation time without any significant effect on the accuracy. Another benefit of the regularization is that it significantly enhances the convergence of the series for both the vector- and scalar-potential PGFs. The theoretical formulation is fully validated with various numerical results for both two-dimensional (2-D) and one-dimensional (1-D) layered-media periodic structures.      

Uniplanar one-dimensional photonic-bandgap structures andresonators

This paper presents uniplanar one-dimensional (1-D) periodical structures, so-called photonic-bandgap (PBG) structures, and defect high-Q resonators for coplanar waveguide, coplanar strip line, and slot line. Proposed uniplanar PBG structures consist of 1-D periodically etched slots along a transmission line or alternating characteristic impedance series with wide band-stop filter characteristics. A stop bandwidth obtained is 2.8 GHz with a stopband rejection of 36.5 dB. This PBG performance can be easily improved if the number of cells or the filling factor is modified in a parametric analysis. Using uniplanar 1-D PBG structures, we demonstrate new high-Q defect resonators with full-wave simulation and measured results. These structures based on defect cavity or Fabry-Perot resonators consist of a center resonant line with two sides of PBG reflectors. They achieve a loaded Q of 247.3 and unloaded Q of 299.1. The proposed circuits should have many applications in monolithic and hybrid microwave integrated circuits     

Hierarchical 2-D DD and HD noise simulations of Si and SiGe devicesII. Results

For pt. I see ibid., vol. 49, pp. 1250-1257 (2002). Terminal current noise is investigated with Langevin-type drift-diffusion (DD) and hydrodynamic (HD) noise models for one-dimensional (1-D) N⁺ NN⁺ and P⁺ PP⁺ structures and a realistic two-dimensional (2-D) SiGe NPN HBT. The new noise models, which are suitable for technology computer aided design (TCAD), are validated by comparison with Monte Carlo (MC) device simulations for the 1-D structures including noise due to particle scattering and generation of secondary particles by impact ionization (II). It is shown that the accuracy of the usual approach based on the DD model in conjunction with the Einstein relation degrades under nonequilibrium conditions. 2-D MC noise simulations are found to be feasible only if the current correlation functions decay on a subpicosecond scale, what is not always the case     

A fast spatial-domain method for the suppression ofexcitation-induced spurious modes in SCN TLM

An efficient method for the suppression of excitation-induced spurious modes in the symmetrical condensed node (SCN) transmission-line matrix (TLM) method is presented for the general case of dielectric, anisotropic, or lossy media in planar structures. A special mapping of the field-excitation onto the wave amplitudes of the TLM algorithm completely prevents the emanation of the spurious modes. The application of the mapping in the k-ω space can be done for waveguides with low computational effort. The method is generalized for planar structures with high spatial frequencies of the field at the discontinuities. We use precomputed field templates at the entrance of the three-dimensional (3-D) structures. The mapping is mainly done in the space domain based on the quasi-TEM propagation of the guided waves to keep the computational effort low. Instead of the four-dimensional (4-D) k-ω transformation, only independent one-dimensional (1-D) transformations to the wave coefficient of the conductors direction and ω are necessary. In the case of propagation with low dispersion, the expenditure can be further reduced to 1-D transformations with respect to ω. The efficiency of the present method is demonstrated by investigation of a coplanar waveguide and a triplate waveguide