• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.6
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• pp.138-144
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• 2013

In XRF systems, various techniques have been developed for the synthesis of pulse shapes using digital methods instead of traditional analog methods. Trapezoidal pulse shaping algorithms can be used for digital multi-channel pulse height analysis in X-ray spectrometer systems. In this paper, an efficient trapezoidal filter architecture is presented. In addition, we present a hardware-efficient peak value detection algorithm. By the proposed algorithm, peak value detection error is decreased by half compared with the conventional algorithm. The proposed Digital Pulse Processing(DPP) algorithm is designed using Verilog HDL and implemented using an FPGA on a test board. It is demonstrated that the implemented DPP board works successfully in practical XRF systems.

• JSTS:Journal of Semiconductor Technology and Science
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• v.15 no.4
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• pp.462-470
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• 2015

In this study, we analyze the impacts of the trapezoidal fin shape of a double-gate FinFET on the electrical characteristics of circuits. The trapezoidal nature of a fin body is generated by varying the angle of the sidewall of the FinFET. A technology computer-aided-design (TCAD) simulation shows that the on-state current increases, and the capacitance becomes larger, as the bottom fin width increases. Several circuit performance metrics for both digital and analog circuits, such as the fan-out 4 (FO4) delay, ring oscillator (RO) frequency, and cut-off frequency, are evaluated with mixed-mode simulations using the 3D TCAD tool. The trapezoidal nature of the FinFET results in different effects on the driving current and gate capacitance. As a result, the propagation delay of an inverter decreases as the angle increases because of the higher on-current, and the FO4 speed and RO frequency increase as the angle increases but decrease for wider angles because of the higher impact on the capacitance rather than the driving strength. Finally, the simulation reveals that the trapezoidal angle range from $10^{\circ}$ to $20^{\circ}$ is a good tradeoff between larger on-current and higher capacitance for an optimum trapezoidal FinFET shape.

• Steel and Composite Structures
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• v.26 no.1
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• pp.17-29
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• 2018

The thermal effects on the buckling, postbuckling and nonlinear vibration behaviors of composite laminated trapezoidal plates are studied. Aiming at the complex plate structure and to simulate the temperature distribution of the plate, a finite element method (FEM) is applied in this paper. In the temperature model, based on the thermal diffusion equation, the Galerkin's method is employed to establish the temperature equation of the composite laminated trapezoidal plate. The geometrical nonlinearity of the plate is considered by using the von Karman large deformation theory, and combining the thermal model and aeroelastic model, Hamilton's principle is employed to establish the thermoelastic equation of motion of the composite laminated trapezoidal plate. The thermal buckling and postbuckling of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results reported in the literature. Moreover, the effects of the temperature with the ply-angle on the thermal buckling and postbuckling of the composite laminated trapezoidal plates are studied, the thermal effects on the nonlinear vibration behaviors of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are also presented for the different temperatures and ply angles.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.231-242
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• 2001

We showed in [2] that if r≤2, zero mean Gaussian of average error of the Trapezoidal rule is proportional to h/sub i//sup 2r+3/ on the interval [0,1]. In this paper, if r≥3, we show that zero mean Gaussian of average error of the Trapezoidal rule is bounded by Ch⁴/sub i/h⁴/sub j/.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.187-193
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• 2014

In this paper, we want to represent a method for ranking of two exponential trapezoidal fuzzy numbers. In this study a new Cardinality between exponential trapezoidal fuzzy numbers is proposed. Cardinality in this method is relatively simple and easier in computation and ranks various types of exponential fuzzy numbers. For the validation the results of the proposed approach are compared with different existing approaches.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.365-372
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• 2003

We show that if ${\gamma}$ $\leq$ 2, the average error of the composite Trapezoidal rule on two consecutive intervals is proportional to h$\^$2h+3/ where h is the length of each subinterval of the interval [0, 1]. As a result, we show that the Trapezoidal rule with equally spaced points is optimal in the average case setting when ${\gamma}$ $\leq$ 2.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.543-546
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• 1987

Trapezoidal wave is suitable for the modulating signal of the microcomputer based PWM inverter for the use of motor drives because the switching patterns can be generated by means of on-line computation. In this paper, the output waveform of three-level modulation inverters for the trapezoidal modulating signal is investigated both theoretically and experimentally.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.903-911
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• 1998

We show that if r $\leq$ 2, the average error of the Trapezoidal rule is proportional to $n^{-min{r＋l, 3}}$ where n is the number of mesh points on the interval [D, 1]. As a result, we show that the Trapezoidal rule with equally spaced points is optimal in the average case setting when r $\leq$ 2.

• Journal of Korea Water Resources Association
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• v.52 no.4
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• pp.255-264
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• 2019

The trapezoidal ribs had been installed in the retaining wall in order to reduce to flood damage in the impingement of mountain rivers. In this study, experiments in open channel with the trapezoidal ribs on sidewall were conducted to evaluate the effect of flow resistance by the trapezoidal shape. The hydraulic flow characteristics according to the flow rates were surveyed where the wall roughness is k-type that dimensionless spacings, ${\lambda}_{nv}$, are 6, 9, and 12. The flow-resistance factors such as roughness and friction coefficients increased generally with increase of the spacing of ribs. In high flow rate the friction coefficient showed the maximum value when ${\lambda}_{nv}$ is 9. Though the trapezoidal ribs has the relatively smaller flow resistance compared to the square ribs, their form drag accounted for mean 62% of the total flow resistance. It was confirmed that the optimal spacing of trapezoidal ribs to maximize the effect of flow resistance as the wall roughness increases are 9 to 12 times of the height of trapezoidal ribs.

• Steel and Composite Structures
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• v.51 no.1
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• pp.73-91
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• 2024

This paper has focused on presenting vibration analysis of trapezoidal sandwich plates with a damaged core and FG wavy CNT-reinforced face sheets. A damage model is introduced to provide an analytical description of an irreversible rheological process that causes the decay of the mechanical properties, in terms of engineering constants. An isotropic damage is considered for the core of the sandwich structure. The classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The First-order shear deformation theory of plate is utilized to establish governing partial differential equations and boundary conditions for the trapezoidal plate. The governing equations together with related boundary conditions are discretized using a mapping-generalized differential quadrature (GDQ) method in spatial domain. Then natural frequencies of the trapezoidal sandwich plates are obtained using GDQ method. Validity of the current study is evaluated by comparing its numerical results with those available in the literature. After demonstrating the convergence and accuracy of the method, different parametric studies for laminated trapezoidal structure including carbon nanotubes waviness (0≤w≤1), CNT aspect ratio (0≤AR≤4000), face sheet to core thickness ratio (0.1 ≤ ${\frac{h_f}{h_c}}$ ≤ 0.5), trapezoidal side angles (30° ≤ α, β ≤ 90°) and damaged parameter (0 ≤ D < 1) are carried out. It is explicated that the damaged core and weight fraction, carbon nanotubes (CNTs) waviness and CNT aspect ratio can significantly affect the vibrational behavior of the sandwich structure. Results show that by increasing the values of waviness index (w), normalized natural frequency of the structure decreases, and the straight CNT (w=0) gives the highest frequency. For an overall comprehension on vibration of laminated trapezoidal plates, some selected vibration mode shapes were graphically represented in this study.