General Design Equations Research Articles

Engineered cementitious composites design framework for pavement applications

Engineered cementitious composites (ECCs) have gained attention as a potential material alternative for extending the lifespan of pavements and overlays due to their exceptional mechanical strength and ductility. This study presents a novel thickness design framework that incorporates the elastic and plastic regimes of ECCs, along with a wide range of mechanical properties, to develop general thickness design equations for the fatigue failure mode of ECC pavements. The pavement thickness design framework proposed in this study integrates three components: (1) experimental models characterizing the beam flexural fatigue performance of ECC materials; (2) Finite Element (FE) analysis to quantify the stress response of ECC pavements under vehicular loading; and (3) empirical stress equivalency functions to combine the FE analysis results with the beam flexural fatigue models and predict the fatigue life of ECC pavements during the plastic regime. Using the proposed framework, two general thickness design equations predicting the service life of ECC pavements were developed, one for the elastic regime and one for the plastic regime of ECCs. The thickness design equations developed are in terms of ECC material properties and empirical coefficients, which can be determined through experimentation and modeling. The analysis of the results indicates that the proposed framework provides a more accurate representation of the service life of ECC pavements, particularly during the plastic deformation regime, compared to previous design frameworks discussed in the literature.

A general design equation for Confined Impinging Jets mixers

A General Design Equation for Confined Impinging Jets (CIJ) is proposed here, giving the prediction of the position of the opposed jets’ impingement point. This equation was validated from numerical and experimental results, using fluids with viscosity ratios between 1 and 9 and density ratios between 1 and 10, both values within the industrial range of application of CIJs. The impingement point position is crucial for achieving effective mixing in CIJs, enabling the reactor’s design at optimal operational conditions. The general design equation considers the stoichiometry ratio, the fluids’ viscosity and density, and the reactors’ dimensions. This paper also establishes a methodology for the design of working conditions and the reactor’s design for the onset of the chaotic flow regime in CIJs.

Design of tri-band filtering power divider with out-of-band transmission zeros based on frequency transformation method

In this brief, a novel tri-band filtering power divider with a pair of out-of-band transmission zeros is presented. It mainly consists of tri-band filter matching structures, transmission lines introducing transmission zeros, and isolation resistors. Through even- and odd-mode analyses, general design equations for the three parts can be derived separately. By applying coupled lines, the circuit size is further compact. For verification, a third-order tri-band filter PD working at three independent bands with a pair of out-of-band TZs θz = 60° is designed. Good agreement between the measured and simulated results is attained so as to successfully validate the correctness of the proposed design approach.

Modified W-type configuration for a single-phase reduced parts count 81-level inverter.

The technology of modern power systems is revolutionizing as renewable energy sources are being integrated with electric power grids. In the form of inverters, power electronic converters are becoming an integral part of power systems due to their massive demand for grid integration of photovoltaic (PV) systems. Existing multilevel inverter topologies either require an output filter to get a sinusoidal voltage or generate a higher number of output voltage levels at the expense of many hardware resources. This paper presents a new single-phase 81-level inverter configuration with the name given as 'Modified W-Type Multilevel Inverter'. The proposed inverter configuration uses only eighteen power switches and four DC voltage sources to generate an 81-level output voltage approaching a sinusoidal waveform without an output filter. The general design equations are developed to calculate the number of switches, the number of voltage levels, and the number of DC sources for the proposed configuration. Loss and efficiency analysis is carried out that verifies a good practical efficiency of the proposed inverter configuration during the dynamic operation. A comparative analysis with the existing MLI topologies is also carried out that validates the effectiveness and novelty in reducing parts count and higher number of voltage levels. The proposed topology offers 1.04% total harmonic distortion of the output voltage which is within the benchmarks specified for grid integration without any filter requirements. The proposed inverter configuration is simulated in MATLAB/Simulink, and the results are validated by the design and development of a hardware prototype.

Pattern Classification and Gear Design of Spatial Noncircular Gear Continuously Variable Transmission

Noncircular gear and curve face gear are collectively referred to as spatial noncircular gear. Combined with the transmission characteristics of spatial noncircular gear, a new classification design method of spatial noncircular gear continuously variable transmission (CVT) pattern was proposed, including two categories named addition type and multiplication type, with a total of five subcategories. Through the combination of the transmission ratio changing mechanism and transmission selection mechanism, it can realize the CVT. The overall transmission ratio depends on the phase angle between the spatial noncircular gear pairs and is independent of the input rotation angle. Firstly, the CVT principle and transmission ratio characteristics of each pattern were analyzed. Then the tooth profile classification design of spatial noncircular gear was carried out, and the general parametric design equations of the tooth surface with different tooth profiles were obtained. Finally, through simulation, the overall transmission ratio of each pattern was compared between theory and simulation, which verified the correctness of the CVT classification design method. The advantages and disadvantages of the two categories were analyzed. Moreover, through the transmission experiments of curve face gear pairs with different tooth profiles, the transmission ratios were compared between theory and experiment. Considering the influencing factors such as machining error, assembly error and measurement error, the experimental error is within a reasonable error range, which verified the correctness of the tooth profile classification design method. This study provides a new idea for the further research and application of spatial noncircular gear CVT.

General design equations for arbitrary odd-way filtering Bagley polygon power divider with notch band

The general design equations are derived for arbitrary odd-way Bagley polygon power divider (BPPD) with filtering response and notch band. Firstly, conditions are derived to achieve a perfect input port impedance matching at centre frequency. Then, the formulas of introduced transmission zeros (TZs) are obtained for high-frequency selectivity, wide upper stopband and notch band. Based on the deduced equations, wideband BPPD (WBPPD), filtering BPPD (FBPPD) and FBPPD integrating notch band (FBPPD-N) with arbitrary odd-way power splitting are designed. Finally, a FBPPD-N with a wide passband bandwidth is fabricated and measured to verify the presented ideal. The experimental results indicate that the proposed FBPPD-N has compact size, high-frequency selectivity, wide upper stopband and required notch band. Consequently, the presented general design equations can provide effective guidance for the design of arbitrary odd-way power splitting FBPPD-N.

General design equations for 3‐way unequal‐split Bagley power dividers

In this study, general design equations for 3-way unequal-split Bagley power dividers (BPDs) are systematically derived. The proposed design procedure allows for obtaining power dividers with the same split ratio but with different solutions for design parameters. Conditions are firstly derived to achieve a perfect input port matching, then, taken into consideration to divide the power unequally between the output ports. A technique to compensate the resulting impractical high-impedance transmission lines is presented, where such lines are replaced by their equivalent single- and dual-frequency T-shaped sections. To validate the derived equations, different dividers with different split ratios, specifically, 1:3:1, 1:10:1, 3:1:3 and 10:1:10 are designed and simulated. Furthermore, 3-way dual-band 10:1:10 BPDs are designed, fabricated and tested. Very good agreement between simulated, theoretical and experimental results is found.

Differential Fed Antenna With High Self-Interference Cancellation for In-Band Full-Duplex Communication System

This paper presents a novel design of high self-interference cancellation (SIC) technique for microstrip antennas. The proposed antenna consists of two closely-spaced orthogonal antennas with differential feeding as SIC circuit so as to achieve high interport isolation between the transmitter and receiver. In order to achieve high RF leakage cancellation, a novel differential feeding network (DFN) is also proposed in this paper, which provides amplitude and out-of-phase imbalances within 0.12 ± 0.03dB and -180 ± 1°, respectively, for the bandwidth of 500 MHz at a center frequency of 2.50 GHz. General analytical design equations are derived for achieving high SIC over the wide bandwidth. For experimental validation, prototypes are designed and fabricated at the center frequency of 2.50 GHz using an FR-4 substrate with dielectric constant of 4.4 and loss tangent of 0.02. A good agreement is observed among the theoretical analysis, and the simulation and measurement results. The first fabricated prototype provides more than 64 dB SIC for the bandwidth of 110 MHz, while the second prototype achieved more than 60 dB SIC for 160 MHz bandwidth. In addition, the SIC of the antenna using the proposed DFN is high over the wideband frequency bandwidth as compared to conventional 180° ring hybrid feeding network. Due to ease of implementation and excellent performances, the proposed antennas have potential application for wideband in-band full duplex systems.

Theory and Experiment of Two-Section Two-Resistor Wilkinson Power Divider With Two Arbitrary Frequency Bands

In this paper, a novel design theory of two-section two-resistor Wilkinson power divider (WPD) is introduced. By selecting two different physical lengths of two-section transmission lines (TLs), two arbitrary frequency band WPD can be achieved. Compared with the former work, the designable frequency ratio range $u$ can be extremely extended from $1 to $1 , general design equations for characteristic impedances, physical lengths, absorption resistors, and frequency ratio ranges are newly derived and proved from even- and odd-mode analysis. Because of no capacitors or inductors, the proposed WPD can be used for high-frequency applications. Spurious band of $S_{21}$ appears between two passbands under the condition of two different physical lengths; therefore, a $\Pi$ -type dual-band transformer is newly introduced to replace single TL for spurious band suppression. We proved that $\Pi$ -type structure could effectively suppress spurious band of $S_{11}$ , maintain two arbitrary frequency passband of $S_{21}$ , and provide an extra isolation band of $S_{32}$ at center frequency. Finally, three proposed WPD examples with $\Pi$ -type structure are selected with different frequency ratios, where frequency ratio $u = 4$ in Example A, $u = 6$ in Example B, and $u = 20$ in Example C are designed and fabricated in the experiment. Measured results show good agreement with the theoretical results.

General design equations for the rotational stiffness, maximal angular deflection and rotational precision of various notch flexure hinges

Abstract. Notch flexure hinges are often used as revolute joints in high-precise compliant mechanisms, but their contour-dependent deformation and motion behaviour is currently difficult to predict. This paper presents general design equations for the calculation of the rotational stiffness, maximal angular elastic deflection and rotational precision of various notch flexure hinges in dependence of the geometric hinge parameters. The novel equations are obtained on the basis of a non-linear analytical model for a moment and a transverse force loaded beam with a variable contour height. Four flexure hinge contours are investigated, the semi-circular, the corner-filleted, the elliptical, and the recently introduced bi-quadratic polynomial contour. Depending on the contour, the error of the calculated results is in the range of less than 2 % to less than 16 % for the suggested parameter range compared with the analytical solution. Finite elements method (FEM) and experimental results correlate well with the predictions based on the comparatively simple and concise design equations.

A small wilkinson power divider with complex isolation component

ABSTRACTBy using complex isolation component, the proposed Wilkinson power divider occupy smaller area than that of conventional Wilkinson power divider. General design equations for complex isolation component are derived from even‐ and odd‐mode analysis. Various RLC circuits are chosen to realize complex isolation components, respectively. Considering the bandwidths of S22, S33 and S32, inductors in RLC circuits are omitted to get the widest bandwidths and easy fabrication. Compared with Trantanella's work, the proposed power divider provides wider bandwidths of S22, S33 and S32, and smaller capacitances under the same conditions, furthermore, the resistor in parallel RC circuit is constant value and suitable for industry applications. In experiment, one circuit was fabricated with parallel RC isolation component, experimental results showed good agreement with theoretical results. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 58:2163–2168, 2016

Theoretical demonstration of Brillouin lasing effect in racetrack resonators based on germanium waveguides in the mid-infrared.

In this Letter, we present a theoretical investigation of integrated racetrack Brillouin lasers based on germanium waveguides that are buried in silicon nitride and operate at a wavelength of 4 μm. General design equations in a steady-state regime have been carried out to determine the threshold power and the emitted Stokes power as a function of the resonance mismatch and coupling factor. The pulling effect as induced by the Brillouin gain dispersion and the pushing effects originated by SPM and XPM effects have been accurately investigated to predict the lasing frequency.

Miniaturized Dual-Band Wilkinson Power Divider With Self-Compensation Structure

A miniaturized dual-band Wilkinson power divider with a parallel LC circuit at the midpoints of two coupled-line sections is proposed in this paper. General design equations for parallel inductor L and capacitor C are derived from even- and odd-mode analysis. Generally speaking, characteristic impedances between even and odd modes are different in two coupled-line sections, and their electrical lengths are also different in inhomogeneous medium. This paper proved that a parallel LC circuit compensates for the characteristic impedance differences and the electrical length differences for dual-band operation. In other words, the proposed model provides self-compensation structure, and no extra compensation circuits are needed. Moreover, the upper limit of the frequency ratio range can be adjusted by two coupling strengths, where loose coupling for the first coupled-line section and tight coupling for the second coupled-line section are preferred for a wider frequency ratio range. Finally, an experimental circuit shows good agreement with the theoretical simulation.

Wilkinson Power Divider With Complex Isolation Component and Its Miniaturization

By adding a complex isolation component between two 90 ° transmission lines at an arbitrary phase angle from the input terminal, a small Wilkinson power divider provides physical separation and electrical isolation between two output ports. General design equations for the complex isolation component are derived from even- and odd-mode analysis. Parallel and series RLC circuits are chosen to realize complex isolation components, respectively. Considering the bandwidths of S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">22</sub> , S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">33</sub> , and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">32</sub> , inductors in both parallel and series RLC components are omitted to get the widest bandwidths; mathematical proof and design examples are also presented in this paper. A coupled line section with a compensating capacitor is introduced to reduce the circuit size, where characteristic impedances between even and odd mode are different in the coupled line section, and their electrical lengths are also different in inhomogeneous medium. Mathematical equations and simulation examples prove that the compensating capacitor compensates the characteristic impedance difference in the homogeneous medium and the electrical length difference in the inhomogeneous medium. Finally, an experimental circuit shows good agreement with the theoretical simulation.

Hydraulic design of A-type Piano Key Weirs

Piano Key Weirs (PKWs) are an alternative to linear overflow structures, increasing the unit discharge for similar heads and spillway widths. Thus, they allow to operate reservoirs with elevated supply levels, thereby providing additional storage volume. As they are relatively novel structures, few design criteria are available. Hence, physical model tests of prototypes are required. This study describes comprehensive model tests on a sectional set-up of several A-type PKWs, in which the relevant parameters were systematically varied. Considering data of former studies, a general design equation relating to the head–discharge ratio is derived and discussed. The latter is mainly a function of the approach flow head, the developed crest length, the inlet key height, and the transverse width. To extend its application range, case study model tests were analysed to provide a design approach if reservoir approach flow instead of channel flow is considered.

Planar 10:1 unequal three-port power dividers using general design equations

A microstrip three-port power divider with a power division ratio of 10 is suggested and fabricated. To reduce the size and difference between four transmission-line sections, a modified T-equivalent circuit is employed. The total transmission-line length required for the fabrication is only 44.4% of the conventional design and the measured results are in good agreement with predicted ones, showing that with the power division ratio of 10, return losses at all ports are better than 19.7 dB and isolation is better than 35 dB at a design centre frequency of 1 GHz.

Assessment of an Automation Algorithm for TDR Bridge Scour Monitoring System

Bridge scour is the number one cause of bridge failures. There are high risks associated with scour-induced damages due to their catastrophic nature. Developing real time bridge scour monitoring systems is a pressing task for the research community. Such systems need to be accurate, rugged, and field worthy. Implementing automatic signal interpretation is important to ensure the success of a long term scour monitoring instrument. This paper is part of the efforts to develop a TDR system to monitor the development of scour and sedimentation process. The focus of this paper is on an automation algorithm for TDR signal analyses. It discusses the theoretical foundation of this TDR algorithm for scour depth estimation. The influence of different types of sediments and the conditions of river (including the salinity and the effects of high air entrainment and suspended sediments) on the accuracy are assessed. The study indicates that the scour monitoring algorithm based on extending a physics-based general design equation is accurate under these different conditions. This will help implement a robust algorithm to automate the TDR bridge scour monitoring system.

평면 구조의 마이너스 군지연 회로 설계

본 논문에서는 기존에 제안된 일반적인 집중 소자 마이너스 군지연 회로가 설계시 사용 가능한 소자 값이 제한되어 있다는 점에 착안하여 마이너스 군지연 회로(Negative Group Delay Circuit: NGDC)를 평면 구조로 설계할 수 있는 방법에 관하여 제안한다. 몇 가지 형태의 집중 소자 회로를 해석하여 마이너스 군지연 특성을 얻을 수 있는 조건을 분석하고, 이를 수식화하여 설계에 이용할 수 있도록 하였다. 또한 전송 선로 공진기의 개념을 도입하여 집중 소자를 분산 소자로 변환할 수 있도록 하였다. 설계 예시로써, 군지연 시간이 -8 ns인 집중 소자 및 평면 구조의 1단 NGDC를 설계하여 비교하였다. 상용 주파수 대역 내에서 엄격한 평탄도 요구 조건을 만족시키는 마이너스 군지연 응답을 얻기 위하여, WCDMA(Wideband Code Division Multiple Access) 하향 대역에서 총군지연 시간이 -5.6 ns, 삽입 손실이 -0.2 dB, 대역폭이 30 MHz(2.125~2.155 GHz)이며, 해당 대역 내에서 삽입 손실 평탄도가 0.1 dB, 군지연 평탄도가 0.5 ns 이내인 평면 구조 2단 NGDC를 제작하였다. 제안하는 NGDC의 유용성을 검토하기 위하여 간단한 신호 상쇄 루프에 대한 실험을 수행하였으며, 뛰어난 신호 상쇄 효과를 얻을 수 있었다. In this paper, a planar structure negative group delay circuit(NGDC) is proposed to overcome the limited availability of the component values required for the prototype lumped element(LE) NGDC design. From the prototype LE circuit analysis, general design equations and the conditions to obtain the NGD are derived and illustrated. Then the LE circuit is converted into the planar structure by applying the transmission line resonator(TLR) theory. As a design example, the LE NGDC and the proposed planar structure NGDC are designed and compared. To estimate the commercial applicability, 2-stage reflection type planar NGDC with -5.6 ns of total group delay, -0.2 dB of insertion loss, and 30 MHz of bandwidth together with 0.1 dB and 0.5 ns of the magnitude and group delay flatness, respectively, for Wideband Code Division Multiple Access(WCDMA) downlink band is fabricated and demonstrated. Also, to show the applicability of the proposed NGDC, we have configured a simple signal cancellation loop and obtained good loop suppression performance.

Analysis of Lumped Element Negative Group Delay Circuit

In this paper, we have mathematically analyzed lumped element type negative group delay circuit (NGDC) and derived general design equation. The applicability of the proposed design equation is validated with mathematical and circuit simulation as well as with experimental results for intentional mobile telecommunication 2000 (IMT-2000) downlink band. As a design example, single branch NGDC with -0.8ns of group delay (GD) for narrow bandwidth of the specific frequency is simulated and fabricated. Finally, -network NGDC is proposed and validated to obtain wideband GD response of nsec for 60 MHz.

A Unidirectional Series-Elastic Actuator Design Using a Spiral Torsion Spring

This paper presents a novel series-elastic actuator (SEA) design that uses a spiral torsion spring to achieve drivetrain compliance in a compact and efficient mechanism. The SEA utilizes electromechanical actuation and is designed for use in the experimental biped robot KURMET for investigating dynamic maneuvers. Similar to helical torsion springs, spiral torsion springs are particularly applicable for legged robots because they preserve the rotational motion inherent in electric motors and articulated leg joints, but with less drivetrain backlash and unwanted coil interaction under load than helical torsion springs. The general spiral torsion spring design equations are presented in a form convenient for robot design, along with a detailed discussion of the mechanism surrounding the spring. Also, the SEA mechanism has a set of unidirectional hardstops that further improves the position control by allowing series-elasticity in only one rotational direction.