• Structural Engineering and Mechanics
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• v.30 no.5
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• pp.593-602
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• 2008

This paper presents a new linearization algorithm to find the periodic solutions of the Duffing equation, under harmonic loads. Since the Duffing equation models a single degree of freedom system with a cubic nonlinear term in the restoring force, finding its periodic solutions using classical harmonic balance (HB) approach requires numerical integration. The algorithm developed in this paper replaces the integrals appearing in the classical HB method with triangular matrices that are evaluated algebraically. The computational cost of using increased number of frequency components in the matrixbased linearization approach is much smaller than its integration-based counterpart. The algorithm is computationally efficient; it only takes a few iterations within the region of convergence. An example comparing the results of the linearization algorithm with the "exact" solutions from a 4th order Runge- Kutta method are presented. The accuracy and speed of the algorithm is compared to the classical HB method, and the limitations of the algorithm are discussed.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.67-76
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• 2008

Limit cycle oscillations of a two-dimensional airfoil with quadratic and cubic pitching nonlinearities are investigated. The equivalent stiffness of the pitching stiffness is obtained by combining the linearization and harmonic balance method. With the equivalent stiffness, the equivalent linearization method for nonlinear flutter analysis is generalized to address aeroelastic system with quadratic nonlinearity. Numerical example shows that good approximation of the limit cycle can be obtained by the generalized method. Furthermore, the proposed method is capable of revealing the unsymmetry of the limit cycle; however the ordinary equivalent linearization method fails to do so.

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.3
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• pp.145-148
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• 2015

In this letter, we present a new linearization method for a voltage controlled oscillator (VCO)-based quantizer in an analog-to-digital converter (ADC). The nonlinearity of the VCO generates unwanted harmonic spurs and reduces the signal-to-noise and distortion ratio (SNDR) of the VCO-based quantizer. This letter suggests a frequency-to-current feedback method to effectively suppress harmonic distortion. The proposed method decreases the harmonic spurs by more than 53 dB. And a VCO-based quantizer employing the proposed linearization method achieves a high SNDR of 74.1 dB.

• Journal of Electrical Engineering and Technology
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• v.10 no.4
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• pp.1682-1691
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• 2015

In this paper, a real time implementation of selective harmonic elimination pulse width modulation (SHEPWM) using Real Coded Genetic Algorithm (RGA), Particle Swarm Optimization technique (PSO) and a new technique known as Linearization Method (LM) for Single Phase Matrix Converter (SPMC) is designed and discussed. In the proposed technique, the switching frequency is fixed and the optimum switching angles are obtained using simple mathematical calculations. A MATLAB simulation was carried out, and FFT analysis of the simulated output voltage waveform confirms the effectiveness of the proposed method. An experimental setup was also developed, and the switching angles and firing pulses are generated using Field Programmable Gate Array (FPGA) processor. The proposed method proves that it is much applicable in the industrial applications by virtue of its suitability in real time applications.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.12
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• pp.1339-1349
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• 2008

In this paper, a nonlinear relationship between an input complex envelope and an output complex envelope of m-th harmonic zone is theoretically analyzed, and AM/$AM_m$ and AM/$PM_m$ are defined. A scheme to extract these characteristics from measured in-phase and quadrature-phase data is suggested. The proposed analysis is verified with a fundamental-fundamental and fundamental-third harmonic measurements for a InGaP power amplifier(PA). Based on the harmonic-band nonlinear analysis and extraction scheme, a new technique to send a signal in m-th harmonic band with a harmonic signal Linearization Digital Predistortion(DPD) scheme is presented. A numerical analysis and a Look-Up Table(LUT) based DPD algorithms to linearize output signal on m-th harmonic zone are developed. For a 16- and a 64-QAM input signals, a DPD for third harmonic signal linearization is implemented, and output spectrum and signal constellation are measured. The wholly distorted signals are linearized, and thus the measured Error Vector Magnitudes (EVM) are 6.4 % and 6.5 % respectively. The results show that a proposed scheme linearizes a nonlinearly distorted harmonic band signals. The proposed nonlinear analysis and predistortion scheme can be applied to multiband transmitter in next generation software defined radio(SDR)/cognitive radio(CR) wireless system.

• The Transactions of the Korean Institute of Power Electronics
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• v.3 no.2
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• pp.118-124
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• 1998

This paper describes a relationship of a space vector PWM and a sinusoidal PWM and presents that the space vector PWM can produce linearly the output voltage to the unity MI(modulation index). At first, reference angles and holding angles are derived from expanding a Fourier series of the reference voltage waveform and then the angles are used for the inverter switching to linearize transfer characteristics of the inverter. In addition, the harmonic components of the output voltage are analyzed and on-line control is shown to be feasible by approximating in piecewise-linearization the reference and holding angles versus the MI. In V/f control of the induction motor, it is verified by the experiment that the motor current is changed smoothly for the variation of the inverter input voltage and the change of the reference voltage.

• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.581-597
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• 2008

In this paper, the double displacement coupled statics and dynamics of the electromechanical integrated electrostatic harmonic drive are developed. The linearization of the nonlinear dynamic equations is completed. Based on natural frequency and mode function, the double displacement coupled forced response of the drive system to voltage excitation are obtained. Changes of the forced response along with the system parameters are investigated. The voltage excitation can cause the radial and tangent coupled forced responses of the flexible ring. The flexible ring radius, ring thickness and clearance between the ring and stator have obvious influences on the double displacement coupled forced responses.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09b
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• pp.118-121
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• 2003

Generally, the repeater in CDMA(Code Division Multiple Access) included HPA(HI-Power Amplifier) to amplifier communication signals. Also , HPA contained PD(Predistortor) to maintain the linearization of amplifier characteristics. A configuration component of PD have been used electricity nonlinear devices such that diode. But this diode takes many influences at the circumstance temperature. Consequently, it can't maintain output linearization, and drop the communication quality. The manufacturer set bias of the circuit to the manual at the first out of ware-house low But the Q-point changes according to the change of the high temperature or low temperature. Therefore, we designed a system to maintain the Q-point by FDM(Fuzzy Decision Maker) in this paper.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.283-286
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• 2003

Generally, the repeater in CDMA(Code Division Multiple Access) included HPA(HI-Power Amplifier) to amplifier communication signals. Also, HPA contained PD(Predistortor) to maintain the linearization of amplifier characteristics A configuration component of PD have been used electricity nonlinear devices such that diode. But this diode takes many influences at the circumstance temperature. Consequently, st can't maintain output linearization, and drop the communication Duality. The manufacturer set bias of the circuit to the manual at the first out of ware-house low. But the Q-point changes according to the change of the high temperature or low temperature. Therefore, we designed a system to maintain the Q-point by FDM(Fuzzy Decision Maker) in this paper.