Gokhun Selcuk

Bio: Gokhun Selcuk is an academic researcher from ASELSAN. The author has contributed to research in topics: Phase-locked loop & Volume integral. The author has an hindex of 1, co-authored 9 publications receiving 7 citations.

Evaluation of hypersingular integrals on non-planar surfaces

Abstract: Solving electric field integral equation (EFIE) with Nyström method requires accurate evaluation of hypersingular surface integrals since this method does not use divergence conforming basis and testing functions. The success of the method also depends on accurate representation of non-planar characteristics of the scattering object. In this study Hadamard finite part interpretation is used to evaluate hypersingular integrals over non-planar surfaces, which are represented by their Taylor series expansions. Numerical tests are conducted to show the effectiveness of the formulas. Also a scattering problem is solved which confirms the accuracy.

Evaluation of hypersingular integrals on curvilinear surface elements

Abstract: In this study finite part integrals are utilized for evaluation of hypersingular and nearly-hypersingular surface integrals on curvilinear elements. These integrals are related to the second derivative of the free space Green' function and arise in the solution of electric field integral equation (EFIE) via locally corrected Nystrom (LCN) method. The curvilinear elements are represented by the Taylor series expansion of the surface function around the observation point. The hypersingular integral, defined on a curvilinear element, is written as a summation of hypersingular and weakly singular integrals which are defined on a flat surface. Numerical studies show that increased accuracy is obtained for hypersingular integrals on curvilinear elements.

Low phase-noise oscillator design using large signal transfer function and complex quality factor

Abstract: In this study we use large signal closed loop transfer function and complex quality factor to design a low phase noise feedback oscillator. The method offers two major advantages. First it evaluates the closed loop transfer function, which inherently takes into account the impedance mismatch between the elements of the loop and the nonlinear behavior of the active device. These factors affect the loaded quality factor of the frequency stabilization element, as well as the location of frequency at which minimum phase noise is obtained. Secondly the method uses complex quality factor to estimate the frequency of best phase noise performance. Unlike the conventional quality factor which only uses the derivative of phase response, complex quality factor takes into account both amplitude and phase variations and provide better insight for low noise design. It has been shown experimentally that complex quality factor changes significantly for saturated loop. By using complex quality factor of saturated loop, phase noise performance can be more accurately predicted compared to the methods which do not take saturation effects into account.

Solution of volume integral equations with novel treatment to strongly singular integrals

Abstract: Locally corrected Nystrom (LCN) method is applied for the solution of volume integral equations (VIEs). Unlike the conventional method of moments (MoM) procedure, LCN method does not use divergence conforming basis and testing functions to reduce the order of singularity of the integrand. Therefore LCN method needs to handle kernels with higher order singularities. For VIEs, worst singularity is due to the double derivative operator acting on free space Green's function and resulting integrals are referred to strongly singular integrals. Using finite part interpretation, we converted strongly singular integrals to regular integrals, for the solution of which conventional numerical methods can be applied. We have solved a three-dimensional scattering problem from a dielectric cube and showed the validity of the method.

A Ka-Band Front-End in 100nm GaAs Process for In-Band Full Duplex Communications

Abstract: In this study the authors introduce a Ka-band front-end to be used for in-band full-duplex (IBFD) communications. The design consists of a Rat-Race coupler to provide self-interference cancellation (SIC), a low noise amplifier (LNA), a power amplifier (PA) and an electrical balancing impedance; all implemented in 100nm low noise GaAs process provided by UMS. The circuit provided an isolation above 40 dB between the PA and the LNA. The 1 dB compression point of the transmitter at the antenna terminal is 12 dBm and the total noise Figure (NF) is better than 5 dB. The balancing impedance covers 3:1 voltage standing wave ratio (VSWR) circle in Smith chart. The chip consumes 500 mW power and has a die area of 7mm2.

Ultrarelativistic (Cauchy) spectral problem in the infinite well

Abstract: We analyze spectral properties of the ultrarelativistic (Cauchy) operator $|\Delta |^{1/2}$, provided its action is constrained exclusively to the interior of the interval $[-1,1] \subset R$. To this end both analytic and numerical methods are employed. New high-accuracy spectral data are obtained. A direct analytic proof is given that trigonometric functions $\cos(n\pi x/2)$ and $\sin(n\pi x)$, for integer $n$ are {\it not} the eigenfunctions of $|\Delta |_D^{1/2}$, $D=(-1,1)$. This clearly demonstrates that the traditional Fourier multiplier representation of $|\Delta |^{1/2}$ becomes defective, while passing from $R$ to a bounded spatial domain $D\subset R$.

Nearly Hypersingular Integrals by Double-Arctan Transformation in Higher Order Geometry Modeling

Abstract: In order to directly utilize the dyadic Green’s functions in surface integral equations (SIEs), a novel double-arctan transformation for nearly hypersingular integrals is proposed in this communication. This new transformation is flexible and applicable to nearly hypersingular integrals in the forms of $\hat {R}\hat {R}/R^{3}$ , $\hat {R}/R^{3^{^{}}}$ , and $1/R^{3}$ over the curved surfaces by a fully numerical method. With the help of the sigmoidal transformation to improve the stability of this new singularly handling method, there results an efficient solution for the third-order near-singularity problems in SIEs. Moreover, the proposed method is also effective for the lower orders of the nearly singular integral kernels. With typical testing cases, the performance of this method is fairly evaluated, and its validity and stability is well demonstrated.

Evaluation of hypersingular integrals on curvilinear surface elements

Abstract: In this study finite part integrals are utilized for evaluation of hypersingular and nearly-hypersingular surface integrals on curvilinear elements. These integrals are related to the second derivative of the free space Green' function and arise in the solution of electric field integral equation (EFIE) via locally corrected Nystrom (LCN) method. The curvilinear elements are represented by the Taylor series expansion of the surface function around the observation point. The hypersingular integral, defined on a curvilinear element, is written as a summation of hypersingular and weakly singular integrals which are defined on a flat surface. Numerical studies show that increased accuracy is obtained for hypersingular integrals on curvilinear elements.

Convergence rates of the TE EFIE scattering solutions from a PEC cylinder

Abstract: The method of moments (MoM) is implemented to simulate scattering from a PEC (perfectly electric conductor) cylinder in the TE(transversw electric) EFIE (Electric Field Integral Equation) approach. The procedure expresses the singularity integral and the hypersingularity integral in terms of an analytic function and employs a singularity isolation process coupled with numerical technique along the discretized segment to evaluate the self terms. It is known that, in the MoM technique, the choice of base functions and test functions is very important for the accuracy and convergence of the numerical analysis. Thus, in this paper, three conditions, obtained from the combination of basis functions and test functions, are adopted to get the induced currents on the PEC surface. These currents are compared to the analytical one in the relative rms current error to get the condition that shows fast convergence rate. The fast order of convergence of the current error, 2.528, is obtained under the combination of pulse basis function/delta test function.