Transcendental Equation

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P. C. Kendall - One of the best experts on this subject based on the ideXlab platform.

  • Transcendental Equation for the vectorial modes of buried optical waveguides
    IEEE Photonics Technology Letters, 1997
    Co-Authors: P. Sewell, T.m. Benson, M Reed, P. C. Kendall
    Abstract:

    The free-space radiation mode (FSRM) method is extended to allow full vector modal analysis of buried optical waveguides to be computed semi-analytically in a very fast, efficient, yet accurate, manner. Both TE and TM dominated modes are investigated, identifying propagation constants via an explicit Transcendental Equation, and full field profiles.

  • exact Transcendental Equation for scalar modes of rectangular dielectric waveguides
    Optical and Quantum Electronics, 1994
    Co-Authors: C J Smartt, T.m. Benson, P. C. Kendall
    Abstract:

    A Fourier operator method has been used to derive for the first time an exact closed-form eigenvalue Equation for the scalar mode propagation constants of a buried rectangular dielectric waveguide. The new method has been implemented and the results used to determine the accuracy of the scalar finite-difference approach. It is hoped that the exact results obtained here may assist in the validation of the accuracy of the other numerical and semi-analytical methods.

Kui Liu - One of the best experts on this subject based on the ideXlab platform.

  • A new method for determining the undeformed chip thickness in milling
    Journal of Materials Processing Technology, 2001
    Co-Authors: Kui Liu
    Abstract:

    Abstract The determination of the instantaneous undeformed chip thickness is one of the key issues in the modelling of milling processes. The traditional chip thickness model, with an approximation form of h=f t sin θ , assumes the tooth path to be circular, and thus lacks accuracy. In this paper, a new approach for determining the undeformed chip thickness in milling with much higher accuracy is proposed. Through analysis of the true tooth trajectories, the true instantaneous undeformed chip thickness can be calculated by solving the deduced Transcendental Equation. Rather than using the cumbersome numerical method, a Taylor’s series is used to approximate the involved infinitesimal value in the Transcendental Equation, which results in an explicit expression for practical determination of the undeformed chip thickness with higher accuracy compared to the traditional model.

P. Sewell - One of the best experts on this subject based on the ideXlab platform.

T.m. Benson - One of the best experts on this subject based on the ideXlab platform.

  • Transcendental Equation for the vectorial modes of buried optical waveguides
    IEEE Photonics Technology Letters, 1997
    Co-Authors: P. Sewell, T.m. Benson, M Reed, P. C. Kendall
    Abstract:

    The free-space radiation mode (FSRM) method is extended to allow full vector modal analysis of buried optical waveguides to be computed semi-analytically in a very fast, efficient, yet accurate, manner. Both TE and TM dominated modes are investigated, identifying propagation constants via an explicit Transcendental Equation, and full field profiles.

  • exact Transcendental Equation for scalar modes of rectangular dielectric waveguides
    Optical and Quantum Electronics, 1994
    Co-Authors: C J Smartt, T.m. Benson, P. C. Kendall
    Abstract:

    A Fourier operator method has been used to derive for the first time an exact closed-form eigenvalue Equation for the scalar mode propagation constants of a buried rectangular dielectric waveguide. The new method has been implemented and the results used to determine the accuracy of the scalar finite-difference approach. It is hoped that the exact results obtained here may assist in the validation of the accuracy of the other numerical and semi-analytical methods.

Arti Vaish - One of the best experts on this subject based on the ideXlab platform.

  • An Investigation of Resonant Modes in Rectangular Dielectric Resonator Antenna Using Transcendental Equation
    Wireless Personal Communications, 2017
    Co-Authors: Mahender Singh, Rajveer Singh Yaduvanshi, Anil Kumar Gautam, Arti Vaish
    Abstract:

    This article presents an analysis of resonant modes in a rectangular dielectric resonator antenna and investigates the generation of higher order modes. Mathematical analysis of resonant frequency and Transcendental Equation using MATLAB has been performed. A prototype model for rectangular DRA has been developed. Resonant frequency of higher modes based on delta (δ) variation (where delta = 0.1–0.9) on Eigen vector has been investigated. The paper demonstrates that the design of a compact size dielectric resonator antenna (DRA) covering wide range of frequency with multiple modes is possible by selecting the value of p less than 1 (p 

  • An Investigation of Resonant Modes in Rectangular Dielectric Resonator Antenna Using Transcendental Equation
    Wireless Personal Communications, 2017
    Co-Authors: Mahender Singh, Rajveer S. Yaduvanshi, Abhishek Kumar Gautam, Arti Vaish
    Abstract:

    This article presents an analysis of resonant modes in a rectangular dielectric resonator antenna and investigates the generation of higher order modes. Mathematical analysis of resonant frequency and Transcendental Equation using MATLAB has been performed. A prototype model for rectangular DRA has been developed. Resonant frequency of higher modes based on delta (ź) variation (where delta = 0.1---0.9) on Eigen vector has been investigated. The paper demonstrates that the design of a compact size dielectric resonator antenna (DRA) covering wide range of frequency with multiple modes is possible by selecting the value of p less than 1 (p < 1), where p is number of half-wave variations in the z-direction of TEmnp modes. An orthogonal feed has been used to cancel out the undesired modes. Simulations and experimental measurements were carried out to verify the proposed idea. Theoretical, simulated, and experimental results of resonant frequency and gain of the antenna have been compared and are found to be in agreement with each other. The results presented should have useful potential applications in wireless communication systems and satellite applications.