• Journal of electromagnetic engineering and science
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• 제4권2호
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• pp.68-71
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• 2004

The limitation of telegrapher's equations for analysis of nonuniform transmission lines is investigated here. It is shown theoretically that the input impedance of a nonuniform transmission line cannot be derived uniquely from the Riccati equation only except for the exponential transmission line of a particular frequency-dependent taper. As an example, the input impedance of an angled two-plate transmission line is calculated by solving the telegrapher's equations numerically. The numerical results suffer from larger deviation from its rigorous solution as the plate angle increases.

• 한국전자파학회논문지
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• 제28권5호
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• pp.391-399
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• 2017

최근 기술의 증가로 인하여 전 분야의 전자제품은 더욱 경량화, 집적화되어가고 있으며, 안테나 역시 출력의 향상으로 전송선로 단에서의 EMC(Electromagnetic Compatibility) 해석이 중요해지고 있다. 본 논문에서는 외부의 안테나로부터 전송선로에 유기되는 노이즈를 예측하기 위하여 이론적 해석을 하였으며, 이를 전자기 시뮬레이션 해석과 비교, 검증하였다. 외부 안테나의 대표적인 예로서 본 논문에서는 전기 다이폴을 상정하였고, 이로부터 발생되는 전자기파에 의해 전송선로에 유기되는 전압, 전류를 얻어내기 위하여 수정된 전송선 방정식(modified telegrapher's equations)을 이용하여 수식을 유도하였다. 유도된 이론식은 전송선로에 대하여 전기 다이폴이 임의의 지점에 위치할 수 있도록 유도하여, 전송선로에 대하여 다양한 위치에 있는 전기다이폴에 의한 노이즈를 조사하였다.

• 한국전자파학회논문지
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• 제18권6호
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• pp.680-688
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• 2007

본 논문에서는 무손실을 가정한 다중 전송 선로에서 전압, 전류로 결합되어 나타나는 텔레그래프(telegrapher) 방정식의 시간 영역 Closed-form 해석해를 EP(Explicit Propagator) 방법을 이용하여 구하였다. 전송 선로에서 전압과 전류를 정확하게 얻기 위한 시간 영역의 표현식을 얻었으며, 본 논문의 결과를 검증하기 위하여 대칭 결합스트립 선로, 선형 테이퍼 형태의 비균일 결합 스트립 선로 그리고 삼중 비대칭 스트립 선로에 대한 과도 응답 특성을 구하고 상용 소프트웨어 결과와 비교하였다. 본 논문에서 개발된 시간 영역의 수치 해석 방법은 균일, 비균일 또는 대칭, 비대칭 스트립 선로의 시간 영역 파형에 대해 매우 정확한 결과를 보여주며, 다양한 결합 선로의 해석에 유용하게 사용할 수 있다.

• Smart Structures and Systems
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• 제18권2호
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• pp.335-354
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• 2016

This contribution presents an extended one-dimensional theory for piezoelectric beam-type structures with non-ideal electrodes. For these types of electrodes the equipotential area condition is not satisfied. The main motivation of our research is originated from passive vibration control: when an elastic structure is covered by several piezoelectric patches that are linked via resistances and inductances, vibrational energy is efficiently dissipated if the electric network is properly designed. Assuming infinitely small piezoelectric patches that are connected by an infinite number of electrical, in particular resistive and inductive elements, one obtains the Telegrapher's equation for the voltage across the piezoelectric transducer. Embedding this outcome into the framework of Bernoulli-Euler, the final equations are coupled to the wave equations for the longitudinal motion of a bar and to the partial differential equations for the lateral motion of the beam. We present results for the wave propagation of a longitudinal bar for several types of electrode properties. The frequency spectra are computed (phase angle, wave number, wave speed), which point out the effect of resistive and inductive electrodes on wave characteristics. Our results show that electrical damping due to the resistivity of the electrodes is different from internal (=strain velocity dependent) or external (=velocity dependent) mechanical damping. Finally, results are presented, when the structure is excited by a harmonic single force, yielding that resistive-inductive electrodes are suitable candidates for passive vibration control that might be of great interest for practical applications in the future.

• Smart Structures and Systems
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• 제18권2호
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• pp.355-374
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• 2016

This paper presents and compares a one-dimensional (1D) bending theory for piezoelectric thin beam-type structures with resistive-inductive electrodes to ANSYS$^{(R)}$ three-dimensional (3D) finite element (FE) analysis. In particular, the lateral deflections and vibrations of slender piezoelectric beams are considered. The peculiarity of the piezoelectric beam model is the modeling of electrodes in such a manner that is does not fulfill the equipotential area condition. The case of ideal, perfectly conductive electrodes is a special case of our 1D model. Two-coupled partial differential equations are obtained for the lateral deflection and for the voltage distribution along the electrodes: the first one is an extended Bernoulli-Euler beam equation (second-order in time, forth order in space) and the second one the so-called Telegrapher's equation (second-order in time and space). Analytical results of our theory are validated by 3D electromechanically coupled FE simulations with ANSYS$^{(R)}$. A clamped-hinged beam is considered with various types of electrodes for the piezoelectric layers, which can be either resistive and/or inductive. A natural frequency analysis as well as quasi-static and dynamic simulations are performed. A good agreement between the extended beam theory and the FE results is found. Finally, the practical relevance of this type of electrodes is shown. It is found that the damping capability of properly tuned resistive or resistive-inductive electrodes exceeds the damping performance of beams, where the electrodes are simply linked to an optimized impedance.