Quasi-static conductor loss calculations in transmission lines using a new conformal mapping technique

Tuncer, E.; Lee, Beom-Taek; Islam, Md. Shahidul; Neikirk, Dean P.

doi:10.1109/22.310592

Cited by 28 publications

(12 citation statements)

References 20 publications

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“…The effective dielectric constant εeff and the overall capacitance for the CMS can be obtained: The scaling of the metal conductivity and the surface impedance concept, which has proven to be an efficient method for accurately evaluating the frequency dependent series impedance of transmission lines [10], is used to evaluate the frequency dependent inductance and the resistance of the CMS. Based on the mapping above, the scaling factor for the CMS and its series impedance equation are given as follows: δ is the skin depth and σ and t are the metal conductivity and the thickness of the metal, respectively.…”

Section: ⅲ Coplanar Multi Stripmentioning

confidence: 99%

Modeling of an On-Chip Power/Ground Meshed Plane Using Frequency Dependent Parameters

Hwang¹,

Kim²,

Pak³

et al. 2011

Journal of electromagnetic engineering and science

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This paper proposes a new modeling method for estimating the impedance of an on-chip power/ground meshed plane. Frequency dependent R, L, and C parameters are extracted based on the proposed method so that the model can be applied from DC to high frequencies. The meshed plane model is composed of two parts: coplanar multi strip (CMS) and conductor-backed CMS. The conformal mapping technique and the scaled conductivity concept are used for accurate modeling of the CMS. The developed microstrip approach is applied to model the conductor-backed CMS. The proposed modeling method has been successfully verified by comparing the impedance of RLC circuit based on extracted parameters and the simulated impedance using a 3D-field solver. Ⅰ. IntroductionRecently, communication, computing, and sensing systems have incorporated noise-sensitive analog RF circuits, and noisy digital circuits into a single chip/package for small form factors and high performance. In this type of mixed-mode system, however, the simultaneous switching noise (SSN) caused by high-speed digital circuits not only affects digital functionality but also degrades the receiver sensitivity and reliability of neighboring analog and RF circuits [1], [2].The amount of SSN is determined by the amount of current consumption of the circuits and the impedance profile of the power distribution network (PDN) seen from the circuits. An efficient way to reduce the amount of SSN is to design a PDN that has low impedance at the switching frequency and its harmonics. Therefore, estimation of the impedance properties of the PDN is important for the reliable operation of the system. As the operating frequency exceeds GHz levels, the highfrequency performance of the PDN should also be taken into consideration.For on-chip PDNs in high-speed systems, a meshed plane, as shown in Fig. 1, has been widely adopted because of its low inductance. The on-chip power/ground meshed plane has been extensively analyzed [3]～ [5]. However, it is difficult to apply previous works to meshed planes that are fabricated with standard CMOS processes because they are not compatible with the SPICE Fig. 1. Conventional on-chip power/ground meshed plane composed of two metal layers.simulator [3]. They are also not suitable for a standard CMOS process because of the vertical configurations; the metal thickness and the dielectric layer stack-up are different. Consequently, the applicable frequency range of the works is limited to a very narrow frequency range in a standard CMOS process [4], [5]. This paper provides details about the modeling of an on-chip meshed plane on low-resistivity silicon substrates. Quasi-static analysis using conformal mapping and the scaled conductivity concept are applied to calculate the frequency dependent parameters of the coplanar multi strip (CMS) structure. For a conductor-backed CMS, the developed microstrip approaches are simplified to suit the physical dimensions of the targeted structure and are applied to extract parameters. The impedance profiles of the...

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Section: ⅲ Coplanar Multi Stripmentioning

confidence: 99%

Modeling of an On-Chip Power/Ground Meshed Plane Using Frequency Dependent Parameters

Hwang¹,

Kim²,

Pak³

et al. 2011

Journal of electromagnetic engineering and science

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“…El modelo matemático comúnmente utilizado para describir diversos fenómenos físicos que ocurren en nuestro alrededor, producto de la interacción de campos eléctricos y magnéticos, carga y corriente eléctrica, se describe en la teoría electromagnética propuesta por J.C. Maxwell, [25,26], simplemente conocida como ecuaciones de Maxwell. En algunos procesos termo-eléctricos de interés práctico se puede asumir que los campos electromagnéticos varian de manera senoidal con respecto al tiempo como, por ejemplo, el conformado eléctrico o proceso de deformación de piezas metálicas sometidas a la acción de campos electromagnéticos de gran intensidad [18]; en soldadura eléctrica donde se estudia el comportamiento termoeléctrico de los electrodos y del material de soldadura, producto del efecto de Joule, [13,6]; y, en el diseño de circuitos eléctricos que trabajan con señales digitales y analógicas, para poder determinar la variación de la capacitancia, resistencia e inductancia eléctrica del sistema por medio del campo eléctrico y magnético [32,15]. Dada una frecuencia fija y aplicando la transformación de Fourier en tiempo, las ecuaciones de Maxwell se reducen a un conjunto de ecuaciones estacionarias en el dominio de la frecuencia; las cuales a su vez pueden ser compactadas en una sóla ecuación diferencial de segundo orden conocida como ecuación vectorial de Helmholtz.…”

Section: Introductionunclassified

Precondicionamiento del método LDG para la ecuación vectorial de Helmholtz

Alvarado

Castillo

2016

RMTA

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Se presenta un estudio numérico de un precondicionador para la ecuación vectorial de Helmholtz; el cual se deriva de la técnica del Laplaciano desplazado. Se utiliza una nueva versión del método “Local Discontinuous Galerkin” (LDG) como técnica de discretización espacial. Se valida la escalabilidad del precondicionador mediante una serie de experimentos numéricos en dominios poliédricos y aproximaciones de alto orden en problemas de bajas frecuencias en el caso real.

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“…Conformal mapping is one of the most powerful tools of complex analysis, and has been applied in many mathematical and physical fields, including those dealing with transmission lines12345, integrated circuit components67891011, electrostatic actuators1213141516, transformation optics1718192021, channel flows2223, and rough surfaces242526. Conformal mapping transforms a structure with a complex shape into a geometry that makes the problem more easily solvable.…”

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confidence: 99%

Conformal mapping for multiple terminals

Wang

et al. 2016

Sci Rep

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Conformal mapping is an important mathematical tool that can be used to solve various physical and engineering problems in many fields, including electrostatics, fluid mechanics, classical mechanics, and transformation optics. It is an accurate and convenient way to solve problems involving two terminals. However, when faced with problems involving three or more terminals, which are more common in practical applications, existing conformal mapping methods apply assumptions or approximations. A general exact method does not exist for a structure with an arbitrary number of terminals. This study presents a conformal mapping method for multiple terminals. Through an accurate analysis of boundary conditions, additional terminals or boundaries are folded into the inner part of a mapped region. The method is applied to several typical situations, and the calculation process is described for two examples of an electrostatic actuator with three electrodes and of a light beam splitter with three ports. Compared with previously reported results, the solutions for the two examples based on our method are more precise and general. The proposed method is helpful in promoting the application of conformal mapping in analysis of practical problems.

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Quasi-static conductor loss calculations in transmission lines using a new conformal mapping technique

Cited by 28 publications

References 20 publications

Modeling of an On-Chip Power/Ground Meshed Plane Using Frequency Dependent Parameters

Modeling of an On-Chip Power/Ground Meshed Plane Using Frequency Dependent Parameters

Precondicionamiento del método LDG para la ecuación vectorial de Helmholtz

Conformal mapping for multiple terminals

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