Capacitance Of Transmission Line Research Articles

New matrix algorithm for calculating diagonally matched impedance of packaging interconnecting lines

A novel numerical algorithm is developed for computation of diagonally matched impedance matrix of multiple coupled interconnecting lines in high-speed digital circuits. The algorithm is based on the properties of capacitance and inductance matrices of transmission lines and has unconditional monotonic convergence. The mathematical development is based on the theory of M matrices. The algorithm was applied to various metal lines with different dimensions, showing very good accuracy in comparison to other methods.

Evaluation of the high voltage transmission line inductance and capacitance using the finite element approach

In this paper the per phase inductance and the capacitance to neutral of a 220kV three‐phase overhead transmission line are calculated using a 2D finite element formulation. This study was performed considering the phase conductors transposition as well as the effect of the earth wires in the capacitance. The results produced by the finite element approach are compared with the analytical solutions showing a close agreement. Finally some conclusions are presented.

Capacitance of transmission line of parallel cylinders with variable radial width

This paper presents a formulation for evaluation of the capacitance of a pair of cylinders of unequal radii with variable and different width of dielectric on the cylinders. Conformal transformation using co-tangent hyperbolic function transforms the conductor boundaries to parallel plates and dielectric boundaries to curved contours. The expression for the capacitance is derived taking into account the changes in signs of the functions representing the curved contours. Numerical data on capacitance are presented.

The current–voltage characteristic in an ultrasmall junction

The current–voltage characteristics of ultrasmall superconductor–insulator–normal metal (S–I–N), and a superconductor–insulator–superconductor (S–I–S) junctions are computed in the presence of a dissipative transmission line. The amplitude of the discontinuous jump at the energy gap of a single-particle current is greatly influenced by the size of the capacitance and the impedance of the external transmission line in the small junction. The results agree with Ambegaokar–Baratoff in the limit of vanishing impedance of a transmission line or large junction capacitance.

Electrodeless thin film conductance measurements using the Sommer–Tanner method

A method to determine the electrical conductance of thin films such as a-Si:H that does not require contacting electrodes is presented. This method, introduced by Sommer and Tanner, is based on measuring the phase shift of a capacitive transmission line. The lower detection limit for the geometry used here is 10−11 Ω−1, which makes it suitable to determine the photoconductivity of a-Si:H thin films. The method shows reasonable agreement with classical conductance measurements using sputtered electrodes.

A novel method of measuring microelectronic interconnect transmission line parameters and discontinuity equivalent electrical parameters using multiple reflections

This paper describes a novel technique which measures the electrical properties of transmission lines (such as microstrip) and extracts equivalent electrical parameters for discontinuities in transmission lines with remarkable precision using a modern network analyzer and newly developed de-embedding software. This technique has successfully measured the per-unit-length inductance (L'), resistance (R'), capacitance (C'), and dielectric loss conductance (G') of microstrip transmission lines made from solid copper and conductive polymer. These materials have been studied at frequencies up to 201 MHz, and higher frequencies are possible. Discontinuities, such as an opening in the ground plane under the microstrip, have also been characterized at frequencies up to 2400 MHz. Measurements of characteristic impedances and skin resistances made by this method are in agreement with theoretical models. Higher frequency measurements should be feasible using a higher frequency network analyzer.

Full wave analysis of transmission lines in a multilayer substrate with heavy dielectric losses

The worldwide CMOS integrated circuits industry relies on heavily doped silicon wafers as the starting material for chip fabrication; the resulting integrated circuits are confined to the upper few microns of the wafer, which itself is as much as 600-/spl mu/m thick. These heavily doped silicon substrates are not insulators, but are actually very lossy; a loss tangent of 10/sup 5/ at 1 MHz is a fairly typical characteristic of the wafers. Although it is becoming increasingly necessary to model accurately the currents which flow between transistors and interconnects into the substrates, existing computer-aided design (CAD) simulation packages fail to provide accurate results in modeling such heavy dielectric losses, because most CAD packages rely on small perturbation methods in the analysis of dielectric losses. In this paper, the problem of computing the electrical behavior of lossy dielectrics is analyzed by the full wave method, and the mutual capacitances of transmission lines above such heavily doped CMOS substrates are computed and compared with laboratory experimental measurements. Good agreement between analytical and measurement results has been obtained.

A hybrid wavelet expansion and boundary element analysis for multiconductor transmission lines in multilayered dielectric media

In this paper the wavelet expansion method, in conjunction with the boundary element method (BEM), is applied for the evaluation of the capacitance and inductance matrices of multiconductor transmission lines in multilayered dielectric media. The integral equations obtained by using a Green's function above a ground plane are solved by Galerkin's method, with the unknown total charge expanded in terms of orthogonal wavelets in L/sup 2/([0,1]). The difficulty of using wavelets on the real line to expand unknown functions defined in finite intervals is overcome by the utilization of wavelets in L/sup 2/([0,1]). The adoption of the geometric representation of the BEM converts the two-dimensional problem into a one-dimensional problem, and provides a versatile and accurate treatment of curved conductor surfaces and dielectric interfaces. A sparse matrix equation is developed from the set of integral equations, which is extremely valuable, in particular when a large system of equations must be solved. Finally, we compare our numerical results with previously published data, and demonstrate good agreement between the two sets of results. >

Application of ring oscillators to characterize transmission lines in VLSI circuits

This paper presents a method that enables an estimation of the per-unit-length capacitance of transmission lines on VLSI CMOS chips with the help of ring oscillators. For the determination of the line capacitance four different ring oscillators possessing transmission lines of various lengths are implemented upon test chips for process characterization. A simple analytical model of the ring oscillator is developed and a formula derived that estimates the per-unit-length capacitance of the transmission lines out of the periods of oscillation of the ring oscillators. SPICE simulation results (E-SPICE as well as H-SPICE) using process parameters for a 1.5-/spl mu/m CMOS process are included. An experimental verification was also performed by implementing the ring oscillators on a test chip for a 0.8-/spl mu/m CMOS technology. The determined line parameters are valid for a frequency range up to about 500 MHz. >

Capacitance of transmission line of parallel cylinders in the presence of dielectric coating

The paper presents a method for the evaluation of variation of capacitance of a dielectric coated two-wire line of parallel cylinders, each of unit radius with a change in thickness of the dielectric along the radial direction. A conformal transformation is used to transform the conductor and dielectric boundaries to appropriate contours extending over a fixed region along the imaginary axis in the transformed plane. Approximating the continuous curve obtained through transformation of dielectric boundaries by a very large number of discrete steps, the expression for the capacitance is derived in the form of a definite integral. Numerical data on capacitance as a function of width of the dielectric in the absence and presence of a conducting ground plane are presented. >

Comparison of methods for determining the capacitance of planar transmission lines with application to multichip module characterization

Comparison of methods for determining the capacitance of planar transmission lines with application to multichip module characterization

Simplified Green's functions for calculating capacitance and inductance of multiconductor transmission lines in multilayered media

Using the impedance formula and the asymptotic property of the hyperbolic tangent function, the Green's function due to a line source embedded in a general layered medium has been analytically converted into a more suitable form for numerical calculation of capacitance and inductance. The new form is designed to eliminate slow convergence when the vertical distance of the source and field points is small. Another simplified Green's function for the layered medium shielded by two rectangular outer conductors is also given. Numerical results are compared with published data. The agreement is excellent.

Comparison of methods for determining the capacitance of planar transmission lines with application to multichip module characterization

The techiques for determining the capacitance of embedded interconnects in an MCM-D MCM (multichip module) are compared. The error is estimating this capacitance in generally the greatest contributor to the overall error in determining the impedance of interconnects and discontinuities. Using in situ calibration microwave characterization of various MCM interconnects fabricated using an alumina on polyimide MCM-D process is reported. >

A new technique for location of transmission line faults using single-terminal voltage and current data

This paper presents a new technique for location of transmission line faults using voltage and current measurements from one end of the faulted line. The method differs from past techniques in many respects. The main feature of the new technique is that it considers the influence of the remote-end infeed of the transmission line, the effect of the transmission line capacitance, fault resistance, prefault loading conditions, and the effect of mutual coupling between different phases of the line, and then computes with a microprocessor the distance to the fault point without any approximations. It uses recorded phase voltages and currents at the near end, then the fundamental components of the measured signals are extracted using microprocessor filters. The modal values of the extracted signals are computed then processed to indicate the precise location of the fault.

Transmission line capacitance measurement

The capacitance of coplanar lines is measured with two new techniques, one utilizing the resistance of the line and the other that of a resistor embedded in the line. The results of both measurements agree closely with calculations. A technique for directly comparing the capacitances of two similar transmission lines is also demonstrated. The relevance of these measurements to the determination of characteristic impedance is discussed. >

A backyard experiment for electromagnetics. I

The author presents an interesting experiment involving the determination of soil conductivity which can be introduced as a homework problem in an introductory course in electromagnetic theory. The experiment utilizes the two important topics of resistance-capacitance analogy and transmission line capacitance treated in typical courses.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Calculation of capacitance for rectangular coaxial strip transmission line

The field matching method is used to calculate the capacitance of coaxial rectangular strip transmission line. This method is simple, can be used conveniently and the magnitude of error can be effectively controlled.

Modelling the TRIUMF RF Cavity Using the Code RFQ3D

Development work on the TRIUMF cyclotron RF cavity requires an efficient code to study the effects on voltage distributions of resoaator geometry nonuniformity, including misalignment of the cantilevered cavity walls, the end flux guides and the centre post. A quasi-three-dimensional code, RFQ3D, although originally written for radio frequency quadrupole cavity studies, has been successfully adapted to simulate the TRIUMF cavity. The code uses four one-dimensional coupled transmission line equations to calculate the voltage distributions along the dee gap and allows for local variations in the transmission line inductance and capacitance. The effects of individual resonator components on the accelerating voltage profile and the RF leakage for both the fundamental and third harmonic frequencies are calculated and compared with precise 1:10 model measurements.

Use of FFT in microstrip capacitance calculations

A method is described which can be used to calculate the capacitances of microstrip-like transmission lines on a dielectric substrate contained with a conducting box. The FFT is used once to sum a large number of series, and, by the judicious use of the resulting summations, the approximate capacitances of any strips on the dielectric substrate can be obtained after the solution of a set of simultaneous equations.

UPPER AND LOWER BOUNDS TO THE CHARACTERISTIC IMPEDANCE OF TRANSMISSION LINES USING THE FINITE‐ELEMENT METHOD

This paper describes a technique for computing characteristic impedance and capacitance of transmission lines using the finite‐element method, which guarantees both upper and lower bounds to the exact solution without any additional programming beyond that required for the initial problem description. The paper also attempts to simplify the essential steps of pre‐processing of data while maintaining flexibility of the method.