Length Of Transmission Line Research Articles

Gain limitations in narrow width Josephson junction vortex flow transistors

The number of devices required to achieve a practical gain from a Josephson junction vortex flow transistor (JVFT) distributed amplifier is inversely proportional to the gain or the transresistance, r/sub m/ of each active device. A large number of devices means longer transmission line lengths associated with increased loss and size. Reducing the junction width results in increased r/sub m/, however there is a fundamental limit for achievable r/sub m/. This is basically due to two reasons, increased fringing field effects and edge penetration at smaller aspect ratios. Field analyses made on devices with various dimensions show this limitation in the magnitude of r/sub m/ for narrower junctions. The analysis also provides valuable information on parasitic elements in the circuit model for a JVFT. Results of the analyses on devices having different geometries suitable for high frequency operation are presented. >

Hierarchal triangular elements using orthogonal polynomials

AbstractHierarchal elements are finite elements which have the useful property that elements with different polynomial orders can be used together in the same mesh without causing discontinuities. This paper introduces a new hierarchal triangular element in which the basis functions are constructed from orthogonal polynomials—Jacobi polynomials. The resulting element is shown to be better conditioned than the earlier hierarchal element of Rossow and Katz.1 Recursive formulas allow the complete set of basis functions for an element to be efficiently evaluated at a given point. In addition, the formulas can be used to generate pre‐computed (universal) matrices. Examples are given of universal matrices, up to order 4, for the generalized Helmholtz equation. An electromagnetic problem involving a length of transmission line is used to show the usefulness of the new elements.

Closed-form solution for lossy exponential transmission line problem in frequency and time domains

An exact and explicit solution for the reflection and transmission problem of a lossy exponential transmission line of finite length is derived in both the frequency and the time domain via a wave-splitting approach. The problem is formulated first in the frequency domain. Wave-splitting is defined and the solution for internal voltages and currents is derived. Closed-form solutions for the reflection and transmission coefficients are obtained. The explicit solution for a transmission line consisting of several exponential pieces (each with different taper) in series is then easily written down. To obtain the transient response of the lossy exponential line, a time domain Green function approach based on wave-splitting is used. Linear partial differential equations for the Green functions together with the initial and boundary conditions are derived and solved explicitly. The exact and explicit solutions for the transient reflection and transmission up to arbitrary large times are given.

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. >

Multigap parallel-plate bracelet resonator frequency determination and applications

A loop made from a length of transmission line with alternate electrical discontinuities (gaps) on the two conductors behaves as a resonator whose resonant frequency is a function of the transmission line parameters as well as its form and the number (n) of gaps. For a given loop diameter, one can thus design a wide range of resonant frequency by choice of n and the characteristic impedance Zc of the line. The analysis is illustrated by a parallel-plate transmission line resonator in the form of a bracelet. Experimental resonant frequencies obtained from resonators of various dimensions are in good agreement with calculated values. Two resonators were tested on a 3 T NMR imager: A 11 cm diameter 1H surface coil, yielding results comparable to those obtained from a lumped capacitor coil and a 13 cm diameter volume coil to perform in vivo muscle 13C spectroscopy without 1H decoupling.

Cooper-pair current through ultrasmall Josephson junctions.

The current-voltage characteristics of ultrasmall Josephson junctions sensitively depend on the electromagnetic environment of the junction. When the charging energy exceeds the Josephson coupling energy, the usual supercurrent at zero voltage is completely suppressed. However, for typical environmental impedances, which are small compared to the resistance quantum, stochastic Cooper-pair tunneling leads to a supercurrent peak at a small finite voltage which is proportional to the temperature and the low-frequency resistance of the external circuit. An analytic expression for the form of this universal peak, which is independent of the high-frequency behavior of the environment, is given. With increasing Josephson coupling the peak merges into the usual supercurrent of a Josephson junction. At larger voltages the Cooper-pair current depends on details of the environment. Current peaks are shown to result from resonances in the environmental impedance. Specifically, the case of an [ital LC] transmission line of finite length is discussed.

Time domain characterization of lossy arbitrary characteristic impedance transmission lines

This paper deals with the characterization of lossy transmission lines. The method developed here delivers the complex propagation constant /spl gamma/ of any arbitrary length and characteristic impedance transmission line, embedded in an arbitrary environment. This approach is based upon time domain analysis of short pulse propagation. Measurements are done with a commercial digital sampling oscilloscope. Only two transmission lines of different lengths are required in order to extract /spl gamma/ and to correct systematic errors of the measurement system. The problem of random errors is also addressed. The method is demonstrated with microstrip lines. A comparison of the developed technique with an other existing time domain approach and a classical frequency domain extraction is also carried out. >

Compact conical antennas for wide-band coverage

A broadband antenna with a vertically polarized, omnidirectional electric field is studied. The design of the antenna and its feeding system in the wide frequency range from 20 to 1000 MHz is described and the driving-point impedance determined. Also calculated are the voltage standing-wave ratio (VSWR) and the input impedance of a transmission line connected to the antenna. More efficient operation at low frequencies is obtained by adding a length of transmission line to form a resonant section with the antenna. The effect of the different properties of the earth's surface on the field pattern is treated in a companion paper.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

AN INVESTIGATION OF THE STATISTICAL RELATIONSHIP BETWEEN THE 345 KV TRANSMISSION LINE LENGTH AND THE OUTAGE RATE

Finding the factors that are related to varying transmission outage rates has been one of the major concerns of the reliability practitioners in the electric power industry. One of the potentially influential factors is the length of the transmission line. In this paper, a random effects Poisson regression model is used to quantify the relationship between the outage rate to the transmission line length. The method suggested is applied to analyze two sets of the 345 KV transmission line outage data of the Commonwealth Edison Company: group 1 contains transmission lines that had been installed before January 1974; group 2 consists of the lines that have been installed since January 1974. Results indicate that in both cases there is a significant log linear relationship between the transmission line outage and the line length. However, the annual outage rate elasticity of transmission lines of group 2 turns to be 0.33 while that of group 1 is 0.64. This would imply apparent quality improvement on the transmission lines in group 2.

Closed-form formulas for frequency-dependent resistance and inductance per unit length of microstrip and strip transmission lines

Based on numerical results obtained from solutions to integral equations, other numerical results and theoretical considerations, a set of closed-form formulas is presented for approximate calculation of frequency-dependent resistance and inductance per unit length of microstrip and strip transmission lines. Extensive verifications reveal that the accuracy obtained by these closed-form formulas is better than 10% for a wide range of parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computational models of transmission lines with skin effects and dielectric loss

We present circuit models of a length of transmission line with skin effect and frequency-dependent dielectric loss, treating the ordinary RLGC line as a special case. The line is modeled as a characteristic two-port in which the characteristic impedance is approximated as the input impedance of a lumped circuit and the propagation function is approximated as the transfer function of a second lumped circuit plus an ideal delay. A unified approach based on frequency matching is presented to form the model. In the approximation, the skin effect is represented as the impedance of an RL ladder, and the complex dielectric parameter as the admittance of an RC ladder. A table of the rms error of the approximation is derived from which the complexity of the model can be found for a desired accuracy. The model is guaranteed to be stable, and since it consists entirely of lumped circuit elements and ideal delay lines and since the model parameters can be easily computed, it can be incorporated as a subcircuit model in a general circuit simulator, and the solution can be obtained by integrating the circuit equations in the usual manner. No FFT or convolution is required. >

A 100 GHz coplanar strip circuit tuned with a sliding planar backshort

A means of mechanically altering the electrical length of a planar transmission line would greatly enhance the use of integrated circuit technology at millimeter and submillimeter wavelengths. Such a mechanically adjustable planar RF tuning element, successfully demonstrated at 100 GHz, is described here. It consists of a thin metallic sheet, with appropriately sized and spaced holes, which slides along on top of a dielectric-coated coplanar-strip transmission line. Multiple RF reflections caused by this structure add constructively, resulting in a movable RF short circuit, with mod s/sub 11/ mod >>APX=/-0.3 dB, which can be used to vary the electrical length of a planar tuning stub. The sliding short is used here to produce a 2-dB improvement in the response of a diode detector. This tuning element can be integrated with planar circuits to compensate for the effect of parasitic reactance inherent in various devices including semiconductor diodes and superconductor-insulator-superconductor (SIS) junctions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Accurate transmission line characterization

A method for the characterization of transmission lines fabricated on lossy or dispersive dielectrics is introduced. The method, which is more accurate than conventional techniques, is used to examine the resistance, inductance, capacitance, and conductance per unit length of coplanar waveguide transmission lines fabricated on lossy silicon substrates. >

Microwave noise measurement errors caused by frequency discrepancies and nonzero bandwidth

We develop analytical expressions for two frequency-related errors encountered in noise parameter measurements of devices with high-reflection coefficients such as GaAs FET's and HEMT's. The first error is caused by a discrepancy between the measurement frequency of the noise-measuring receiver and the frequency of the reflection coefficient-measuring apparatus. The second is caused by variation of the noise power spectral density across the bandwidth of the noise-measuring receiver. A noise power measurement on a cooled GaAs FET is presented as a demonstration, in which the noise power level exhibits narrow peaks which rise about 10 dB above the general level at regular frequency intervals. It is shown that the severity of both of the frequency-related errors is related to the shape of these peaks. Simple expressions are derived which allow the severity of these two types of errors to be estimated when values are available for the reflection coefficient magnitudes and transmission line lengths in a system. Expressions are also derived which give the variation with frequency of the measured noise power and also of the two error terms, if the noise parameters of the device under test are also available. This analysis accounts successfully for the main features of the experimental noise power observation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Frequency and Time Domain Green Function Technique for Nonuniform LCRG Transmission Lines with Frequency-Dependent Parameters

The reflection and transmission of waves on a nonuniform LCRG transmission line of finite length with frequency-dependent parameters are considered. A Green function technique combined with wave splitting is used both in the frequency domain and the time domain. In the frequency domain ordinary differential equations (ODEs) for the time-harmonic Green functions are obtained. In the time domain the transmission line model is established through a set of dispersion kernels. Partial differential equations (PDEs) for the time-domain Green functions are derived. Numerical results for transient reflected, transmitted and internal currents are presented. Furthermore, it is noted that a special case of the present formalism can be used to determine the reflected, transmitted and internal fields for normal plane wave incidence on a stratified dispersive and dissipative slab.

Highly accurate quasi-static modeling of microstrip lines over lossy substrates

A highly accurate quasi-static model of a microstrip over a semiconductor layer has been developed. The model agrees with full-wave calculations in all three modes of propagation (skin-effect, slow-wave, and dielectric quasi-TEM), for both the attenuation constant alpha and the propagation constant beta over a very wide range of dimension, substrate conductivity, and frequency. To achieve this level of agreement, a nonuniform cross-section, transverse resonance technique has been applied to find the series impedance per unit length of the microstrip transmission line.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The measurement of dynamic differential pressúre with reference to the determination of pulsating flows using DP devices

Commercially available DP transmitters are generally unsuitable for dynamic measurements. The dynamic characteristics of a measurement system using a differential pressure transducer with transmission lines coupled to the pressure tapping points imposes particular constraints upon the measurements. The effects of both transmission line length and the use of liquids and gases upon the measurement system resonant frequencies and, hence, its dynamic performance are investigated. Practical aspects and calibration procedures are discussed.

Time Domain Wave Splitting Approach to Transmission Along a Nonuruform LCRG Line

The calculation of the transient voltage and current along a nonuniform LCRG transmission line of finite length is considered. The model equations form a system of first order coupled differential equations for the voltage and current, and it is solved by a combination of a wave splitting technique and an invariant imbedding approach as well as a Green's functions approach. Partial differential equations for the reflection kernel, transmission kernel and the Green's functions are derived. Results from two different types of splittings are compared. Numerical results for the direct and also for particular inverse problems are presented. Finally it is noted that the system of equations obtained in a special case corresponds to Maxwell's equations for plane wave propagation in a slab where the permittivity, conductivity, and permeability vary with the depth.

A new interpolation theorem with application to pulse transmission

An interpolation theorem is determined for the case when there are a finite number of arbitrarily placed sampling instants and the interpolation function is the output of a known filter. They are also the interpolation functions with the specified properties that have minimum energy. The theorem is used to determine the input to a communications channel given a finite number of samples of its output. This provides a generalization of matched filters and a perspective on the benefits of fractionally spaced equalization. The theorem is also used to construct masks of a family of pulses that are specified by the range of pulse voltages at a finite number of sampling instants. The theory determines how the pulse masks thus constructed is transformed when the pulse family is transmitted through a filter such as a length of transmission line.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The design of protection circuitry for high-frequency ultrasound imaging systems

Transmission line lengths in the protection circuitry of a high-frequency (>20-MHz) ultrasound imaging system have an important effect on the frequency, amplitude, and bandwidth of the pulse-echo response of the system. A model that includes the transmission line lengths between the pulser, transducer, and receiver and the electromechanical properties of high-frequency transducers is used to illustrate the importance of correctly choosing these line lengths. An iterative optimization procedure for designing the protection circuitry for a broadband system is proposed. A theoretical and experimental analysis of the validity of this approach is reported for a 45-MHz PVDF transducer.