Distributed RC Line Research Articles

Gate electrode RC delay effects in VLSI's

A poly-silicon gate electrode can be considered as a distributed RC line. The delay induced by this RC time constant can become a limitation in designing high-speed VLSI's. This effect, called the gate electrode RC delay effect (GERDE), is studied for short-channel MOSFET's. A simple formula is derived to roughly estimate the GERDE, which can be used as a rule-of-thumb in VLSI design. An approximation of the GERDE by a simple lumped-circuit model is also described. The future trends of the GERDE are investigated and it is concluded that the GERDE gets more severe for shorter channel MOSFET's, but, if the gate width is confined up to 30 µm, the GERDE can be neglected for MOSFET's with a channel length of more than 0.8 µm. For a large conductance, division of the MOSFET width is shown to be effective through experiments.

Gate Electrode RC Delay Effects in VLSI's

A poly-silicon gate electrode can be considered as a distributed RC line. The delay induced by this RC time constant can become a limitation in designing high-speed VLSI's. This effect, called the gate electrode RC delay effect (GERDE), is studied for short-channel MOSFET's. A simple formula is derived to roughly estimate the GERDE, which can be used as a rule-of-thumb in VLSI design. An approximation of the GERDE by a simple lumped-circuit model is also described. The future trends of the GERDE are investigated and it is concluded that the GERDE gets more severe for shorter channel MOSFET's, but, if the gate width is confined up to 30/spl mu/m, the GERDE can be neglected for MOSFET's with a channel length of more than 0.8 /spl mu/m. For a large conductance, division of the MOSFET width is shown to be effective through experiments.

A Transmission-Line Analog Simulating Thin-Film Distributed-RC Elements

Methods of modeling distributed-RC lines by finite-ladder networks are discussed. This culminates in the design and construction of a 20-section adjustable transmission-line analog capable of simulating a variety of uniform and tapered, three-terminal and four-terminal structures. The model also takes into account stray effects and permits performance insight without the otherwise complex irrational-function analysis and numerical evaluation or integrated-circuit fabrication. Its utility is demonstrated with respect to the characteristics of a distributed-lumped notch filter. A range of further applications is suggested.

Voltage response of distributed RC lines with a discontinuous initial potential distribution

Prior work by this author has shown how the voltage step response of an initially quiescent RC line can be concisely expressed in terms of a set of higher transcendental functions. For convenience, the latter were defined in termsof integrals of elliptic theta functions and are termed “diffusion functions”. These same diffusion functions are also found to be useful in expressing closed-form solutions for the voltage response of distributed RC lines with a non-quiescent and discontinuous initial potential distribution. Results herein provide functional expressions for this voltage response with either open-circuited or short-circuited terminations. A variety of solution plots show how the responses change for different positions of the discontinuity. Also, plots of the diffusion functions are supplied showing their behavior over one complete cycle and more information on their symmetry properties is provided than was included in the initial paper.

Instantaneous frequency measurements of neural events: application of non-uniformly distributed RC line.

The display of instantaneous frequency as a function of real time (Frequencygram) is an efficient type of data presentation in studies of point processes such as neuronal events. This paper surveys and compares various methods for its analog implementation.

Closed-form solutions for voltage-step response of open and shorted distributed RC lines

The current response of a finite distributed RC line to a voltage-step driving function has a closed-form solution in terms of elliptic theta This seems to have gone unrecognized in previous circuit theory literature. Different types of theta functions will appear depending on whether the solution is for open-circuited or short-circuited terminations. Furthermore, the voltage response to the same driving function can be expressed in terms of integrals of theta These integrals constitute a possibly new set of higher transcendental functions, to be denoted here as diffusion functions. Relationships among and properties of the various solutions and functions are given in mathematical identities and families of curves. Thus expressing the solutions in terms of individual functions whose properties are well-documented, rather than using the mostly opaque series form, allows a more distinct view of the physical behavior of the distributed RC line to emerge.

Modelling distributed RC lines for the transient analysis of complex networks†

The development of an approximately equivalent representation of uniformly distributed RClines is described for the transient analysis of complex networks on digital Computers. The representation is a two-port network consisting of an R1C1,‘L’ section in cascade with an R2C2 ‘L’ section. The frequency range for which the model is applicable, and the characteristic of error between the actual response and the response of the approximate representation are examined. The error is found to be within 3.21% of the step input.

Active filter with distributed RC line having zero Q-sensitivity

The concept and properties of an active filter with a fourlayer distributed RC line in a feedback loop are presented. Due to specific properties of the four-layer RC line, it is possible to obtain zero Q -sensitivity of the filter to active-element gain variations. A design procedure for the bandpass filter with prescribed Q and center frequency \omega_{o} -values is given.

Stability of electrical networks containing distributed RC components

This paper presents a study of the stability of electrical networks consisting of the interconnection of linear lumped parameter elements and memoryless nonlinear elements with uniformly distributed RC lines. It is shown that a large class of such networks can be represented by a functional-differential equation of the retarded type of the form: x ̇ (t) = f(x t), t ⩾ 0 where x t , is the state of the system and f is a nonlinear functional defined on a subset of C((−∞, 0], E n ), the space of all bounded continuous functions mapping the interval (−∞, 0] into E n with the compact open topology. The principal result of this work is the presentation of a functional defined on the function space C, and the use of this functional to derive a set of theorems and corollaries concerning the stability and instability of the network. To illustrate the results, some examples are given.

Some Applications and Properties of One- and Two-Dimensional Position-Sensitive Proportional Counters

A new method was developed for determining the position of ionizing events by measuring the risetime of output pulses from detectors having high resistance collectors. Basically, these detectors are distributed RC lines; information about the location of an ionizing event is obtained from the analysis of the frequency spectrum of the detector output pulse, and the energy loss of this event in the detector is measured by analyzing the amplitude of the same output pulse. Three typical prototype detectors were constructed and tested in a series of imaging and diffraction experiments using ionizing radiation. The spatial uncertainty for collimated 210Po alpha particles was 0.15 mm fwhm for a 200-mm-long proportional detector. The spatial uncertainty for collimated 20-kev x rays was 0.5 mm fwhm for a 400-mm-long detector. A two-dimensional system using parallel wires was developed and evaluated. With only four preamplifiers and relatively simple shaping and timing circuitry, 24,000 resolution elements (measured at fwhm) were obtained with a 30-wire counter having a sensitive area of 75 × 120 mm2. These position-sensitive detectors are well suited for application in the life sciences for the localization of radioactive tracers in medical studies or in the structure determination of large organic molecules, with x-ray or neutron diffraction; in fluorescent x-ray or neutron spectroscopy; small-angle scattering experiments with x rays or neutrons.; magnetic spectroscopy of protons and other charged particles; two-dimensional chromatography; x-ray astronomy; and fission physics experiments.

Effect of Load Admittance on the Low-Pass Characteristics of Distributed RC Lines

The purpose of this paper is to investigate the relative effects of terminating impedances on the low-pass voltage transfer characteristics of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> lines. Four general shapes of these lines,with constant <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r(x)c(x)</tex> product along the line, are included in the investigation. Previous studies of the open-circuit performance of networks from these four general shapes provide a basis for continued investigations of their characteristics with terminations limited to parallel combinations of a resistance and a capacitance. The investigation shows that in order to reduce the effect of the load admittance on the open-circuit characteristic, the line should be shaped such that its resistance at the output end is as low as practicable.

Transformed hypergeometric transmission lines

A transformation procedure is described for determining a set of nonautonomic distributions which are complementary to previously described general classes of lines. A table of these distributions is presented, together with the conditions necessary for their evaluation. In particular, for the Gaussian distributed RC line, which is inherent, for example, in some diffused-semiconductor realisations, a solution is obtained in terms of a convergent confluent hypergeometric series which is equivalent to an earlier solution in terms of Hermite polynomials. Finally, its performance is evaluated and experimentally compared with a well known distribution.

Synthesis of Rational Transfer Function Approximations Using a Tapped Distributed RC Line With Feedback

This paper describes a simple procedure for synthesizing an active distributed RC network which, by using dominant poles and zeros, realizes a very accurate approximation of an arbitrary stable rational transfer function. The network uses a single uniformly distributed RC line with taps spaced along its length. A linear combination of tap voltages is added to the input signal to form the driving voltage for the RC line; the output signal is also a linear combination of the tap voltages. The network offers a number of significant advantages. Since it realizes a nearly rational transfer function, the approximation problem can be conveniently solved using readily available results on rational function approximation. Also, the network uses only one uniform RC line, the transfer function can be changed simply by changing resistor values, and the frequency can be scaled by minor connection changes. Thus one standard network with minor modification is useful for a wide variety of applications. This paper develops the design procedure and derives the various sensitivity functions of importance. Two example designs are carried out: an approximation to a second-order low-pass transfer function and an approximation to a second-order band-pass transfer function with a Q of 100. The sensitivities for the examples are very reasonable and the measurements made on laboratory models indicate excellent agreement with theoretical predictions.

Tapered Distributed Filters

The study of distributed networks has been prompted by the trend in electronic equipment toward smaller and smaller physical structures. Various investigators have determined the network characteristics of rather complex distributed RC structures. It is the purpose of this paper to point out the effects of geometrical tapering on the characteristics of distributed RC structures. Uniform (untapered), exponential, and linear tapers are analyzed for the distributed RC line and for a distributed narrow-band-rejection filter. It is shown that tapering is useful for sharpening the cutoff of gain vs frequency for the RC line and it is also useful for narrowing the rejection band of the "notch" filter. Transient behavior of the RC line is also investigated. Analytical expressions are presented for the network parameters and for the unit step response of both types of tapered RC structures.