Distributed RC Networks Research Articles

Single-transistor oscillators with distributed RC networks

Three single-transistor oscillators with distributed RC networks are presented. The design problem of these circuits is investigated, and generalised diagrams are given. The method may be applied also to other types of oscillators.

Transient and frequency response of the distributed RGC network

The distributed RGC network differs from the conventional distributed RC network in that its shunt capacitance is leaky; i.e. the dielectric layer used to realise the distributed capacitance is lossy. It is shown that the transient and frequency response of the distributed RGC network are superior to those of the distributed RC network. The price to be paid for this improved response is a sacrifice in the output level; this can be compensated to some extent by tapering the network, which also results in a further improvement in the transient and frequency response.

N-Port Rectangular-Shaped Distributed RC Networks

Necessary and sufficient condition derived for generating rational functions of n-port rectangular structure for distributed RC networks

Synthesis of Active Distributed RC Networks

This work presents a general method for the synthesis of any open-circuit transfer function, which is expressed as a rational function with real coefficients. It is shown that such functions can be realized by using two distributed RC elements (modified by active units if necessary), one negative impedance converter and one lumped capacitor. The distributed RC element used here is a three-layer structure, a pure dielectric sandwiched in between a perfect conductor and a resistive film.

On the effective dominant pole of the distributed RC networks

A technique is developed to determine the effective dominant pole of the distributed circuits. The concept of the effective dominant pole facilitates enormously the time and frequency domain calculations. Key features of the steady-state and transient response such as bandwidth, rise time and time delay, etc., of the network functions can be easily and accurately determined without much effort. Although transfer functions of the exponentially tapered distributed RC network are considered in this paper, the method has a much broader application for all types of distributed RC circuits with arbitrary taper and diffused base transistors. The method of approximation which makes use of the product expansion of transcendental functions permits the location of the effective dominant pole by means of a simple algebraic formula and to a degree of accuracy acceptable for most engineering purposes.

Tapered Distributed RC Networks with Similar Immittances

In this paper the poles and zeros of the two-port short-circuit admittance parameters of a class of tapered distributed RC networks are discussed. They are shown to be the zeros of an orthogonal set of solutions of the network differential equation. When the differential equation is written in Normal Form, it is possible to define a class of tapered networks which have closed form solutions and similar pole-zero patterns. This class is shown to include the uniform, exponentially-tapered, hyperbolic, square and trigonometric-tapered distributed RC networks.

Frequency response of distributed RC networks

The properties of the transformation t = tanh √(RCs), as used in the synthesis of distributed RC networks, are described with particular reference to real frequencies. Various functions of t which appear in the admittances of uniform distributed RC networks with no transmission zeros at zero frequency are examined at real frequencies, and conclusions as to the general behaviour of these admittances are drawn.

Synthesis Using Distributed RC Networks

This paper presents necessary and sufficient conditions for a function to be the driving point impedance of a network composed of uniform RC lines all having the same RC product connected in an arbitrary manner. Foster type realizations are developed for an impedance function satisfying these conditions. Analogous to the vector approach for the s plane analysis of lumped circuits, a method for determining the frequency response of driving point impedance and transfer functions in the P = cosh x1s.R- plane is considered. A transfer function synthesis procedure based upon a ladder realization is developed which is capable of realizing transmission zeros along the real axis of the P plane between +1 and - \infty . By locating a zero at P = -11.6 using this procedure, a zero can be obtained on the j \omega axis of the s plane. The use of lattice networks and negative immittance converters for obtaining complex conjugate P plane poles and zeros is also discussed. Finally, it is pointed out that the foregoing work is applicable to three terminal networks that are both symmetrical and reciprocal. These networks may consist of lumped as well as distributed elements.

Transfer characteristics of a class of distributed RC networks

Transfer characteristics of a class of distributed RC networks

Realizability and Synthesis of a Restricted Class of Distributed RC Networks

Realizability conditions and synthesis procedures are given for a class of distributed RC networks consisting of a cascade connection of two-port RC networks (unit elements), series shortcircuited stubs, and shunt open-circuited stubs. Each element of the network is a distributed RC section where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sqrt{RC}</tex> is an integral multiple of some common minimum factor, (i.e., commensurate lengths). Necessary conditions have been found for realization of any shortor open-circuit immittance parameter, together with sufficient conditions for the simultaneous realization of any two such parameters. A nontrivial example of the synthesis procedure is given.

Approximations to the Equations Describing Distributed RC Networks

Approximations to the Equations Describing Distributed RC Networks

The effect of shaping and loading on distributed RC networks

Distributed RC networks are frequently used with integrated circuitry to perform network functions such as frequency selectivity, pulse transmission and coupling. In this paper the effects of network shaping and loading on the transient and frequency response of distributed RC networks are examined analytically and experimentally. An analytic technique is employed which effects determination of the frequency and transient response of the network without the use of a computer, which is usually required for exact analysis. It is shown that both the shaping and loading have significant effects on the performance of distributed RC networks. Experimental results show close agreement with theoretical predictions.

A Frequency-selective RC Feedback Circuit with Relatively Low Component Tolerance Sensitivity†

ABSTRACT The ‘ total Q sensitivity ’, ΣQ, is presented as a useful figure of merit, for quantitative comparisons of the relative stability of different frequency-selective feedback networks. Physically, ΣQ gives the percentage change in Q which would result if each parameter of the network were changed by 1 % in a direction such that the effects are additive. A very simple selective feedback circuit using a distributed RC network is analysed and compared with other well-known selective networks. It is shown that ΣQ for this network (including the effects of the active element) is considerably less than that for other comparable active feedback networks (for which the active elements are not included). Therefore this network has significant advantages wherever it is not practical to use an LC tank circuit for tuning.

The Transient Response of Tapered Distributed RC Networks

The Transient Response of Tapered Distributed RC Networks

Distributed RC Networks with Rational Transfer Functions

A distributed RC circuit analogous to a continuously tapped transmission line can be made to have a rational short-circuit transfer admittance and one rational short-circuit driving-point admittance. A subcircuit of the same structure has a rational open-circuit transfer impedance and one rational open-circuit driving-point impedance. Hence, rational transfer functions may be obtained while considering either generator impedance or load impedance. The functions have poles only along the negative real axis. Although the number of poles is arbitrary, only two may be chosen with complete freedom in a single unit. The realization of a transfer function with many poles may require a number of units either connected in parallel or isolated. Even for a structure with only two poles, there is a considerable saving in the number of interconnections over the lumped circuit. The loss and total capacity required is often the same order of magnitude as those for lumped circuits.

Equivalent Distributed RC Networks of Transmission Lines

There are any number of pairs of resistance and capacitance density functions, i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r(x)</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c(x)</tex> , which can provide the same electrical performance as a given distributed RC laddernetwork. In general these equivalent networks will have different lengths. A criterion for equivalence of density functions is expressed in the following: Networks with the same <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</tex> ratio, expressed as a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> , are equivalent at network-lengths which correspond to the same value of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> . The variable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</tex> is related to the distance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</tex> by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z = \int_0^x \sqrt{rc} dx</tex> . The equivalency criteria can be used to find alternate networks to a given network. Such alternates may be more suitable for fabrication. Examples of networks equivalent to the exponential, proportional and Bessel networks are given. The results apply to tapered transmission lines as well.