Realization of transfer impedances using distributed RC elements in a common ground Linvill configuration

One of several synthesis procedures available for the realization of a transfer admittance is that of Linvill. This synthesis procedure employs an active element, a negative impedance converter (NIC), to shift the poles of passive immittance functions from the negative real axis into the complex plane to realize the desired transfer immittance function. The Linvill synthesis procedure is extended to networks containing cascaded distributed RC elements and the conditions which must be satisfied to realize a transfer impedance using these distributed elements are defined

An advanced symbolic analyzer for the automatic generation of analog circuit design equations

A tool for symbolic analysis of analog integrated circuits is presented featuring accurate simplification, pole/zero extraction, and tools for parametric AC circuit characterization. The program, called ASAP, uses signal flowgraph methods and has been written in C for portability. In its current version, ASAP is able to deal with the complexity levels arising in typical analog building blocks when described by device-level models. The ASAP inputs and outputs, the architecture, and the graphical interface are discussed

Minimal symmetric Darlington synthesis

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue

RC-gyrator ladder and RLC symmetrical lattice network synthesis - A state-space approach

This dissertation presents two network realization procedures using the state-space approach. The first procedure is the realization of a transfer function. A state model (A,B,C,D) is obtained from the given transfer function by inspection, where A is a companion matrix. Through a similarity transformation T, another state model (F,G,H,J) is obtained, where F is a tridiagonal matrix and can be realized by a RC-gyrator ladder network. The input source is inserted in the proper position of the ladder network, and the output is obtained through a summing circuit. It is a unified procedure and uses simple algebraic computation. A general expression of the similarity transformation T is derived for any order. It is a minimal realization. The second procedure is the realization of an A matrix with a symmetrical lattice network. It is shown that the network functions of a symmetrical lattice network have a common factor in their numerators and denominators. Also, the eigenvalues of the A matrix are the poles and zeros of the driving-point functions. The A-matrix realization procedure is based on these properties. The synthesized network that consists of RC, RL , LC, or RLC elements depends on the locations of the eigenvalues of A. It is not a minimal realization --Abstract, page ii

Communication Research

Contains reports on nine research projects.Bell Telephone Laboratories, Incorporate

Cost-Effective Design of Amplifiers for Hearing Aides Using Nullors for Response Matching

This chapter starts reviewing Fixator-Norator Pairs (FNP) as an effective tool used to design analog amplifiers for a prescribed bandwidth and frequency profile. Among number of cases and applications, designing for hearing aides are particularly important, where the hearing frequency profiles, known as audiograms, are changing from person to person, and also for a person by the age. The design is mainly focused on front-end or stand-alone amplifiers. In case of a front-end the response from the amplifier can be digitized, properly controlled and adjusted to fit the digital application. Here is how the design proceed. For a given audiogram, an Audiogram Generator Circuit (AGC) is initially constructed. This AGC, usually a complete passive circuit, produces a frequency response that closely matches with the audiogram, obtained from a hearing impaired patient. The AGC is then embedded in an amplifier circuit where a fixator is placed at its output port, “forcing” the amplifier to generate the desired output frequency response profile. A flat band frequency response, for example, compensates the hearing losses and provides a uniform hearing to the patient in the entire audio bandwidth. The amplifier can be further enhanced to perform other requirements, for example, to cancel undesirable noises in certain frequencies or to magnify the voice in critical frequencies for clarity. Another alternative design methodology is also introduced in this chapter, which uses the negative feedback technique

Computer-Aided Design of Switched-Capacitor Filters

This thesis describes a series of computer methods for the design of switched-capacitor filters. Current software is greatly restricted in the types of transfer function that can be designed and in the range of filter structures by which they can be implemented. To solve the former problem, several new filter approximation algorithms are derived from Newton's method, yielding the Remez algortithm as a special case (confirming its convergency properties). Amplitude responses with arbitrary passband shaping and stopband notch positions are computed. Points of a specified degree of tangency to attenuation boundaries (touch points) can be placed in the response, whereby a family of transfer functions between Butterworth and elliptic can be derived, offering a continuous trade-off in group delay and passive sensitivity properties. The approximation algorithms have also been applied to arbitrary group delay correction by all-pass functions. Touch points form a direct link to an iterative passive ladder design method, which bypasses the need for Hurwitz factorisation. The combination of iterative and classical synthesis methods is suggested as the best compromise between accuracy and speed. It is shown that passive ladder prototypes of a minimum-node form can be efficiently simulated by SC networks without additional op-amps. A special technique is introduced for canonic realisation of SC ladder networks from transfer functions with finite transmission at high frequency, solving instability and synthesis difficulties. SC ladder structures are further simplified by synthesising the zeros at +/-2fs which are introduced into the transfer function by bilinear transformation. They cause cancellation of feedthrough branches and yield simplified LDI-type SC filter structures, although based solely on the bilinear transform. Matrix methods are used to design the SC filter simulations. They are shown to be a very convenient and flexible vehicle for computer processing of the linear equations involved in analogue filter design. A wide variety of filter structures can be expressed in a unified form. Scaling and analysis can readily be performed on the system matrices with great efficiency. Finally, the techniques are assembled in a filter compiler for SC filters called PANDDA. The application of the above techniques to practical design problems is then examined. Exact correction of sinc(x), LDI termination error, pre-filter and local loop telephone line weightings are illustrated. An optimisation algorithm is described, which uses the arbitrary passband weighting to predistort the transfer function for response distortions. Compensation of finite amplifier gain-bandwidth and switch resistance effects in SC filters is demonstrated. Two commercial filter specifications which pose major difficulties for traditional design methods are chosen as examples to illustrate PANDDA's full capabilities. Significant reductions in order and total area are achieved. Finally, test results of several SC filters designed using PANDDA for a dual-channel speech-processing ASIC are presented. The speed with which high-quality, standard SC filters can be produced is thus proven

A unified structural interpretation of some well-known stability-test procedures for linear systems

A number of well-known stability-test procedures for continuous-and discrete-time systems are re-examined in a unified manner, leading to well-defined network-theoretic interpretations. The representation and network interpretation are based on the fact that the stability of any linear system (scalar or multivariable) is equivalent to the stability of a related all-pass system, which in turn can always be synthesized as a cascade of (scalar or matrix) two-pair all-pass (lossless) networks. The original system of interest is stable if and only if each all-pass two-pair is stable (and hence "lossless bounded real"). As a result of this interpretation, a number of related issues, such as enumeration of unstable poles, prematured terminations, and singularity situations can all be approached in a unified manner, based only on "two-pair extraction formulas." In addition, the network interpretation also leads to direct test procedures for testing relative stability, and the stability of multi-input, multi-output systems