A Computer-Aided Design Toolkit For Continuous/Discrete Systems Based On Continued Fractions

This paper presents new algorithms (1) to generate complete mathematical symbolic expressions of continued fraction expansion coefficients in the s-domain, (2) to determine their numeric values and (3) to perform continued fraction inversion in the s-domain. A software package in PASCAL and LISP to implement these algorithms is developed. In addition, a simple z-domain inversion algorithm used in the computer implementation of bilinear s-z transformation is also included in the software package. These algorithms play an important role in the analysis and synthesis of complex electrical networks and control systems. Especially, the s-domain expansion and inversion algorithms have potential applications in model simplification and system order reductions. the paper also shows that the package, as such, serves as a comprehensive computer-aided analysis and design (CAD) toolkit for both continuous and discrete systems. the software is interactive and runs on computers equipped with a PASCAL or LISP compiler. It is noted that the iterative implementation of these methods using the new continued fraction algorithms saves considerable memory space and processing time. Numerical examples and computer data are given to demonstrate the development of the new algorithms and the usefulness of the software toolkit in the CAD design of continuous and discrete systems.     

A valuable tool: symbolic computation

The use of symbolic computation is proposed here as an effective tool for studying electric circuits. Using well established methods to write electric circuit equations, a student can generate a set of equations involving only state variables. With the help of symbolic computation, these equations can be rewritten in a normal form. They then can be solved for any input-output pair. Furthermore, the influence of a certain parameter can be analyzed in detail via analytic expressions     

Two‐graph analysis of pathological equivalent networks

Recently, abstract current mirror and voltage mirror elements have been proposed for behavioral modeling of active analog blocks. Such artificial elements and the traditionally used nullor element together are called pathological elements in the literature. Pathological elements are very useful in modeling and analysis of active network. Hence, researchers have been motivated to study symbolic analysis methods for networks containing pathological elements. However, so far, only nodal admittance matrix analysis has been formulated. In this work, an alternative two‐graph method is formulated, which has the advantage of providing a compact intermediate form for subsequent symbolic term generation. With a compact two‐graph representation, either a matrix method or a tree enumeration method can be employed. For completeness, the classical two‐graph theory has been extended in this paper to encompass all four types of dependent sources and all pathological elements. Illustrative examples are presented to demonstrate the principle of compact symbolic term generation by the presented two‐graph method. Copyright © 2014 John Wiley & Sons, Ltd.     

Envelope analysis of nonlinear electronic circuits based on harmonic balance method

We propose here a Spice‐oriented envelope analysis based on the HB (harmonic balance) method, where Fourier coefficients are assumed to be slowly varying. The Fourier expansions of nonlinear devices are executed by MATLAB in the symbolic forms. In this time, the nonlinearities need to be approximated by the polynomial functions. The determining equation of the HB method is formulated as Sine–Cosine circuit in the form of schematic diagram using ABMs (analog behavior models) of Spice. Each sub‐circuit corresponding to the higher harmonic component is almost the same circuit topology as the original one and has dynamic elements such as capacitors and inductors. The Sine–Cosine circuit can be solved by the transient analysis of Spice. Thus, our method is rather a symbolic approach in the meaning that the HB determining equation is given by the schematic diagram of Spice. Our method can be easily applied to the analysis of middle order of nonlinear communication circuits such as mixers and amplitude modulators and to the analysis of interesting phenomena in the nonlinear oscillations. After many simulation experiments, the results show that our envelope analysis is about 50 times faster than the direct transient analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Symbolic analysis of electric networks with higher order summative cofactors and parameter decision diagrams

The paper introduces the concept of higher order summative cofactors (HOSCs) to the circuit analysis. Although the concept is not new, it is not well known. In the paper, some mathematical background of HOSCs is presented. The further development of the concept of HOSC will yield computer implementation arithmetic of HOSC. A cancellation‐free symbolic analysis technique, which is based on HOSC arithmetic, is presented. This technique allows results to be created directly from a netlist in the form of a binary decision diagram, which is called a parameter decision diagram. Additionally, HOSC arithmetic allows the calculation to be started in many places (sometimes distant) simultaneously. The techniques of rolling up the already analyzed parts of a circuit, which is built into HOSC arithmetic, result in a novel multilevel hierarchical analysis method that is called hierarchical parameter decision diagram (HPDD). Unlike in most hierarchical methods, the results that are obtained based on the subcircuit representation in HPDD always maintain a cancellation‐free form. The HPDD always represents the sum of the product form, which is heavily compressed due to the self‐similarities of the actual circuit. The time that is required for any recalculation of the transfer functions is greatly reduced. Analysis of models that are based on pathological components is also a natural consequence of using HOSC arithmetic.     

A new symbolic analysis approach to the DC load flow method

A new symbolic analysis approach is proposed to the DC load flow method. The power system network parameters are given by symbols and the system active line power flows are derived analytically as closed-form symbolic expressions. An original program SALF is presented as a universal tool to find the line powers by an automated computer-aided algorithm. The theory of the DC load flow method is reviewed. The approach is illustrated by standard network examples. The approach exposed is targeted at researchers and experts dealing with analysis, planning and operation of transmission power system networks.     

Partial fraction expansion–based realizations of fractional-order differentiators and integrators using active filters

Approximations of the fractional-order differentiator and integrator operators s^±r are proposed in this work. These approximations target the realization of these operators using standard active filter transfer functions. Hence, circuit implementations in integrated circuit form or in discrete component form are significantly facilitated. Complementary metal-oxide-semiconductor (CMOS) realizations of the proposed approximations are given and validated via simulations using the AMS 0.35 μm CMOS technology, while experimental results using operational amplifier circuits are tested and confirm the proposed theory.     

Efficient computer analysis of ideal switched-capacitor circuits using matrix compaction techniques

In this paper we describe how three simple observations can be used in order to obtain an efficient algorithm for the computer analysis of ideal switched-capacitor circuits. the resulting algorithm is linear in the number of phases. the first observation uses the structure of the r-domain MNA-matrix to come up with a new LU-decomposition scheme which is gradual per timeslot. the second observation allows a great reduction in size of the z-domain MNA-matrix by a matrix compaction algorithm which also operates gradually per timeslot and which can be interleaved with the first gradual LU-decomposition process. This leads to a small matrix which can then be used for a time- and direct frequency-domain analysis. Third, the computations of transfer functions, aliasing functions and sensitivities can be optimized by applying appropriate excitations and making appropriate combinations of the terms in the expressions. These algorithms have been implemented in the SC-analysis program DIANA.SC. the usefulness and efficiency of the program is then illustrated with some examples.     

Symbolic analysis of (MO)(I)CCI(II)(III)‐based analog circuits

New nullor‐based models are introduced to describe the behavior of the first generation current conveyor (CCI), second generation current conveyor (CCII), third generation current conveyor (CCIII), their inverting equivalents (ICCI(II)(III)), and/or their multiple output topologies (MO(I)CCI(II)(III)). These nullor equivalents include only grounded resistors to improve the formulation of equations in symbolic nodal analysis. In this manner, it is highlighted the usefulness of the proposed models to calculate analytical expressions in MO(I)CCI(II)(III)‐based analog circuits. Copyright © 2009 John Wiley & Sons, Ltd.     

A factored form of the instrumental variable algorithm

A UDV^T-factored form of the instrumental variable (IV) identification algorithm is developed for identification of systems with coloured noise. The algorithm uses a UDV^T factorization technique to reformulate the conventional instrumental variable method and simultaneously produces the parameter estimates and loss functions for all models from order one to a user-specified number n with approximately the same computational effort as the conventional IV algorithm. The algorithm possesses a unique compact structure that facilitates the interpretation and implementation of IV-type algorithms. The UDV^T factorization technique used in this algorithm also results in better numerical performance than the conventional instrumental variable method.     

Signal Flow Graphs as an Aid in Network Analysis

Signal flow-graph techniques provide not only numeric but also symbolic expressions for network functions in terms of component parameters; these procedures are also useful in obtaining sensitivity coefficients. The paper presents the method of analysis of circuits using signal flow-graphs. The development includes the determination of transfer functions, sensitivity coefficients, worst case analysis and tolerance analysis. Two examples illustrate the method.     

A Novel Approach to Compact Model Parameter Extraction for Excimer Laser Annealed Complementary Thin Film Transistors

A unified physical-based model parameter extraction technique for excimer laser annealed lower temperature polycrystalline silicon (LTPS) complementary thin film transistors (TFTs) is for the first time proposed. For two well-known compact models of LTPS TFT, Rensselaer Polytechnic Institute (RPI) V1 and V2 models, our approach sequentially optimizes the model parameters in the regions of linear, subthreshold, saturation, and leakage. Compared with the measured results, the extracted I_D−V_G, I_D−V_D, transconductance, and output conductance are within 3% of accuracy. The agreement with the experimental data is excellent for the n- and p-type LTPS TFTs with different length and width. This extraction technique bridges the fabrication of LTPS TFTs and the design of complementary system on panel circuits.     

Simulation of Linear and Nonlinear Circuits for Symbolic Analysis and Transient Response

For pedagogical reasons, classroom examples of analysis are usually performed symbolically. A student can frequently attain insight as to the relative effects of various circuit elements when they have symbolic labels. A prototype program has been devised which is capable of determining symbolic equations for a class of circuits. The equations are written in FORTRAN type notation. Although the original intention of the program was to determine circuit state equations, several other applications exist. For instance, dc analysis, such as that which is required for steady-state analysis, may be performed. If a circuit is linear, it is possible to obtain a transfer function for which the s polynomial coefficients are symbolic. Transient responses often yield information which is not discernible from symbolic relationships. For this reason, a companion program which integrates the state equations determined by the preceding program has been written. Currently, the integration routine must be run separately by the user. This entails the insertion of the state equations and other integration control statements. It is believed that a program which relieves the user from this task will be available by the time this paper is published. Numerical examples are also included in the paper.     

Periodic noise analysis of electric circuits: Artifacts,singularities and a numerical method

In this paper it is shown that a numerical method largely adopted for the simulation of noise in autonomous circuits is affected by singularities that manifest when the frequency at which the noise analysis is carried out approaches a harmonic of the autonomous circuit. The resulting noise power spectral density (PSD) is thus characterized by spurious spikes. The presence of these singularities is for the first time justified from an analytical standpoint and their effects are shown by simulating some oscillators, employed as benchmarks. Furthermore, the presented approach justifies the 1/(f_s?f)² shape of the PSD of noise at the output when the f_s frequency approaches the f fundamental of a stable oscillator and the 1/|f_s?f|³ shape when the effects of flicker noise are manifest. Copyright © 2009 John Wiley & Sons, Ltd.     

A three-terminal piecewise-linear modelling approach to dc analysis of transistor circuits

The simulation of electronic circuits by computer has become an important part of present-day circuit analysis and design, especially in the area of integrated circuit design. One of the goals in computer simulation of integrated circuits is to have a program ‘package’ for which the input consists of chip fabrication data (mask dimensions, impurity profiles, material data such as carrier lifetimes) and the output displays the complete circuit response. This requires both an efficient modelling approach and a fast circuit analysis method. In this paper a simulation method is described which generates dc responses (in the form of operating points or transfer characteristics) of transistor circuits directly from physical parameter data. The basis of the method is a two-dimensional piecewise-linear approach to the dc modelling of bipolar transistors. The model is directly used in a piecewise-linear circuit analysis program to simulate the dc response of a given circuit.     

A prototype tool for the design-oriented symbolic analysis of analogue circuits

New methodologies for the ‘design-oriented’ symbolic analysis of analogue circuits are presented. the objective of this analysis is to obtain results that will give more insight into the circuit behaviour. the feature of the presented methods is to allow the network function to be stated in several parts, with an eventual hierarchical dependence on each other, but without loss of interpretability. Several methods are combined. the first one consists of a rule-based algorithm for network reduction which allows significant simplification before the main analysis is performed. Initially, simple models can be used, since the effects of parasitic elements can be computed afterwards at little CPU expense, thanks to the implementation of the extra element theorem.³ the network is divided into blocks by a simple decomposition algorithm. Each block is analysed and the network function is next calculated. To reduce the size of the calculated expressions, the symbolic calculator uses the concept of ‘correction factor’, based on a comparison between the orders of magnitude of the symbolic terms. A PROLOG prototype tool has been written in order to validate these methods. A simple two-stage amplifier is taken as an example. the solution contains 11 products, to be compared with the 174 that would give a direct topological analysis.     

s-Domain analysis of lightning surges in three-phase systems using nonuniform single-phase line model

Surge response of the transmission tower in a three-phase transmission system is computed using s-domain nonuniform single-phase transmission line modelling. First, tower top voltage is obtained considering the tower and the ground wire by excluding the effect of the phase conductors, and then the induced voltages on the phase conductors as a result of the current flowing through the ground wire are computed using the magnetic coupling between the ground wire and the phase conductors. The first step of the analysis is the formulation of the system response in the s-domain, and the second step is the frequency to time domain conversion, which is carried out using fast inverse Laplace transform (FILT). The voltages on the phase conductors and the voltages across the tower insulators are computed, and some of the results obtained using s-domain analysis are compared with those obtaining using electromagnetic transients program (EMTP). The effect of frequency dependence of the line parameters is investigated.     

On a family of new two-op-amp switched-capacitor biquads for high-frequency applications

This paper presents three novel biquads derived by applying the concept of so-called basic elements for switched-capacitor (SC) circuits. These biquads are without continuous feedback and comprise two op-amps. They were derived assuming a transfer function denominator of the same form as the Fleischer-Laker type E circuit. It is shown that by a simple modification of the switching arrangement, i.e. by changing the type of the basic SC element, the effect of the amplifier finite gain on the performance of SC filters can be significantly reduced. the efficiency of this approach has been established by extensive simulation studies using the dedicated symbolic analysis program SCYMBAL. Design equations and comparison with already known biquads of this type are presented. Examples are provided to demonstrate that the proposed circuits require a low total capacitance while finite-gain effects are considerably reduced.     

基于粒子群算法的时序电路测试生成

本文论述了将粒子群算法应用在时序电路自动测试生成的研究结果。结合时序电路的特点,构造测试生成的粒子表达方式,建立自动测试生成离散粒子群速度-位置模型,通过群体中粒子间的合作与竞争产生的群体智能指导优化搜索。针对国际标准时序电路的验证结果表明,与同类算法相比,该算法可以获得较高的故障覆盖率和较小的测试矢量集。