Variation range based simplification for meaningful symbolic analysis of analog integrated circuits

This paper presents a variation range based symbolic simplification technique, where each circuit parameter is represented via a range of variation. We generate a database to handle the variation ranges of the circuit parameters and perform simulated annealing algorithm to achieve the most compact symbolic expressions. In contrast to the existing techniques, the main advantage of the proposed method is that the simplified symbolic expressions have an acceptable generalizability in the whole ranges of variations of the circuit parameters. The maximum allowable simplification error can be controlled by the user based on the required accuracy level that he needs. Simulation results demonstrate that the proposed method outperforms the conventional techniques in terms of expression complexity, accuracy and generalizability of the simplified expressions. The resultant expressions are only as complicated as necessary to give the required accuracy in the results, which help in giving a better insight into the circuit behavior.     

Interactive AC modeling and characterization of analog circuits via symbolic analysis

An advanced symbolic analyzer, called ASAP, has been developed for the automatic ac modeling of analog integrated circuits. ASAP works on a data base of model primitives and provides error-free symbolic expressions for the different system functions of analog circuits composed by the primitives. Both complete and simplified expressions can be calculated. Two simplification criteria have been implemented. The basic one is based on pruning the least significant terms in the different system function coefficients. This may yield important errors in pole and zero locations. To avoid that, an improved criterion has been developed where pole and zero displacements are forced to remain bounded. Also implemented are routines for symbolic pole/zero extraction and parametric ac circuit characterization. ASAP uses the signal flow graph method for symbolic analysis and has been written in the C language for portability. Together with portability, efficiency and ability to manage complexity have been fundamental goals in the implementation of ASAP. These features are demonstrated in this paper via practical examples.     

Automated simplified analysis of analogue circuit behaviour based on fully symbolic relations between parameters

Symbolic circuit analysis provides the key for understanding the mechanisms underneath circuit operation, and it can be used to obtain predictive models of circuit behaviour. Symbolic analysis has many applications in the design of analogue circuits but is severely limited by the size of the resulting expressions. Thus an efficient approximation strategy is required for successful symbolic analysis of large analogue circuits. A fully symbolic procedure for the simplification of large expressions, which mimics the heuristic procedures followed by an experienced designer (based on the relations between the parameters of the circuit), is presented in this paper. This simplification strategy is particularly well suited to be combined with some circuit level partition algorithms, leading to a blend between simplification after generation (SAG) and simplification during generation (SDG). The algorithms have been implemented and integrated on a prototype software package for the automated analysis and design of analogue circuits.     

Symbolic pole/zero calculation using SANTAFE

The aim of symbolic analysis is to gain insight into circuit behavior. To study the behavior of analog circuits, the locations of the poles and zeros have to be known. Unfortunately, no general method exists to calculate the poles and zeros symbolically for polynomials of degree greater than four from transfer functions in coefficient form. The CAD tool SANTAFE (Symbolic Analysis of Transfer Functions) applies the signal-flow graph method, which permits to keep the result in a factorized or partially factorized form. The graphic view provided by a signal-flow graph offers insight into the internal interactions between the circuit elements and, as will be demonstrated, enables the user to perform circuit knowledge-based approximations. A novel procedure based on symbolic Newton-iteration, accurately calculates high-order transfer functions in the desired pole/zero form. Another special routine, based on element weight ratios rather than numerical values, enables the simplification of large symbolic expressions without numerical values for each parameter. With the program SANTAFE, even large networks can be analyzed symbolically. This will be shown with an example of a wide band BiCMOS operational amplifier     

Improvements to the standard theory for photoreceiver noise

The standard theory for photoreceiver noise unrealistically defines the system transfer function solely in terms of the input and output pulse shapes, based on the assumption that equalization is provided at the receiver output. Most photoreceivers reported in the literature, however, are only front ends and do not include equalizers, making direct application of the conventional noise expressions inappropriate. Even if equalization is provided, a signal-dependent definition of the transfer function will be accurate only under certain limited conditions. Furthermore, it is unrealistic to assume a given pulse shape at the input. In this paper we consider the effect of incorporating a more realistic transfer function into the conventional noise theory. We choose the transimpedance amplifier for our analysis due to its widespread popularity; however, our approach is general and can he applied to a broad class of photoreceivers. Since our transfer function is based on a physical circuit, our results can be used to estimate photoreceiver noise performance without making any assumptions on the input or output pulse shapes     

Symbolic analysis of simplified transfer functions

This contribution presents new algorithms for the automatic simplified computation of symbolic transfer functions of linear circuits. The problem of symbolic simplification of transfer functions is defined and a set of algorithms able to cope with this problem and the simplified computation of poles and zeroes is developed and discussed. Results are reported with examples of circuits analyzed by our algorithms, showing good accuracy in their approximation, when compared to the corresponding SPICE simulations. Our technique merges the simplification procedure and the evaluation of the transfer functions, thus achieving significant improvements in terms of CPU time, compared with direct evaluation of the functions themselves.     

Efficient symbolic computation of approximated small-signalcharacteristics of analog integrated circuits

A symbolic analysis tool is presented that generates simplified symbolic expressions for the small-signal characteristics of large analog integrated circuits. The expressions are approximated while they are computed, so that only those terms are generated which remain in the final expression. This principle causes drastic savings in CPU time and memory, compared with previous symbolic analysis tools. In this way, the maximum size of circuits that can be analyzed, is largely increased. By taking into account a range for the value of a circuit parameter rather than one single number, the generated expressions are also more generally valid. Mismatch handling is explicitly taken into account in the algorithm. The capabilities of the new tool are illustrated with several experimental results     

Backing control problem of a mobile robot with multiple trailers:fuzzy modeling and LMI-based design

The paper presents backing control of computer simulated mobile robots with multiple trailers by fuzzy modeling and control. We deal with two kinds of mobile robots: a mobile robot with five trailers and a mobile robot with ten trailers. To design fuzzy controllers, nonlinear models of the mobile robots with multiple trailers are represented by Takagi-Sugeno fuzzy models (TS fuzzy model). Before making TS fuzzy models, we simplify the nonlinear dynamics of the mobile robots. Under an assumption, TS fuzzy models are made from the simplified nonlinear models. The so-called parallel distributed compensation (PDC) is employed to design fuzzy controllers from the TS fuzzy models. Next, we derive a stability condition based on the Lyapunov approach. The stability condition of the designed fuzzy control system is cast in terms of linear matrix inequalities (LMI's) since it is reduced to a problem of finding a common Lyapunov function for a set of Lyapunov inequalities. Convex optimization techniques based on LMI's are utilized to solve the problem of finding stable feedback gains and a common Lyapunov function for the designed fuzzy control system. The simulation results show the effects of the fuzzy modeling, the controller design via the PDC, and the stability analysis based on LMIs     

Symbolic Determinant Decision Diagrams and Their Use for Symbolic Modeling of Linear Analog Integrated Circuits

An efficient technique for the symbolic modeling of the frequency behavior of a linearized analog circuit is presented. It uses a compact graph representation based on the Laplace expansion of the system determinant, called determinant decision diagram or DDD. The construction of a circuit's DDD is explained and an analysis of the time and space complexity is given. These DDD's can be used in behavioral modeling by representing the exact numerical transfer function in a compact way. DDD's also enable the generation of symbolic transfer functions, resulting in a symbolic analysis technique with lower computational complexity than techniques not based on DDD's.     

A Method of Transformation from Symbolic Transfer Function to Active-RC Circuit by Admittance Matrix Expansion

Active-RC circuits containing 2-terminal linear passive elements and ideal transistors or operational amplifiers are derived from symbolic voltage or current transfer functions by admittance matrix transformations without any prior assumption concerning circuit architecture or topology. Since the method is a reversal of symbolic circuit analysis by Gaussian elimination applied to a circuit nodal admittance matrix, it can generate all circuits using the specified elements that possess a given symbolic transfer function. The method is useful for synthesis of low-order circuits, such as those used for cascade implementation, for deriving alternative circuits with the same transfer function as an existing circuit or for realizing unusual transfer functions, as may arise, for example, where a transfer function is required that contains specific tuning parameters     

ISAAC: a symbolic simulator for analog integrated circuits

The symbolic simulator ISAAC (interactive symbolic analysis of analog circuits) is presented. The program derives all AC characteristics for any analog integrated circuit (time-continuous and switched-capacitor, CMOS, JFET, and bipolar) as symbolic expressions in the circuit parameters. This yields analytic formulas for transfer functions, CMRR (common-mode rejection ratio), PSRR (power-supply rejection ratio), impedances, noise, etc. Two novel features are included in the program. First, the expressions can be simplified with a heuristic criterion based on the magnitudes of the elements. This yields interpretable formulas showing only the dominant terms. Second, the explicit representation of mismatch terms allows the accurate calculation of second-order effects, such as the PSRR. ISAAC provides analog designers with more insight into the circuit behavior than do numerical simulators and is a useful tool for instruction or designer assistance. Moreover, it generates complete analytic AC circuit models, which are used for automatic sizing in a nonfixed topology analog module generator. The program's capabilities are illustrated with several examples. The efficiency is established by a dedicated sparse-matrix algorithm     

MERLIN: a device diagnosis system based on analytic models

An approach to computer-aided interpretation of parametric test data for integrated circuit process-problem diagnosis is presented. In contrast to a conventional expert system, which reasons with a knowledge base consisting of rules acquired from human experts, the system presented centers its knowledge around analytic device equations. By using equations as the basis of the system knowledge, a more universal, well-organized, and concise level of knowledge is encoded. With the use of objects to present this knowledge, a great deal of useful information outside that described by only the symbolic expressions can be represented, and extension to qualitative or numeric models should be straightforward. The result is an expressive, well-organized, easily built, and easily maintained knowledge base. The authors describe the system's interactive graphical displays and the automatic data interpretation algorithms. Examples evaluating n-channel metal oxide semiconductor (NMOS) parameter variations, interconnect parameter variations, and interconnect yields are used for illustration     

Computation of Approximate Symbolic Pole/Zero Expressions

The symbolic LR algorithm using simplification during LR iterations is used for the computation of the approximate symbolic pole/zero expressions. It is shown that this approach is competitive or better with respect to the best known approaches. A two transistor amplifier is redesigned using these formulas.     

A hierarchical approach to large circuit symbolic simulation

This paper presents a new approach to symbolic analysis of large circuits. The proposed procedure is grounded on circuit decomposition by node tearing, symbolic analysis at subcircuit level and circuit function generation. Symbolic analysis is based on matrix-determinant method implemented within our original symbolic simulator. The crucial part of this procedure is circuit function generation. Opposed to classic symbolic simulation that gives final result in canonical sum-of-product form, hierarchical approach results in compact nested form. Proposed method is described in details using a simple example. The comparison with two other similar techniques is given using a benchmark example. The overall time reduction in comparison with the circuit function extraction in fully expanded form is 30 times.     

Algorithm for efficient symbolic analysis of large analoguecircuits

An algorithm is presented that generates simplified symbolic expressions for the small-signal characteristics of large analogue circuits. The expressions are approximated while they are computed, so that only the most significant terms are generated which remain in the final expression. This principle leads to dramatic savings in CPU time and memory compared to existing techniques, significantly increasing the maximum size of circuits that can be analysed. By taking into account a range for the value of a circuit parameter rather than one single number the generated symbolic expressions are also generally valid     

Hybrid artificial intelligence methods in oceanographic forecast models

An approach to hybrid artificial intelligence problem solving is presented in which the aim is to forecast, in real time, the physical parameter values of a complex and dynamic environment: the ocean. In situations in which the rules that determine a system are unknown or fuzzy, the prediction of the parameter values that determine the characteristic behavior of the system can be a problematic task. In such a situation, it has been found that a hybrid artificial intelligence model can provide a more effective means of performing such predictions than either connectionist or symbolic techniques used separately. The hybrid forecasting system that has been developed consists of a case-based reasoning system integrated with a radial basis function artificial neural network. The results obtained from experiments in which the system operated in real time in the oceanographic environment, are presented.     

MSK信号的最大似然非相干检测算法研究

针对最小频移键控(MSK)信号,本文研究了一种性能优异的低复杂度最大似然非相干检测(MLNCD)接收模型,通过利用有限的几个符号构成的观测序列检测中间符号解调信息。本文给出了MLNCD模型的判决表达式,并推导了基于MLNCD算法的MSK信号软解调简化表达式,降低了实现复杂度。本文还仿真分析了采用MLNCD算法的无编码MSK系统和有编码MSK系统的误码率(BER)性能,结果表明MLNCD算法比传统MSK非相干解调算法具有显著的BER性能优势,与MSK相干解调性能接近,而且软信息的简化几乎没有造成系统性能损失。      

复合卡诺图在多输出组合逻辑电路设计中的应用

为了使设计的多输出组合逻辑电路达到最简,运用复合卡诺图化简多输出函数,找出其各项的公共项,得到的表达式不一定是最简的,但是通过找公共项,使电路中尽量使用共用的逻辑门,从而减少电路整体的逻辑门,使电路简单。结果表明,利用复合卡诺图化简后设计出的电路更为简单。     

系统电磁兼容性问题预测实例

系统电磁兼容性预测不仅在方案阶段需要,在工程阶段仍然重要,是进行合理电磁兼容性设计,争取时间、减 少费用的有效手段。系统电磁兼容性预测可以使用专业软件进行仿真计算、分析,在特殊情下也可以采用工程简化方法 计算、分析,还可以用工程经验进行分析评估。在电磁兼容性预测计算、分析中,仿真软件一般考虑全面,简化方法计 算相对快捷,建立简化且与实际接近的干扰源模型、传输特性模型以及敏感度域值模型是计算、分析准确程度的关键。 本例中是用简化方法对实际系统电磁兼容性问题解决提供了理论依据,并进行了仿真和试验验证,结论一致。说明,除 了用专业仿真软件进行预测计算,用工程简化方法计算也会常常遇到;实际电磁兼容工作中系统预测是重要的并且不一 定非常复杂,供参考     

用符号法分析恒频电流模控制的变换器闭环系统的稳态

将等效小参量符号分析法推广到恒频电流模控制的变换器闭环系统的稳态分析中,提出了占空比的精确确定法及简化确定法.其中,前者不需要有波形线性及小纹波假设,具有广阔的适用性.而后者对工程简化分析具有重要意义.所得结果均为符号表达式,易于理解电路的工作机理.