Worst-case tolerance analysis of linear DC and AC electric circuits

Introduction to Linear Circuit Analysis and Modelling

Computationally efficient large-change statistical analysis of linear electronic circuits

This paper presents a state-of-the-art review of the recent advances in computer methods for analysis and design of switched circuits in both time and frequency domains. It also presents new research results on time-domain analysis and sensitivity of switched nonlinear circuits, time- and frequency-domain statistical analysis of switched linear and nonlinear circuits, and efficient modeling and analysis of clock feedthrough and charge injection in switched linear circuits. In time-domain analysis, the modeling of switches and its effect on the simulation of switched circuits are investigated. Formulation methods for these circuits are examined. Inconsistent initial conditions arising from ideal switching are investigated and numerical methods that derive the consistent initial conditions are examined. Sampled-data simulation (SDSIM) of switched linear circuits including clocked sigma-delta modulators is investigated. SDSIM is extended to switched nonlinear circuits. Time-domain sensitivity of switched linear and nonlinear circuits is analyzed using SDSIM. Efficient time-domain statistical analysis of switched linear and nonlinear circuits is introduced, and their effectiveness is assessed using Monte Carlo simulation. Methods that compute the effect of the clock jitter of periodically switched linear (PSL) circuits are examined. Time-domain noise analysis of PSL circuits is investigated. In frequency-domain analysis, exact frequency analysis of multiphase PSL circuits is reviewed. Sensitivity analysis of these circuits is examined in detail. Adjoint network theory and its usefulness in noise and sensitivity analysis of switched linear circuits are studied. Group delay of PSL circuits is investigated briefly. Efficient modeling and analysis of clock feed-though and charge injection of PSL circuits are introduced. Distortion and sensitivity of periodically switched nonlinear circuits with mild nonlinearities are investigated. Finally, frequency-domain noise analysis of PSL circuits is examined.

Analysis of large linear mesh circuits is critical in modern IC extraction and verification tools due to the complex 3-D effects associated with parasitic coupling through interconnects and the chip substrate. The limited availability of computer resources, however, is a major obstacle in the fast and accurate analysis of such circuits. This paper introduces a technique that divides the mesh into a number of partitions, develops macromodels of each partition using a compaction technique and then combines them in a nested fashion to determine a macromodel for the original mesh circuit, which can then be used in simulation. This method makes much better use of CPU time and memory and allows for the fast analysis of extremely large meshes.

This chapter introduces the analysis and design of linear circuits. It reviews basic direct‐current (DC) analysis using traditional circuits theorems with application to circuit analysis and design. Using node voltage instead of element voltages as circuit variables can greatly reduce the number of equations that must be treated simultaneously. The chapter treats the analysis and design of circuits containing active devices such as transistors or operational amplifiers (op amps). It also discusses alternating current (AC) circuits. Those ac circuits that are excited by a single frequency, for example, power systems, can be easily and effectively analyzed using sinusoidal steady‐state techniques. Linear circuits are often characterized by their behavior to sinusoids, in particular, how they process signals versus frequency. Audio, communication, instrumentation, and control systems all require signal processing that depends at least in part on their frequency response.

This paper presents novel free open-source software JuliaCAP for symbolic analysis of linear time-invariant electric circuits in the complex domain of the Unilateral Laplace Transform or Phasor Transform. Modified Nodal Analysis (MNA) has been chosen for formulation of circuit equations in JuliaCAP. JuliaCAP has been developed by Kristina Rajković, Glorija Došlo, Nikola Radojević, Tamara Petković and Ivana Stanojević, at the University of Belgrade - School of Electrical Engineering, Belgrade, Serbia. JuliaCAP is written in Julia, a free open-source (MIT licensed) programming language. Whereas Julia is a relatively new language, there will be some words about it. As a free opensource software package, the underlining algorithm is revealed in full detail, so anybody can get a better understanding of the used methods. We offer JuliaCAP as a useful tool for solving linear time-invariant electric circuits. The future directives should be the improvement of simplifying expressions and the absence of the possibility to solve electric circuits in the complex domain of the Unilateral Laplace Transform. Also, it is shown through examples how this software operates. Electric circuits that are used in examples are Riordan gyrator network, 3rd order Butterworth Low-pass Filter, Subtractor and Adder.

PLMAP — A piecewise linear MOS circuit analysis program

The general framework of a symbolic analysis environment for linear time-invariant circuits is presented. Such a framework consists of two major parts: a simplification at circuit level and a simplifying expression-generation. An overview of the known techniques for both circuit simplification and expression generation is given, and in addition a new nonhierarchical expression generation technique based on the concept of determinant decision diagrams (DDDs) is presented. The DDD-based technique is evaluated on a set of benchmark circuits together with a known fast symbolic analysis algorithm, and turns out to be the most efficient. The DDD-based expression generation algorithm is, therefore, the best solution for nonhierarchical linear symbolic expression generation to the authors' knowledge.

A few techniques based on an efficient use of memory resources, called matrix caches, to speed up the transient analysis of piecewise linear circuits such as power electronic circuits are presented. These techniques use the fact that the matrix in the linear equation solving routines can only have a finite number of different values. Hence, by adding a cache memory management technique to store the LU factor of these matrices for future reuse, the linear equation solver can be performed much faster than that of a general purpose simulation program in which these LU factors have to be recomputed every time. Since most of the CPU analysis time is spent in solving linear equations, these techniques can actually speed up the transient analysis of piecewise linear circuits significantly. An experimental circuit simulator has been developed to implement the matrix cache and tested with a few piecewise linear power electronic circuits. The results indicate a speed increase of 2–10 times as compared with its non-matrix cache version.

Linear circuit analysis is a foundational course for electrical engineers. Instructors of linear circuit analysis courses have traditionally relied on print textbooks for student learning materials. With the rise of student use of computers and the internet, materials like lecture slides and online videos have also been used for learning materials. Increasingly, traditional textbooks (including online formats) are experiencing a decline, while interactive textbooks are growing in popularity. This paper describes auto-graded learning tools, called challenged activities, from various topics in an online linear circuit analysis textbook. Instructors often assign challenge activities as homework. Each challenge activity has 3-5 levels of increasingly difficult problems. Each level randomly generates a question from a large set of questions of similar difficulty. Students must correctly answer a question in a level to progress to the next level. This paper describes the student usage of 4 challenge activities in an online circuit analysis textbook. The average time spent per activity was under 10 minutes and the vast majority of students who started a level ended up completing that level, indicating little attrition. In fact, most levels had 0% of students give up and the highest was only 8%, which is remarkably low based compared to more traditional paper-and-pencil activities based on the teaching experience of the authors.

This paper presents a few techniques based on an efficient use of memory resources to speed up the transient analysis of piecewise linear circuits, such as power electronic circuits. These techniques use the fact that the matrix in the linear equation solving routines can only have a finite number of different values. Hence, by adding a cache memory management technique to store the LU factor of these matrices for future reuse, the linear equation solver can be performed much faster than that of a general purpose simulation program in which these LU factors have to be recomputed every time. Since most of the CPU analysis time is spent in solving linear equations, these techniques can actually speed up the transient analysis of piecewise linear circuits significantly (100-600%).

The development, expansion, and assessment of a step-based computer-aided tutoring system to teach linear circuit analysis is described. Circuit problems and fully worked, error-free solutions to same are created automatically and randomly with any desired characteristics, varying both the layout and numerical values. Students therefore have access to an unlimited source of both examples and practice problems of variable difficulty. A unique feature is that students input each stage of their work in a variety of forms including redrawn circuit diagrams, equations, matrix equations, numerical answers, multiple choice answers, and sketches of time-dependent waveforms. Students receive immediate feedback on the correctness of each step of their work. The solutions use analytical methods, rather than the numerical methods used in a tool like PSPICE. A total of 15 tutorials are now available, including DC and AC circuits and two on Laplace transforms. The system has been used by over 1950 students to date. A randomized, controlled laboratory-based study finds a statistically significant learning gain of 1.21 standard deviations compared to working conventional textbook problems. Another randomized, controlled classroom study found a strong preference of students for this system over a widely-used commercial publisher-based homework system, as well as higher scores.

In this paper, we explored a new way for linear circuit transient analysis based on the accompanying network method. This new method is simple and convenient, tries to avoid differential equation from the beginning of the establishment of circuit equations, makes use of accompanying network by which the transient process can be divided into a series of discrete time intervals Δt, replaces the dynamic components L, C with corresponding discrete model which is called their accompanying network. To every interval Δt, there is no dynamic component in the accompanying network, so the transient analysis of the linear circuit can be divided into a series of steady state analysis of resistance network.

PSSOH conference paper on symbolic analysis of linear electronic circuits in free software. The SALECx software code is developed and maintained by Dr. Dejan V. Tošić, Full Professor from the University of Belgrade – School of Electrical Engineering. It is available at GitHub PSSOH page. On November 2, 2019 at the University of Belgrade - School of Electrical Engineering workshop titled "Symbolic circuit analysis on Android" was held as part of the post-conference PSSOH events. More information at https://zenodo.org/record/3516733#.XdrWC9V7nIU3.

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