Introduction to Linear Circuit Analysis and Modelling

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.

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.

Computationally efficient large-change statistical analysis of linear electronic circuits

Electric circuit has a very important role in electronics field progressing. From simple to complex form of circuits, actively support the establishment of new innovations in engineering technology. To build a good concept of circuit, it is necessary to have proper understanding on basic concept and circuit analysis. Starting from Ohm and Kirchhoff’s laws, another circuit laws and formulas are derived from analysis and theorems, to give better calculation and solution in problems. This paper will do an analysis on relationship between resistances in delta circuit, and apply basic electric circuit theory to calculate the total resistance. This analysis is conducted by doing comparison and calculation to derive the expected formula.

This paper addresses the problem of worst-case tolerance analysis of steady states in linear DC and AC electric circuits. The statement of the problem considered is in the form of linear algebraic equations whose elements are, in the general case, nonlinear functions of a given set of independent interval parameters. Three kinds of solutions are considered: 1) outer solution; 2) inner solution and 3) exact solution. A direct method for computing an outer solution and an iterative method for finding an inner solution are suggested. The inner and outer solutions thus found provide a tight two-sided bound on the exact solution of the tolerance problem investigated. The exact solution can be determined if certain monotonicity conditions are fulfilled. The verification of the conditions involves solving several associated outer solution problems. The computational efficiency of the methods suggested is demonstrated by a numerical example.

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 book is concerned with circuit simulation using National Instruments Multisim. It focuses on the use and comprehension of the working techniques for electrical and electronic circuit simulation. The first chapters are devoted to basic circuit analysis. It starts by describing in detail how to perform a DC analysis using only resistors and independent and controlled sources. Then, it introduces capacitors and inductors to make a transient analysis. In the case of transient analysis, it is possible to have an initial condition either in the capacitor voltage or in the inductor current, or both. Fourier analysis is discussed in the context of transient analysis. Next, we make a treatment of AC analysis to simulate the frequency response of a circuit. Then, we introduce diodes, transistors, and circuits composed by them and perform DC, transient, and AC analyses. The book ends with simulation of digital circuits. A practical approach is followed through the chapters, using step-by-step examples to introduce new Multisim circuit elements, tools, analyses, and virtual instruments for measurement. The examples are clearly commented and illustrated. The different tools available on Multisim are used when appropriate so readers learn which analyses are available to them. This is part of the learning outcomes that should result after each set of end-of-chapter exercises is worked out. Table of Contents: Introduction to Circuit Simulation / Resistive Circuits / Time Domain Analysis -- Transient Analysis / Frequency Domain Analysis -- AC Analysis / Semiconductor Devices / Digital Circuits

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.

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%).

Introduction to Circuit Analysis and Design

One function of the protection system is to avoid or reduce damage to electrical equipment due to abnormal conditions such as undervoltage, overvoltage, overcurrent, underfrequency and harmonics. This protection system requires a Smart 7KT Multi-Function Meter and a PLC. Where the Smart 7KT Multi-Function Meter is used for monitoring then transferred to the PLC and detecting any abnormalities in the system when a disturbance occurs then the Smart 7KT Multi-Function Meter will send data to the PLC, then send a signal to the circuit breaker to disconnect the network that is experiencing disturbance. While the PLC is used to execute data that has been taken by the Multi-function Meter Smart 7KT for control or control on the Multi-function Meter Smart 7KT. When a disturbance occurs, the program on the PLC will protect and the type of disturbance will be displayed on the HMI screen. The results of this project were successful in securing undervoltage disturbances of 314.2 V for line voltages, overvoltage of 412.1 V for line voltages, overcurrent of 1.6 A, and testing of THD voltage between phases V12 of 1.3%, THD V23 of 1.1%, and THD V13 of 1.1%, for THD currents of 14.6% for THD I1, THD I2 of 9.4%, and THD I3 of 10.6% which occur in the electric power installation network which causes damage to electrical equipment.

Lcapy is an open-source Python package for solving linear circuits symbolically. It uses a superposition of DC analysis, AC (phasor) analysis, transient (Laplace) analysis, and noise analysis. Expressions are evaluated using the computer algebra system SymPy. Lcapy can model circuits comprised of combinations of one-port and two-port networks or circuits specified using a netlist with a Spice-like notation. Lcapy can present the system of equations produced from nodal analysis, modified nodal analysis, loop analysis, and state-space analysis. Expressions can be formatted into many representations, parameterized, and transformed to other domains. Dimensional analysis is performed to reduce user errors and to present results with units. Both continuous and discrete signals are supported. Lcapy produces high-quality output. Textbook quality schematics in a number of different formats can be generated from netlists and customized for different conventions. Expressions can be formatted into LaTeX format for inclusion into a document or numerically evaluated and plotted. An overview of the features and capabilities of Lcapy is presented, along with implementation details and performance considerations.

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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