Circuit analysis by quasi-analog computation

Introduction to Circuit Analysis and Design

This chapter contains sections titled: Introduction The Superposition Method The Th��venin Method Norton's Method The Mesh Method of Analysis The Nodal Method of Analysis Which One Is the Best Method? Using all the Methods Summary and Conclusions Further Reading Problems

This chapter discusses the conversion of voltage source to an equivalent current source and vice versa. Know the methods of voltage sources in series and parallel operation and also current sources. Understand the branch current analysis method, mesh analysis method and node voltage analysis method applied to circuit analysis.

Parallel to algebraic methods, graphical circuit analysis methods have the advantage of cancellation-free. This paper proposes a graph reduction method for hierarchical symbolic circuit analysis by applying a binary decision diagram (BDD) for data sharing. This method is extended from the Graph-Pair Decision Diagram (GPDD) method which was developed for two-port dependent sources. New graph construction rules for multiple-port dependent sources are introduced, with which large analog circuits can be analyzed hierarchically. The new hierarchical method guarantees the cancellation-free property at each layer of hierarchy. The BDD-based hierarchical analysis method can greatly reduce the analysis complexity of the entire circuit, while the software construction and circuit partition remain easy. The new method is compared to the algebraic hierarchical method based on DDD (Determinant Decision Diagram) which does not have the cancellation-free property. Comparable performance can be achieved with the new method which has the extra cancellation-free property.

A method for the nonlinear electric circuit analysis with the use of the orthogonal components of instantaneous admittance and resistance is proposed. The mechanism of the generation of the admittance orthogonal components of a nonlinear electric circuit is demonstrated. The analytical expressions for the components of instantaneous admittance and resistance are given and analyzed. The balance equations for the components of instantaneous admittance and resistance are analyzed. On their basis, the harmonic components of the current of the nonlinear electric circuit consisting of an active linear and nonlinear resistance, connected in series, are determined. The accuracy and adequacy of the developed method are proved by the comparative analysis of the current harmonic components calculated with the use of the proposed method and the ones obtained as a result of the numerical calculation of the researched circuit mathematical model. The advantages of the proposed method include its versatility in the use, the possibility to assess the circuit parameters influence on the current spectrum composition, good adaptation to the automation of the calculations in the frequency domain, the ability to obtain the predicted result independently of the degree of the approximating polynomial and the number of the analyzed harmonics.

Symbolic circuit analysis using Mathematics A method of symbolic circuit analysis using Mathematica is reported. With the powerful symbolic manipulation capacity of Mathematica, symbolic circuit analysis is significantly simplified. The analysed circuits can be passive or active, with active devices modelled by nullors. Non-trivial circuit analysis examples are presented and the program list is given.

Chapter 3 - Development of the Ideal Op Amp Equations

In this paper, a new bridge-type chopper having power electronic switches is proposed for low-voltage superconducting magnetic energy storage (SMES) applications. The energy charge and discharge characteristics of a high temperature superconducting (HTS) SMES device, including transient current through the HTS coil, maximum discharge time duration for the load, effective energy utilization factor, are numerically studied using the circuit analysis and iterative calculation methods, and finally verified by measurements on the developed chopper device. One new theoretical modeling in corporation with a simple digital control method is presented. Experimental and numerical comparisons of the bridge-type and conventional choppers show that the new developed bridge-type chopper is favorable for long-time power compensation with very high operation efficiency in the low-voltage power applications.

The well forgotten master equation from the seminal article by Ragazzini, Randall and Russell [J. R. Ragazzini, R. H. Randall and F. A. Russell, “Analysis of Problems in Dynamics by Electronic Circuits”, Proc. of the I.R.E., 35, pp. 11–19, (1947)] is recovered as indispensable tool for the analysis of contemporary circuits with operational amplifiers. This equation gives the relation between time dependent the output voltage U0(t) and the difference between the input voltages (U+(t) and U−(t)). The crossover frequency f0 parameterizes the time constant τ0 of this equation. The work of the master equation is illustrated by two typical examples: a) the stability criterion of the devices with negative impedance converters, which we consider as a new result b) the frequency dependence of the amplifiers with operational amplifiers given in the technical specifications. A simple circuit for determination of f0 is suggested and the method is illustrated by determination of crossover frequency for the low-noise and high speed ADA4898 operational amplifier. It is concluded that for an exact calculation of the pass bandwidth of amplifiers with active filters the 70 years old master equation is indispensable.

A Tonpilz type piezoelectric ceramic ultrasonic transducer is investigated through the methods of equivalent circuit and finite element analysis(FEA). The emphasis of this paper lies in the difference between the two methods. Essentially, the piezoelectric constitutive equation is the common law of them. Derived from this equation, the Mason’s equivalent circuit and the frequency equation of the piezoelectric transducer is obtained, and then the finite element control equation is obtained. A mason’s equivalent circuit model and a 1/4 symmetry finite element model of the Tonpilz type piezoelectric ceramic ultrasonic transducer are both constructed. A comparison about the frequency performance and the admittance performance which are respectively obtained from the two methods and the corresponding test shows that, the method of FEA is more quickly and accurately, and its analysis error is controlled within 5%. What is worth to mention is that some performance and the vibration of the transducer have been predicted distinctly through FEA. So FEA is suitable to the piezoelectric transducer. A transducer prototype which is made according to the analysis result has a good performance and satisfying applied requirements.

Ophthalmic Imaging

In this paper, isomorphism identification algorithm of planar multiple joint kinematic chains by circuit analysis method has been presented. Firstly, topological model is introduced. Then, corresponding equivalent circuit model is established to obtain node voltage sequence; By the solved node voltage sequence, an algorithm to identify isomorphic kinematic is obtained. Lastly, examples are carried out to show this useful method.

A coupled-inductor step-down switching DC-DC converter with continuous input and output current is investigated by use of a new time averaging equivalent circuit (TAEC) analysis method. By using the TAEC, one can analyze such a converter in a more simple way as the parameters of the TAEC model can easily be determined by the new approach. As a result, the analytical expression for the DC steady state and AC small signal equivalent circuit model of the converter are obtained. DC and AC small signal analysis can then be performed. >

It is very important that undergraduate teaching of analog circuits be rigorous, involve a laboratory component and stimulate student interest. This paper describes a three week module on active circuits that incorporates circuit design, analysis and testing. The lectures are integrated with the laboratory component and all appropriate concepts in mathematics are covered. Assessment results are based on running the project at three universities, namely, Rowan, Bucknell and Tennessee State. Quantitative results based on student surveys, a concept inventory test and faculty formulated rubrics demonstrate the accomplishment of the learning outcomes. INTRODUCTION AND MOTIVATION A course on the principles of analog circuits is fundamental in the early part of an Electrical and Computer Engineering curriculum. A long standing debate is on how to get students more interested in circuit theory and simultaneously comprehend and apply the basic concepts [1][2]. Project-based learning has been shown to increase student interest, basic design skills [3] and comprehension of the concepts in basic engineering and mathematics through vertical integration [4][5]. Vertical integration is the principle of having a project or experiment in a course build upon concepts gained through experiments and/or projects performed in a parallel or previous course. Students will realize that the courses are part of a flow that contributes to a unified knowledge base. This paper describes a project on active circuits that is performed at three universities, namely, Rowan, Bucknell and Tennessee State. The project has been formulated such that it can be taught at any university that has a course that covers the basic laws of circuit theory, introduces passive and active circuits, teaches the appropriate mathematical techniques and has a hands-on laboratory component. Specifically, the curriculum will include (but not limited to) mesh and nodal analysis, Thevenin equivalent, operational amplifier circuits, first and second order circuits, Laplace transform analysis, AC circuits, transformers and the frequency response of simple filters. The project reinforces circuit analysis, accomplishes simple design, involves the use of MATLAB and exposes the student to an operational amplifier chip. The project relies on concepts learned previously or concurrently like calculus and computer programming. It also leads into projects in follow-up courses like (1) building an audio amplifier or a power supply in an electronics course and (2) analog and digital filter design in a signals and systems course. Three different forms of assessment are carried out. They are based on student surveys, a concept inventory test and faculty formulated rubrics.

In this chapter, the problems of the third chapter are fully solved, in detail and step-by-step. In solving the problems of the first-order circuits, the subjects discussed in the first chapter, that is, the methods of circuit analysis and circuit theorems, are applied. In this chapter, the concepts and the parameters of equivalent capacitance, equivalent inductance, time constant of a capacitive first-order circuit, time constant of an inductive first-order circuit, transient response, voltage continuity principle of capacitor, current continuity principle of inductor, primary value, final value, steady state condition, stored energy of circuit, switching operation, and current-voltage and voltage-current relations of capacitor and inductor are explained.