Methods of DC circuit analysis

In this chapter, the problems of the first chapter are fully solved, in detail, step-by-step, and with multiple methods, by using mesh analysis, nodal analysis, and heuristic techniques. In all the problems’ solutions, Kirchhoff current law (KCL) and Kirchhoff voltage law (KVL) as well as the concepts of mesh current, node voltage, supermesh, and supernode are clearly described. Moreover, in the application of circuit theorems, the concepts of open circuit voltage, short-circuit current, Thevenin voltage, Thevenin resistance, Norton current, and Norton resistance are explained. In addition, this chapter shows how to deal with circuit components like resistors, dependent current and voltage sources, and independent current and voltage sources.

A metal-only reflectarray (MOR) antenna for 77 [GHz] was analyzed with the equivalent surface current sources. The equivalent current sources can be used to produce the incident fields radiated from a feed. When a feed is an open-ended rectangular waveguide (OERW), the calculated antenna gains for the equivalent current sources, point source, and CST Microwave Studio (MWS) are 31.8, 30.0, and 31.6 [dBi], respectively. The simulated results of the equivalent current sources and CST MWS are in good agreement with each other in terms of the antenna gain.

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

Recently a study of the analog behavior of ring oscillators was presented from the perspective of VCO ADC design [1]. In this study it was shown that the electrical behavior between the two tuning terminals of such a ring oscillator can be modeled by a diode element. The VCO (phase-)noise can be modeled as an equivalent input-referred noise voltage source in series with this diode. Unfortunately, it was found that this input-referred noise was dependent on the driving impedance. In the prior study only ideal voltage and ideal current control were elaborated. In this work, we generalize the VCO noise model for an arbitrary driving impedance. This enables the noise optimization of a VCO with an arbitrary driving circuit which was not possible with the prior theory. In this work we present such a noise optimization for the linearizing resistive VCO drive circuit of [2], [3]. We show that for this circuit the biasing of the ring is rather uncritical, which is in strong contrast with the result for a pure voltage mode drive circuit, where the biasing of the ring has a major impact on the noise performance.

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.

This paper presents an equivalent model of an inductive magnetic harvester, taking nonlinear effects of magnetic field into consideration. Conventional models consist of one AC voltage source in series with an inductor and are unable to predict harvester performance precisely; a more accurate approach is introduced by considering the nonlinear effects of the magnetic fields. The new model uses a magnetizing inductance and a leakage inductance rather than a single series inductor. In the proposed equivalent model, magnetizing and leakage inductance can be found by detecting flux variation in the air gap between magnets and coil cores. The finite element analysis (FEA) method is used to estimate the electromagnetic field and flux linkage of the coils. The optimum harvesting system design is only possible based on the more accurate modeling of the inductive magnetic harvester.

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.

This paper proposes an extension of Finite Element Time Domain (FETD) method for the global electromagnetic analysis of complex active microwave circuits. The equivalent current sources and capacitances of the distributed part of the circuit, derived from FETD analysis, are incorporated into state equations to solve the lumped element part of the circuit. Benchmark tests on a microwave amplifier and self-oscillating mixer indicate that this extended FETD is not only superior in mesh flexibility but also gives much better results than a simulated FDTD-based algorithm.

A method of analog circuit analysis is proposed that is based on the use of the transistor as its own dc model. Time-scaled carrier storage effects are simulated by capacitors that are driven, through operational amplifiers, by voltages that are proportional to terminal currents.

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.

2 - Circuit Analysis: A Graph-Theoretic Foundation

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.

A fast Thvenin equivalent model for IGBT considering the dynamic performance of both IGBT and antiparallel diode based on datasheet is proposed to increase the efficiency of power electronics transient simulation. In this paper, the conducting details of an IGBT with antiparallel diode switch are represented by a fixed topology equivalent: a voltage source in series with a constant resistance. For the first time, three devices are intergrated inside one model, and the conducting device is dynamically alternative among three statuses: IGBT, diode and open circuit, reflected in the changeable voltage source. So unchangeable admittance matrix is gained despite of the variation of conducting devices, which tremendously accelerates the calculation. A single phase half-bridge inverter circuit is tested applying the proposed model, and its accuracy and efficiency are validated.

The aim of this paper is to propose a protection strategy for the voltage generator based inverter against the large load currents. This strategy proposes an algorithm for generators output current limiting. It depends on decreasing the amplitude of the voltage reference in case of over current on generator output current. We aim to give the source a behavior similar to that of a voltage source in series with a virtual resistance. This resistance is activated only above a certain current threshold. Simulation results for the application of this strategy on resistive and resistive-inductive load will be demonstrated, in this paper. The effectiveness of the proposed current limiting method was tested on high load current resulting from the asynchronous motor startup. The last part will discuss the implementation of this current limiting strategy on real time simulation environment RT-LAB. An experimentation using Power Hardware in the Loop and realtime simulation was realized to verify the theoretical analysis.

Piezoelectric and electrostatic based sensors are commonly used to measure pressure, acceleration, strain and force. These sensors can be modeled as a voltage source in series with a capacitive source impedance. There is a misconception that these sensors have infinitesimal resolution. This work describes the noise sources that contribute to the resolution of sensors with capacitive source impedances. The power spectral density (PSD) of each relevant noise source is derived in order to estimate the resolution. Expressions for the root-mean-square (RMS) and peak-to-peak noise are developed. These expressions are experimentally verified by estimating the resolution of a sensor with a 10 nF capacitance and 100 MΩ leakage resistance. The estimated resolution of 390 mV compares well with the measured resolution of 420 mV.