LCR meter

Abstract: Preface. 1 Introduction. 1.1 Historical Background. 1.2 Fundamental Concepts of Lumped Circuits. 1.3 Outline of the Book. 1.4 "Loop" Inductance vs. "Partial" Inductance. 2 Magnetic Fields of DC Currents (Steady Flow of Charge). 2.1 Magnetic Field Vectors and Properties of Materials. 2.2 Gauss's Law for the Magnetic Field and the Surface Integral. 2.3 The Biot-Savart Law. 2.4 Ampere's Law and the Line Integral. 2.5 Vector Magnetic Potential. 2.5.1 Leibnitz's Rule: Differentiate Before You Integrate. 2.6 Determining the Inductance of a Current Loop:. A Preliminary Discussion. 2.7 Energy Stored in the Magnetic Field. 2.8 The Method of Images. 2.9 Steady (DC) Currents Must Form Closed Loops. 3 Fields of Time-Varying Currents (Accelerated Charge). 3.1 Faraday's Fundamental Law of Induction. 3.2 Ampere's Law and Displacement Current. 3.3 Waves, Wavelength, Time Delay, and Electrical Dimensions. 3.4 How Can Results Derived Using Static (DC) Voltages and Currents be Used in Problems Where the Voltages and Currents are Varying with Time?. 3.5 Vector Magnetic Potential for Time-Varying Currents. 3.6 Conservation of Energy and Poynting's Theorem. 3.7 Inductance of a Conducting Loop. 4 The Concept of "Loop" Inductance. 4.1 Self Inductance of a Current Loop from Faraday's Law of Induction. 4.1.1 Rectangular Loop. 4.1.2 Circular Loop. 4.1.3 Coaxial Cable. 4.2 The Concept of Flux Linkages for Multiturn Loops. 4.2.1 Solenoid. 4.2.2 Toroid. 4.3 Loop Inductance Using the Vector Magnetic Potential. 4.3.1 Rectangular Loop. 4.3.2 Circular Loop. 4.4 Neumann Integral for Self and Mutual Inductances Between Current Loops. 4.4.1 Mutual Inductance Between Two Circular Loops. 4.4.2 Self Inductance of the Rectangular Loop. 4.4.3 Self Inductance of the Circular Loop. 4.5 Internal Inductance vs. External Inductance. 4.6 Use of Filamentary Currents and Current Redistribution Due to the Proximity Effect. 4.6.1 Two-Wire Transmission Line. 4.6.2 One Wire Above a Ground Plane. 4.7 Energy Storage Method for Computing Loop Inductance. 4.7.1 Internal Inductance of a Wire. 4.7.2 Two-Wire Transmission Line. 4.7.3 Coaxial Cable. 4.8 Loop Inductance Matrix for Coupled Current Loops. 4.8.1 Dot Convention. 4.8.2 Multiconductor Transmission Lines. 4.9 Loop Inductances of Printed Circuit Board Lands. 4.10 Summary of Methods for Computing Loop Inductance. 4.10.1 Mutual Inductance Between Two Rectangular Loops. 5 The Concept of "Partial" Inductance. 5.1 General Meaning of Partial Inductance. 5.2 Physical Meaning of Partial Inductance. 5.3 Self Partial Inductance of Wires. 5.4 Mutual Partial Inductance Between Parallel Wires. 5.5 Mutual Partial Inductance Between Parallel Wires that are Offset. 5.6 Mutual Partial Inductance Between Wires at an Angle to Each Other. 5.7 Numerical Values of Partial Inductances and Significance of Internal Inductance. 5.8 Constructing Lumped Equivalent Circuits with Partial Inductances. 6 Partial Inductances of Conductors of Rectangular Cross Section. 6.1 Formulation for the Computation of the Partial Inductances of PCB Lands. 6.2 Self Partial Inductance of PCB Lands. 6.3 Mutual Partial Inductance Between PCB Lands. 6.4 Concept of Geometric Mean Distance. 6.4.1 Geometrical Mean Distance Between a Shape and Itself and the Self Partial Inductance of a Shape. 6.4.2 Geometrical Mean Distance and Mutual Partial Inductance Between Two Shapes. 6.5 Computing the High-Frequency Partial Inductances of Lands and Numerical Methods. 7 "Loop" Inductance vs. "Partial" Inductance. 7.1 Loop Inductance vs. Partial Inductance: Intentional Inductors vs. Nonintentional Inductors. 7.2 To Compute "Loop" Inductance, the "Return Path" for the Current Must be Determined. 7.3 Generally, There is no Unique Return Path for all Frequencies, Thereby Complicating the Calculation of a "Loop" Inductance. 7.4 Computing the "Ground Bounce" and "Power Rail Collapse" of a Digital Power Distribution System Using "Loop" Inductances. 7.5 Where Should the "Loop" Inductance of the Closed Current Path be Placed When Developing a Lumped-Circuit Model of a Signal or Power Delivery Path?. 7.6 How Can a Lumped-Circuit Model of a Complicated System of a Large Number of Tightly Coupled Current Loops be Constructed Using "Loop" Inductance?. 7.7 Modeling Vias on PCBs. 7.8 Modeling Pins in Connectors. 7.9 Net Self Inductance of Wires in Parallel and in Series. 7.10 Computation of Loop Inductances for Various Loop Shapes. 7.11 Final Example: Use of Loop and Partial Inductance to Solve a Problem. Appendix A: Fundamental Concepts of Vectors. A.1 Vectors and Coordinate Systems. A.2 Line Integral. A.3 Surface Integral. A.4 Divergence. A.4.1 Divergence Theorem. A.5 Curl. A.5.1 Stokes's Theorem. A.6 Gradient of a Scalar Field. A.7 Important Vector Identities. A.8 Cylindrical Coordinate System. A.9 Spherical Coordinate System. Table of Identities, Derivatives, and Integrals Used in this Book. References and Further Readings. Index .

Abstract: As an emerging technology in the area of energy storage, the double-layer capacitor is a promising device for certain niche applications. The double-layer capacitor is a low voltage device exhibiting an extremely high capacitance value in comparison with other capacitor technologies of a similar physical size. Capacitors with values in excess of 1500 F are now available. In slow discharge applications on the order of a few seconds, the classical equivalent circuit for a double-layer capacitor, composed of a capacitance (C), an equivalent parallel resistance (EPR), and an equivalent series resistance (ESR), can adequately describe capacitor performance. The focus of this work is the determination of these parameters for four different capacitors from discharge data using standard laboratory equipment such as an oscilloscope. Capacitance values are calculated using a change in stored energy approach which allows determination of an initial capacitance, a discharge capacitance, and variations in capacitance with voltage. The sensitivity of ESR and capacitance to charge rate and initial charge voltage is also reported.

Abstract: A new method of defining reactive power under non- sinusoidal conditions is proposed. It consists of sub- dividing the current into components which would have the same waveform as the current in a resistance and either an inductance or a capacitance when the voltage is applied to them, and into a residual component. An instrument for subdividing and measuring each current component and its corresponding power is described. The method permits the power system operator to determine if the possibility of improving the power factor by means of a shunt capacitance or inductance exists and to easily identify the proper value required to realize the maximum benefit.

Abstract: The Z-source inverter utilizing a unique LC network and forbidden shoot-through states provides unique features, such as the ability to buck and boost voltage with a single stage simple structure. The analysis and control methods provided in the literature are based on an assumption that the inductor is relatively large and the inductor current is continuous and has small ripple. This assumption becomes invalid when the inductance is small in order to minimize the inductor's size and weight for some applications where volume and weight are crucial. Under this small inductance condition, the inductor current becomes high ripple or even discontinuous. As results, the Z-source inverter exhibits new operation modes that have not been discussed before. This paper analyzes these new operation modes and voltage boost relationship of the Z-source inverter under the low inductance and large current ripple condition.

Abstract: Closed-form expressions of the resistance, capacitance, and inductance for interplane 3-D vias are presented in this paper. The closed-form expressions account for the 3-D via length, diameter, dielectric thickness, and spacing to ground. A 3-D numerical simulation is used to extract electromagnetic solutions of the resistance, capacitance, and inductance for comparison with the closed-form expressions, revealing good agreement between simulation and the physical models. The maximum error for the resistance, capacitance, and inductance is less than 8%.