LR Circuits Research Articles

The iPad as a virtual oscilloscope for measuring time constants in RC and LR circuits

In a university introductory physics laboratory, the measurement of time constants in RC and LR circuits usually employ a conventional oscilloscope. The standard oscilloscope with its many knobs and switches often intimidate first-time users and can cause anxiety especially among non-physics and non-engineering majors. On the other hand, an iPad has a more familiar, less intimidating and friendlier touch-pad interface. We report our experience in using the iPad as a virtual oscilloscope in an introductory algebra-based physics laboratory course. We used a commercial electronic accessory called Oscium iMSO that turns the iPad into a virtual oscilloscope. Using blind surveys and direct observation, we report student responses to this pedagogical tool.

Los problemas resueltos en libros de texto del ciclo básico universitario relativos a circuitos RL en corriente continua

In this paper, we describe and characterize the solved problems concerning LR circuits in direct current that are present in twelve college textbooks commonly used in Argentine Republic. These books were examined through content analysis. The results indicate that in the analyzed sample, in general terms, the explicitness is deficient for the physic systems studied, the proposed hypotheses, their limits of validity and for the verbalized explanations. On the other hand, the displayed resolution of the problems has little coherence with the research work conducted, and this would not promote the scientific work in students. Based on these outcomes and implications for teaching, we noticed that reinforcing the conceptual issues in the classroom that are not enough emphasized in the textbooks is an avoidable task for Physics professors of the basic college cycle.

Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements

Bending vibration of flexible structures can be suppressed passively using piezoelectric electromechanical transducers and optimally tuned LR circuits. Since these systems include both mechanical and electrical elements, the governing equations consist of electrically coupled equations of motion. This paper describes a new method for deriving the governing equations that describe a system’s vibration suppression based on the equilibrium of force principle and using an equivalent mechanical model of a piezoelectric element. Both series and parallel LR circuits are considered in the modeling approach. The optimum values for a mechanical vibration absorber can be formulated by using the two fixed points method. However, exact optimal values for the resistances of the LR circuits have not been formulated in the research literature thus far, and approximate values have been used. Analytical formulations are derived in this paper, and optimum values of the LR circuits are presented, not only in displacement, but also in terms of velocity and acceleration. The effects of the stiffness of the adhesive bond between the host structure and piezoelectric element, the dielectric loss in a piezoelectric element, and the internal resistance of an inductor are considered in the theoretical analysis. The effectiveness of the described analytical method is validated through simulations and experiments.

Influence of the Hall effect on the plasma dynamics in an MTF/MAGO chamber

The role of the Hall effect in experiments on the magnetic implosion of a D-T plasma in a cylindrical MTF/MAGO chamber fed from a helical explosive magnetic generator is investigated. The plasma dynamics is simulated numerically by a 2D code developed for solving the set of MHD equations with account of the Hall effect. In simulations, the generator, the break switch, and other units were replaced with LR circuits. It is shown that taking into account the Hall effect provides better agreement between numerical simulations and experimental data.

PSpice for Circuit Theory and Electronic Devices

PSpice for Circuit Theory and Electronic Devices is one of a series of five PSpice books and introduces the latest Cadence Orcad PSpice version 10.5 by simulating a range of DC and AC exercises. It is aimed primarily at those wishing to get up to speed with this version but will be of use to high school students, undergraduate students, and of course, lecturers. Circuit theorems are applied to a range of circuits and the calculations by hand after analysis are then compared to the simulated results. The Laplace transform and the s-plane are used to analyze CR and LR circuits where transient signals are involved. Here, the Probe output graphs demonstrate what a great learning tool PSpice is by providing the reader with a visual verification of any theoretical calculations. Series and parallel-tuned resonant circuits are investigated where the difficult concepts of dynamic impedance and selectivity are best understood by sweeping different circuit parameters through a range of values. Obtaining semiconductor device characteristics as a laboratory exercise has fallen out of favour of late, but nevertheless, is still a useful exercise for understanding or modelling semiconductor devices. Inverting and non-inverting operational amplifiers characteristics such as gain-bandwidth are investigated and we will see the dependency of bandwidth on the gain using the performance analysis facility. Power amplifiers are examined where PSpice/Probe demonstrates very nicely the problems of cross-over distortion and other problems associated with power transistors. We examine power supplies and the problems of regulation, ground bounce, and power factor correction. Lastly, we look at MOSFET device characteristics and show how these devices are used to form basic CMOS logic gates such as NAND and NOR gates.

Magnetic actuators and sensors

Preface. PART I MAGNETICS. 1. Introduction. 1.1 Overview of Magnetic Actuators. 1.2 Overview of Magnetic Sensors. 1.3 Actuators and Sensors in Motion Control Systems. References. 2. Basic Electromagnetics. 2.1 Vectors. 2.1.1 Gradient. 2.1.2 Divergence. 2.1.3 Curl. 2.2 Ampere's Law. 2.3 Magnetic Materials. 2.4 Faraday's Law. 2.5 Potentials. 2.6 Maxwell's Equations. Problems. References. 3. Reluctance Method. 3.1 Simplifying Ampere's Law. 3.2 Applications. 3.3 Fringing Flux. 3.4 Complex Reluctance. 3.5 Limitations. Problems. References. 4. Finite-Element Method. 4.1 Energy Conservation and Functional Minimization. 4.2 Triangular Elements for Magnetostatics. 4.3 Matrix Equation. 4.4 Finite-Element Models. Problems. References. 5. Magnetic Force. 5.1 Magnetic Flux Line Plots. 5.2 Magnetic Energy. 5.3 Magnetic Force on Steel. 5.4 Magnetic Pressure on Steel. 5.5 Lorentz Force. 5.6 Permanent Magnets. 5.7 Magnetic Torque. Problems. References. 6. Other Magnetic Performance Parameters. 6.1 Magnetic Flux and Flux Linkage. 6.1.1 Definition and Evaluation. 6.1.2 Relation to Force and Other Parameters. 6.2 Inductance. 6.2.1 Definition and Evaluation. 6.2.2 Relation to Force and Other Parameters. 6.3 Capacitance. 6.3.1 Definition. 6.3.2 Relation to Energy and Force. 6.4 Impedance. Problems. References. PART II ACTUATORS. 7. Magnetic Actuators Operated by Direct Current. 7.1 Solenoid Actuators. 7.1.1 Clapper Armature. 7.1.2 Plunger Armature. 7.2 Voice Coil Actuators. 7.3 Other Actuators Using Coils and Permanent Magnets. 7.4 Proportional Actuators. 7.5 Rotary Actuators. Problems. References. 8. Magnetic Actuators Operated by Alternating Current. 8.1 Skin Depth. 8.2 Power Losses in Steel. 8.2.1 Laminated Steel. 8.2.2 Equivalent Circuit. 8.2.3 Solid Steel. 8.3 Force Pulsations. 8.3.1 Force with Single AC Coil. 8.3.2 Force with Added Shading Coil. 8.4 Cuts In Steel. 8.4.1 Special Finite-Element Formulation. 8.4.2 Loss and Reluctance Computations. Problems. References. 9. Magnetic Actuator Transient Operation. 9.1 Basic Timeline. 9.2 Size, Force, and Acceleration. 9.3 Linear Magnetic Diffusion Times. 9.3.1 Steel Slab Turnon and Turnoff. 9.3.2 Steel Cylinder. 9.4 Nonlinear Magnetic Diffusion Time. 9.4.1 Simple Equation for Steel Slab with B-H. 9.4.2 Transient Finite-Element Computations for Steel Slabs. 9.4.3 Simple Equation for Steel Cylinder with B-H. 9.4.4 Transient Finite-Element Computations for Steel Cylinders. Problems. References. PART III SENSORS. 10. Hall Effect and Magnetoresistive Sensors. 10.1 Simple Hall Voltage Equation. 10.2 Hall Effect Conductivity Tensor. 10.3 Finite-Element Computation of Hall Fields. 10.3.1 Unsymmetric Matrix Equation. 10.3.2 2D Results. 10.3.3 3D Results. 10.4 Toothed Wheel Hall Sensors for Position. 10.5 Magnetoresistance. 10.5.1 Classical Magnetoresistance. 10.5.2 Giant Magnetoresistance. 10.5.3 Newest Forms of Magnetoresistance. 10.6 Magnetoresistive Heads for Hard-Disk Drives. Problems. References. 11. Other Magnetic Sensors. 11.1 Speed Sensors Based on Faraday's Law. 11.2 Inductive Recording Heads. 11.3 Proximity Sensors Using Impedance. 11.3.1 Stationary Eddy Current Sensors. 11.3.2 Moving Eddy Current Sensors. 11.4 Linear Variable Differential Transformers. 11.5 Magnetostrictive Sensors. 11.6 Flux Gate Sensors. 11.7 Magnetometers and Motes. Problems. References. PART IV SYSTEMS. 12. Coil Design and Temperature Calculations. 12.1 Wire Size Determination for DC Currents. 12.2 Coil Time Constant and Impedance. 12.3 Skin Effects and Proximity Effects for AC Currents. 12.4 Finite-Element Computations of Temperatures. 12.4.1 Thermal Conduction. 12.4.2 Thermal Convection and Thermal Radiation. 12.4.3 AC Magnetic Device Cooled by Conduction, Convection, and Radiation. Problems. References. 13. Electromagnetic Compatibility. 13.1 Signal-to-Noise Ratio. 13.2 Shields and Apertures. 13.3 Test Chambers. 13.3.1 TEM Transmission Lines. 13.3.2 TEM Cells. 13.3.3 Triplate Cells. Problems. References. 14. Electromechanical Finite Elements. 14.1 Electromagnetic Finite-Element Matrix Equation. 14.2 0D and 1D Finite Elements for Coupling Electric Circuits. 14.3 Structural Finite-Element Matrix Equation. 14.4 Force and Motion Computation by Timestepping. 14.5 Typical Electromechanical Applications. 14.5.1 DC Solenoid with Slowly Rising Input Current. 14.5.2 DC Solenoid with Step Input Voltage. 14.5.3 AC Clapper Solenoid Motion and Stress. 14.5.4 Transformers with Switches or Sensors. Problems. References. 15. Electromechanical Analysis Using Systems Models. 15.1 Electric Circuit Models of Magnetic Devices. 15.1.1 Electric Circuit Software Including SPICE. 15.1.2 Simple LR Circuits. 15.1.3 Tables of Nonlinear Flux Linkage and Force. 15.1.4 Analogies for Rigid Armature Motion. 15.1.5 Maxwell SPICE Model of Bessho Actuator. 15.1.6 Simplorer Model of Bessho Actuator. 15.2 VHDL-AMS/Simplorer Models. 15.2.1 VHDL-AMS Standard IEEE Language. 15.2.2 Model of Solenoid Actuator. 15.3 MATLAB/Simulink Models. 15.3.1 Software. 15.3.2 MATLAB Model of Voice Coil Actuator. 15.4 Including Eddy Current Diffusion Using a Resistor. 15.4.1 Resistor for Planar Devices. 15.4.2 Resistor for Axisymmetric Devices. Problems. References. 16. Coupled Electrohydraulic Analysis Using Systems Models. 16.1 Comparing Hydraulics and Magnetics. 16.2 Hydraulic Basics and Electrical Analogies. 16.3 Modeling Hydraulic Circuits in SPICE. 16.4 Electrohydraulic Models in SPICE and Simplorer. 16.5 Hydraulic Valves and Cylinders in Systems Models. 16.5.1 Valves and Cylinders. 16.5.2 Use in SPICE Systems Models. 16.6 Magnetic Diffusion Resistor in Electrohydraulic Models. Problems. References. Appendix: Symbols, Dimensions, and Units. Index.

Double-Exponential LR Circuit

Simple LR and RC circuits are familiar to generations of physics students as examples of single-exponential growth and decay in the relevant voltages, currents, and charges. An element of novelty can be introduced by connecting two (instead of one) LR coils in parallel with a battery. The resulting circuit can still be treated using little more than the basic tools (Kirchhoff's rules plus a trial exponential solution) employed in the standard LR analysis. But the solution is now a double exponential, as can be verified by constructing such a circuit.

Limitations on Performance of Superconductor Oversampling ADCs

We discuss several general questions related to the development and optimization of superconductor oversampling modulators. We highlight the importance of specially engineered and parasitic components of the feedback loop. In particular, LR circuits operating as low-pass filters are capable of providing a noticeable SNR improvement and dramatically reducing the dynamic range requirements for used SFQ comparators. On the other hand, the feedback loop delay and time-jitter in timing circuits are able to spoil the potentially extremely high performance of superconductor oversampling ADCs. We also developed a simple formula describing time-jitter in superconductor circuits.

Design and modeling of coupled pulse magnets (electrical and thermal)

Design and optimization of pulsed magnets requires development of computer codes that can analyze a multi-coil magnet system magnetically, thermally and mechanically. We present a FORTRAN computer code that can be used to design a multi-circuit pulsed magnet using one or more conductors and reinforcement materials. Xheat is circuit solver that can analyze nonlinear magnetically coupled LR and LRC circuits yielding currents, voltages and temperature distributions in the magnet winding as a function of time. The power source can be one or more of the following: (i) a capacitor bank, (ii) a current source, or (iii) a voltage source. A finite difference technique is used to calculate the properties after a small time step as a function of the temperature at that time. Eddy currents and magnetoresistance are included in resistance calculations. Xheat writes an input file to an elastic and plastic stress calculation codes that can generate stresses, strains and displacement in all magnet layers at the midplane.

Eddy current modelling in a coupled electromagnetic‐mechanical problem

Solves a coupled electromagnetic‐mechanical problem ‐ that of a cantilevered conductive plate in crossed steady and time‐varying magnetic fields ‐ by using a semi‐analytical method and an eddy current model. Assumes that the magnetic flux variation induces two electromotive forces to the plate; one due to the time‐varying magnetic field and the other to the plate movement in the steady magnetic field. Considers two equivalent LR circuits and notes that the superposition of their currents yields the total circulating current in the plate. Couples this electromagnetic model to the one‐dimensional beam bending model, adopted for the structural analysis of the problem and derives the system of the coupled electromagnetic‐mechanical equations. Calculates analytically some of the parameters involved in these equations so that the numerical computation of the remaining unknowns is very rapid. Concludes that the results are in agreement with the experiment and with results obtained by numerical methods treating, in three dimensions, the electromagnetic aspects of the problem. Notes that the fully numerical methods are very much CPU time consuming.

The graphical methods of Sumpner, Drysdale and Marchant: solving the Kelvin equation

The paper commences with the equation derived in 1853 by Kelvin, for circuits containing inductance, resistance and capacitance. From this, the history of a graphical analysis is traced from Sumpner in 1888, to Drysdale who in 1910 published details of his planimeter, a manual device to solve LR and CR circuits. Little was added to the method, until Marchant extended it, in 1960, to cover all three circuit parameters, L, R and C, by one graphical solution. The methods are useful in explaining circuit operation and examples of use are given.