Inductors

6 Key excerpts on "Inductors"

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  eBook - PDF

  Handbook of Power Management Circuits

  • Haruo Kobayashi, Takashi Nabeshima, Haruo Kobayashi, Takashi Nabeshima(Authors)
  • 2016(Publication Date)
  • Jenny Stanford Publishing

    (Publisher)

  6.1 Inductors and Transformers 6.1.1 Inductors 6.1.1.1 Definition of an inductor An inductor is a circuit element that is widely used in electronic circuits. Current flow through a conductive wire produces magnetic flux around the wire, following the Maxwell corkscrew (right-handed screw) rule. The main characteristic of an inductor is the magnetic flux that it produces when a current is passed through it. Although wire conductors also possess inductance components, the value is negligibly small. Chapter 6 Passive Components Yuya Tamai a and Yoshiyuki Ishihara b a Solution R & D Department, R & D Headquarters, Nippon Chemi-Con Corporation, 6-4, Osaki 5-Chome, Shinagawa-ku, Tokyo 141-8605, Japan b Electrical Engineering Department, Faculty of Science and Engineering, Doshisha University, Kyotanabe 610-0321, Japan [email protected], [email protected] Handbook of Power Management Circuits Edited by Haruo Kobayashi and Takashi Nabeshima Copyright © 2016 Pan Stanford Publishing Pte. Ltd. ISBN 978-981-4613-15-6 (Hardcover), 978-981-4613-16-3 (eBook) www.panstanford.com 136 Passive Components Inductance L (H) is the proportionality constant between the current flow I (A) through the wire and the linkage flux Φ , and the relation is expressed as follows: Φ = LI (Wb) (6.1) Here L is the value of inductance. When an inductor is used as a circuit component, it is usually constructed by winding a wire into a coil. This case, inductance is expressed as follows: L = n / R m (H) (6.2) Here, n is the number of turns and R m is the magnetic reluctance (A/Wb). Magnetic reluctance, R m , is given by R m = l /( μS ) (A/Wb) (6.3) Here, l is the average magnetic path length (m), μ is the permeability (H/m), and S is the cross-sectional area of the magnetic path (m 2 ).

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  eBook - ePub

  Transformers and Inductors for Power Electronics

  Theory, Design and Applications

  • W.G. Hurley, W.H. Wölfle(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  Section One Inductors Passage contains an image 2

  Inductance1

  Inductors and transformers are present in almost every power electronics circuit. Broadly speaking, Inductors are dynamic energy storage devices and, as such, they are employed to provide stored energy between different operating modes in a circuit. They also act as filters for switched current waveforms. In snubber circuits, they are used to limit the rate of change of current and to provide transient current limiting. Transformers, on the other hand, are energy transfer devices, for example converting power at a high voltage and a low current to power at a lower voltage and a higher current. In a mechanical analogy, an inductor is like a flywheel which stores energy, while a transformer is like a gearbox which trades speed for torque. Besides transforming voltage levels, transformers are also used to provide electrical isolation between two parts of a circuit; to provide impedance matching between circuits for maximum power transfer; and to sense voltage and currents (potential and current transformers).

  2.1 Magnetic Circuits

  We have seen in Chapter 1 that Ampere's law describes the relationship between the electric current and magnetic field in a magnetic circuit. Figure 2.1 shows a coil with N turns wound on a closed magnetic core of mean length l c and cross-sectional area A c , from Equation 2.1 .

  (2.1)

  Recall that the direction of H around the loop is related to i by the right hand screw rule.

  Figure 2.1 Magnetic circuit.

  At this point we need not concern ourselves with the shape of the core or the shape of the cross-section. For simplicity, we assume that the cross-section is constant over the length of the core. We also assume that the flux density is uniform over the cross-sectional area and that the value of the magnetic field intensity H c is constant around the loop C . This assumption is reasonable as long as there is no flux ‘leaking’ from the core; we can take leakage effects into account later. Thus, applying Equation 2.1 yields the expression for H c in terms of the product Ni

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  eBook - ePub

  Basic AC Circuits

  • Clay Rawlins(Author)
  • 2000(Publication Date)
  • Newnes

    (Publisher)

  9. Given a circuit of series-connected Inductors, the applied voltage, and frequency of the applied voltage, determine the inductive reactance of each inductor, the total inductance, the total current, the voltage across each inductor, the reactive power of each inductor, and the total reactive power in the circuit.

  10. Given a circuit of parallel-connected Inductors, the applied voltage, and frequency of the applied voltage, determine the inductive reactance of each inductor, the total inductive reactance, the total inductance, each inductive branch current, the total current, the reactive power of each inductor, and the total reactive power in the circuit.

  INTRODUCTION

  In the last two chapters, discussion concerned the capacitor and how to analyze circuits composed of only capacitors or capacitors and resistors. This chapter is about the remaining passive circuit element — the inductor.

  Figure 8.1 some types of Inductors. Basically, any inductor is a coil of thin wire wrapped on a cylinder called the core. The core may be hollow, of laminated paper — an air core — or made of some type of iron — an iron core. Often an inductor is also called a choke or coil. The turns of wire of the inductor are electrically insulated from each other by a thin, non–conductive coating.

  Figure 8.1 Typical Inductors

  As shown in Figure 8.2 the schematic symbol used to represent the inductor resembles what it is — wire wrapped on a core. The inductor’s letter symbol is a capital L which represents linkages — flux linkages.

  Figure 8.2 Schematic Symbol for an Inductor

  An inductor has magnetic properties. Therefore, a brief review of the subject of magnetism should help you understand better the electrical properties of an inductor.

  ELECTROMAGNETIC PROPERTIES

  Faraday’s Discovery

  Recall that in 1831, Michael Faraday showed that when a conductor connected in a closed circuit is moved through a magnetic field, an electron current flows as a result of a voltage induced in the conductor. (In this chapter, like in all other chapters in this book, current flow refers to electron current flow.)

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  Electronics and Electronic Systems

  • George H. Olsen(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  The magnetic circuit is completed by a central cylindrical core. For a given inductor some variation of inductance is possible by adjusting the position of the central core or by varying the pressure at which the two ferrite cylinders are held together. Figure 2.9 Physical appearance of two forms of inductor: (a) Construction of an inductor for power frequencies. The shape of the laminations is shown on the left. Either combination may be used; (b) Essential parts of a 'pot-core' inductor Energy storage in Inductors The process of establishing a current and associated magnetic field in an inductor involves the expenditure of energy. The total energy stored, / L , is measured by summing all the increments of work performed during the process of establishing the field, i.e. ni l j L = J V idt = J L ^-idt = | Liai (v is the instantaneous applied voltage, i.e. Ldi/dt.) Passive components 21 As the magnetic field collapses the energy is returned to the source. In a perfect inductor no energy is lost; like the capacitor, an inductor does not dissipate energy. Mutual inductance If two coils are placed close to each other so that a varying magnetic field in one coil induces an e.m.f. in the second coil, the two coils are said to be inductively coupled. The changing magnetic flux due to the current in the first or primary circuit must interlink the secondary circuit in order to induce an e.m.f. in the secondary coil. The phenomenon is called mutual induction. The mutual inductance, M, between the two coils is measured in henries and depends upon (a) the number of turns in the primary coil, (b) the number of turns in the secondary coil, (c) the relative position of the coils, and (d) the permeability of the medium between the coils. ., _ Induced voltage (e) in the secondary coil Rate of change of current in the primary When Inductors are connected in series the total inductance is calculated in the same manner as that used for resistors in series.

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  eBook - ePub

  Passive Components for Circuit Design

  • Ian Sinclair(Author)
  • 2000(Publication Date)
  • Newnes

    (Publisher)

  Chapter 5

  Inductors and inductive components

  Induction and inductance

  Electromagnetic induction was discovered by Michael Faraday in 1831. The principle is that an EMF (a voltage) is generated in a conductor when the magnetic field across the conductor changes. In the early experiments, the change of magnetic field was accomplished by moving either the wire or a magnet, and this is the principle of the alternator and dynamo. An EMF can also be induced without mechanical movement, when the strength or direction of a magnetic field across a wire is altered, and even the presence of a wire is not necessary, because the alteration in a magnetic field can produce an electric field in the absence of any conductor. Inductive components in electronics make use of the EMF that is generated when a field changes either in the same piece of wire (self-induction ) or in another piece of wire (mutual induction ).

  The amount of EMF that is generated in a wire can be greatly increased if the wire is wound into a coil, and as much as possible of the magnetic field is guided through the coil. Figure 5.1 shows the flux path in a solenoidal winding for a steady current. Concentration and guidance of the magnetic field is achieved by using a magnetic core, for which the traditional material was annealed ‘soft’ iron. One way of looking at a soft iron core is as a conductor for magnetism, using the idea of magnetic flux. It is possible to think of magnetic circuits in which magnetic flux (φ) is the counterpart of current, in a path which has reluctance (analogous to resistance), and in which the amount of flux is produced by a magnetomotive force (MMF). The equation that is the magnetic equivalent of V = R × I

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  MSP430-based Robot Applications

  A Guide to Developing Embedded Systems

  • Dan Harres(Author)
  • 2013(Publication Date)
  • Newnes

    (Publisher)

  Figure 3.23 is actually just an inductor. In most instances the wire will be wound around some type of ferromagnetic material, such as iron but there are also Inductors made that have no material in the center. These Inductors are referred to as “air-core Inductors”.

  Storing energy in capacitors and Inductors

  The electric field built up in a capacitor and the magnetic field built up with an inductor can be very useful. Consider the capacitor of Figure 3.21 . If we remove the battery connection to that capacitor, it continues to stay charged and maintains the voltage across its plates until such a time as the capacitor is connected to a circuit that draws current from the capacitor, at which point its voltage will begin to drop in accordance with Eq. 3.14 . Large-value capacitors are sometimes used in this way as a replacement for batteries.

  We will also see in a later section of this chapter that the capacitor’s ability to store charge and its corresponding ability to resist rapid changes in voltage makes it very useful in holding up voltages in circuits that may experience fluctuations in supply voltage.

  Making analog filters out of resistors, capacitors and Inductors

  An analog filter is a circuit that operates on AC signals. Remember from the beginning of this chapter that an AC signal is one which is changing. As we’ve seen earlier, capacitors impede changes in voltage and Inductors impede changes in current. Equations 3.14 and 3.25 give us a clue that the amount of this impedance is time-dependent which, in turn, tells us something about the device’s response to changing signal frequency.

  Resistor/capacitor filters

  Frequency is the number of cycles of change per second. It is given the unit hertz (abbreviated Hz), where 1 Hz=1 cycle per second. The higher the frequency of a signal, the faster it changes with time. Reviewing Eq. 3.14

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