2SWLPDOVROXWLRQIRUFLUFXLWGHVLJQ ٙ7HFKQLFDOLQIRUPDWLRQٙ %DVLF.QRZOHGJHRI,QGXFWRUV KWWSVLQGXVWULDOSDQDVRQLFFRPZZVVWHFKQLFDO INDEX Basic Knowledge of Inductors ・ What Are Inductors? ・・・・・・・・・・ 1 ・ Basic Structure of Inductors and Inductance ・・・・・・・・・・ 1 ・ Inductor-related Graphical Symbols for Electricity ・・・・・・・・・・ 2 ・ Voltage and Current of Inductors ・・・・・・・・・・ 2 ・ Comparing Inductors and Capacitors ・・・・・・・・・・ 5 ・ Basic Functions of Inductors ・・・・・・・・・・・ 5 ・ Characteristics of Inductors ・・・・・・・・・・・ 6 ・ Main Specifications of Inductors ・・・・・・・・・・・ 9 ・ Types of Inductors ・・・・・・・・・・・ 10 Basic Knowledge of Inductors What Are Inductors? Inductors, also referred to as coils, are important passive components along with resistors (R) and capacitors (C). Coils usually refer to wound conductive wires, and among them, those with a single wound wire have in recent years particularly been referred to as inductors. Inductance is usually represented by the symbol "L." Although this L is said to come from Lenz of "Lenz's Law" related to electromagnetic induction, there also appear to be various theories. The basic structure of an inductor consists of a conductive wire wound in a coil shape and is able to convert electric energy to magnetic energy and store it inside the inductor. The storable amount of magnetic energy is determined by the inductance of the inductor and measured in Henry (H). Basic Structure of Inductors and Inductance The most basic inductors consist of a conductive wire wound in a coil shape, with both ends of the conductive wire as external terminals. In recent years, most inductors include a core, around which a conductive wire is wound The inductance of an inductor is determined by the following equation L= kμSN2 l L : Inductance（H） k : Nagaoka coefficient μ : Core permeability（H/m） N : Number of coil turns S : Coil sectional area （m2） l : Coil length（m） 1 Based on this equation, the inductance can be increased by 1) increasing the sectional area S, 2) increasing the number of turns N, or 3) increasing the permeability µ by inserting a core Inductor-related Graphical Symbols for Electricity Type Symbols Inductor (air core) Inductor (iron core) Transformers Voltage and Current of Inductors As explained in connection with their structure, inductors are essentially wound wires and therefore, current basically flows through them when a voltage is applied. However, because inductors are components designed to use the action of electromagnetic induction, current does not simply flow. The action of inductors when DC or AC is applied will be described here. ● When DC is applied As shown by the circuit diagram, when the switch is turned on to apply DC to the inductor, current flows through the inductor, changing a magnetic flux that is generated by changes in the current flowing through the inductor (wound wire), thereby generating an electromotive force (induction electromotive force) on the inductor. Since the inductor is basically a single 2 wound wire, this is referred to as "self-induction." This electromotive force is generated in a direction opposite to that of the current and restricts any increase in current. Conversely, the electromotive force restricts any decrease in current when the switch is turned off. Although the current (IL)starts flowing when the switch is turned on, its increase is restricted by the electromotive force. Therefore, the current rises with a given time constant, and after the rise, a constant current flows depending on the resistance component. When the switch is turned off, the current falls; however, it becomes zero with a given time constant. The voltage (VL) indicates the electromotive force of the inductor when the switch is turned on and off. As shown by the equation, the electromotive force generated on the inductor is proportional to the change rate of the current (ΔI /Δt). V=L V : Electromotive force (V) ΔI L : Inductance (H) Δt ΔI/Δt : Change rate of the current (A/s) As shown by the current waveform diagram, because the current increases relatively slowly when the switch is turned on, the electromotive force rises only up to the power supply voltage. When the switch is turned off, because the current is cut off instantaneously, the decrease in current is sudden compared to when the switch is turned on. As a result, the change rate as a function of time is higher, generating a higher electromotive force. It should be noted that the reason the current does not become zero instantaneously when the switch is turned off is the discharge current flowing between the switch terminals due to the high voltage generated at the inductor. Inductors can generate such a high electromotive force because, as described in the section "What Are Inductors?" at the beginning, an inductor can "convert electric energy to magnetic energy and store it inside the inductor." The storable energy can be expressed by the equation below and is proportional to the magnitude of the inductance. W= 1 2 W : Energy (J) LI2 L : Inductance (H) I : Current (A) 3 ●When AC is applied It was described earlier that the magnitude of the electromotive force generated on an inductor is proportional to the change rate of the current flowing through the inductor. This is the same with AC waveforms. (1) First, the voltage becomes high when the current rises from zero because the change rate of the current is highest. However, the voltage decreases with a decrease in the rising speed of the current and becomes zero when the current reaches its maximum value (the change rate of the current is zero). (2) The generation of a negative voltage starts when the current starts falling from its maximum value; the voltage reaches its minimum value when the current becomes zero (maximum change rate of the current). Regions (3) and (4) can be understood in the same manner as above. Looking at these current and voltage waveforms, you will see that when the current waveform is sinusoidal, the voltage waveform is also sinusoidal, and the current waveform is behind the voltage waveform by 1/4 cycle (the phase of the current is behind by 90°). In addition, a larger voltage is generated when the current change is larger, which means that a larger voltage is generated at higher frequencies at which current changes are larger. However, because the voltage of actual inductors is the same as the voltage of AC power supplies, increasing the frequency at a constant voltage will decrease the flowing current when considering the voltage as the reference. In other words, in the case of AC, inductors work like resistors, passing the flowing current less easily at higher frequencies. This is referred to as the inductive reactance (XL) of coils. The inductive reactance and the flowing current can be expressed by the equation below. XL : Inductive reactance (Ω) V : AC voltage(V) f : Frequency (Hz) I : AC current(A) L : Inductance (H) 4 Comparing Inductors and Capacitors The table below summarizes the features of inductors in comparison with capacitors based on the explanation above. As shown by the table, inductors and capacitors are electronic components with precisely opposite characteristics Items Inductors Capacitors A larger voltage is A larger current flows when Voltage-current relationship generated when the change rate of the current is higher voltage is higher. Pass Do not pass Pass less easily at higher Pass more easily at higher frequencies frequencies Behind by 90° Ahead by 90° DC current AC current Phase of current with respect to voltage the change rate of the Basic Functions of Inductors Inductors basically have the following functions. (1) Generate a magnetic field when current flows through them. Conversely, current flows when their magnetic field changes. (2) Convert electric energy to magnetic energy and store it. (3) Pass DC but do not pass AC easily, and pass AC less easily at higher frequencies (1) and (2) are characteristics caused by the magnetic action of current and its reverse, i.e., electromagnetic induction. (3) refers to the DC and AC characteristics of inductors caused by impedance. The specific examples below show how these characteristics are used. (1) Generate a magnetic field when current flows through them. Conversely, current flows when their magnetic field changes. ⇒ Principle of transformers The structural example has two wound wires on the primary and secondary sides and therefore can be regarded the same as a transformer. Passing current to the primary-side wound wire will generate a magnetic field that will generate current 5 on the secondary-side wound wire. This is due to electromagnetic induction, which is referred to as mutual induction in the case of transformers. Through this action, conversion to a desired voltage is possible based on the ratio of the number of turns between the primary- and secondary-side wound wires. (2) Convert electric energy to magnetic energy and store it. ⇒ Principle of choke coils This is an example of an inductor in a DC/DC converter. Passing current through the inductor by turning the switch on will generate a magnetic field, causing the inductor to store energy in the form of magnetic energy. Stopping the flow of current through the inductor by turning the switch off will discharge the stored magnetic energy (the magnetic field changes), causing current to flow. This is also due to electromagnetic induction, which is referred to as selfinduction in the case of inductors that consist of a single wound wire. (3) Pass DC but do not pass AC easily, and pass AC less easily at higher frequencies. ⇒ Filter function Inductors can be combined with capacitors to create low-pass, high-pass filters, etc. This makes use of their characteristic whereby the ease of passing AC is altered due to changes in impedance in accordance with frequencies. Impedance characteristics will be described later. Characteristics of Inductors Ideal and Actual Inductors (Impedance Characteristics) Ideal inductors have no components other than inductance and suffer no energy losses. However, actual inductors possess resistance components (DC resistance: DCR) and capacitance (stray capacitance: Cp) in addition to inductance (see equivalent circuits). The resistance consists of the resistance components of a wound wire and a core. The capacitance mainly consists of the line capacity of a wound wire. 6 Equivalent circuits of an inductor Impedance characteristics of inductors Ideal inductor Actual inductor (Simplified equivalent circuits) The graph shows a conceptual image of impedance characteristics of ideal and actual inductors with respect to frequency. The impedance of ideal inductors increases linearly with higher frequencies. However, in actual inductors, a self-resonance phenomenon occurs due to stray capacitance, and the impedance decreases at even higher frequencies, causing the inductors to lose their original function. Losses also occur due to resistance components and decreases in impedance. Impedance (Z) of inductors is expressed by the following equation. Z=R+1/(1/jωL+jωC) Z : Impedance [Ω] R : DC resistance component (DCR) [Ω] C : Stray capacitance (Cp) [F] The absolute value of impedance is J : Imaginary number calculated by the following equation ω : 2πf (π︓Pi (3.14)、 f︓Frequency [Hz]) |Z|=√ R2+1/(1/ωL-ωC) 2 L : Inductance [H] Magnetic saturation characteristics Inductors become magnetically saturated when the flowing current exceeds the maximum value of the magnetic saturation allowable current (DC bias allowable current), resulting in a decrease in inductance. As shown by the impedance equation above, when inductors are saturated, impedance becomes small and the current flowing through them becomes abnormally large. As a result, for example, DC/DC converters may suffer lower 7 efficiency and malfunction. Magnetic saturation allowable current is an important characteristic of inductors. AC Resistance (ACR) Although only the DC resistance (DCR) was explained earlier in the impedance section, practical inductors also include resistance components that generate eddy current losses at the core and resistance components of conductive wires that increase due to skin and proximity effects. These components are referred to as AC resistances (ACR). AC resistances (ACR), whose value increases in proportion to frequencies, have a significant impact on power losses and increases in component temperature at high frequencies and therefore need to be taken into consideration in practical use. (Eddy current losses, skin effects, and proximity effects will be described later.) Other Characteristics Other characteristics of inductors and related terms are summarized below. Q factor (quality factor): Q factor, which refers to the ratio of the inductive reactance to the resistance of an inductor at a specific frequency, is an index of inductor performance. The higher its Q factor, the closer an inductor is to an ideal inductor. The value obtained by dividing inductive reactance XL (= ωL = 2ΠfL) by ACR indicates the magnitude of a loss with respect to the frequency. The equation shows that Q is high when ACR is small. Copper losses: Losses due to resistance components when current flows through a conductive wire is referred to as a copper loss. Iron losses: Losses that occur in a core when a magnetic flux passes through it (hysteresis and eddy current losses) are referred to as iron losses. Skin effect: Increasing the frequency of current flowing through a conductor causes the current to flow only through the surface of the conductor, resulting in a higher current density at the surface section and thereby an increase in the resistance value. This is referred to as a skin effect. Proximity effect: When multiple conductive wires are in proximity to each other, the magnetic field formed by each wound wire induces an eddy current. At high frequencies, the current flow in each conductive wire concentrates in a narrow region that contacts an adjacent conductive wire, resulting in a higher current density at the proximity section and thereby an increase in the resistance value. This is referred to as a proximity effect. 8 Eddy current losses: A magnetic field that changes due to electromagnetic induction generates an eddy current in the core of the conductor. The energy that generates this current is converted to heat as a loss due to the electric resistance of the core material. This is referred to as an eddy current loss. Hysteresis losses: Changing or reversing the magnetic field in a core will cause it to return to its original state with a hysteresis (hysteresis loop shown in BH diagrams of core materials). The energy consumed by this hysteresis action is lost as heat. This is referred to as a hysteresis loss, which is proportional to the area of the hysteresis loop. Main Specifications of Inductors The main specifications of inductors are shown below. Although various characteristics of inductors were explained in the previous section, not all the characteristics are designated as specifications. Here, typical characteristics specified in the datasheets of inductors are summarized. It should be noted that the availability of items and prescribed conditions differ by manufacturer and product, and it is therefore necessary to carefully check the notes, etc. of datasheets. Specification items Inductance (L value) [μH] DC resistance (DCR) [Ω] Meaning/condition, etc. Nominal inductance at a specific frequency Resistance component of a conductor (copper wire) that constitutes an inductor Rated current: Rated current value at which the temperature rise temperature rise (ΔT) [A] when AC current is applied reaches 40 K Rated current: DC bias (ΔL) [A] Rated current at which the L value decreases from the initial value to the specified rate when DC current is applied (DC bias) "Inductance," which is obviously an essential item, indicates a value at a specified frequency and has a tolerance, e.g., ±30%. "DC resistance," as explained earlier, consists mainly of the resistance of a wound wire and indicates a tolerance such as ±20%. AC resistance (ACR), which was also explained as a resistance component, is often not indicated in specifications and must be checked with a manufacturer as necessary. "Rated current" has two items. Although "temperature rise" often specifies the rated current 9 at which the temperature rises by 40 K when DC current is applied, its condition may differ by manufacturer and product. The other item "DC bias current" usually indicates the maximum current value at which the inductance becomes -30%, but the condition also differs by manufacturer and product. Although the rated current is an important specification, not both items are always indicated. When only one of them is indicated, that rating is to be followed. However, it may be necessary to check with the manufacturer in some cases. In addition to these items, the "self-resonant frequency" is sometimes specified. As described earlier, it indicates the limit frequency at which inductors are able to function properly as inductors. Types of Inductors There are a variety of types of inductors, and their classification methods vary depending on perspectives. The diagram below divides applications into signal and power and classifies each category by magnetic (core) material and construction method. 10 Related product information Power Inductors for Automotive application https://industrial.panasonic.com/ww/products/inductors/automotive-inductors/automotive-inductors Power Inductors for Consumer https://industrial.panasonic.com/ww/products/inductors/inductors-for-consumer/inductors-for-consumer Voltage Step-up Coils https://industrial.panasonic.com/ww/products/inductors/voltage-stepup-coils/voltage-stepup-coils 11 Optimal solution for circuit design ＝Technical information＝ Basic Knowledge of Inductors First edition : March 15, 2021 Issued by Industrial Solutions Company Panasonic Co., Ltd. Device Solutions Business Division All rights reserved. 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