Inductors
InductorsAn inductor (also called a choke) is simply a coil of wire. It turns out, however, that a coil ofwire can do some very interesting things because of the magnetic properties of a coil. There aremany variations to the Inductor / Coil, below shows some of the variations. Inductors usually arecategorized according to the type of inner core they are wound around, for example, hollow core(free air), solid iron core or soft ferrite core. The different core types are distinguished by addingcontinuous or dotted parallel lines next to the wire coil as shown below.In a circuit diagram, an inductor is shown like this:1K Hinds 2012
An inductor is a passive electronic component which is capable of storing electrical energy in theform of magnetic energy. Basically, it uses a conductor that is wound into a coil, and whenelectricity flows into the coil from the left to the right, this will generate a magnetic field in theclockwise direction.The more turns with which the conductor is wound around the core, the stronger the magneticfield that is generated. A strong magnetic field is also generated by increasing the cross-sectionalarea of the inductor or by changing the core of the inductor2K Hinds 2012
Let's now assume that an AC current is flowing through the inductor. "AC" (alternating current)refers to a current whose level and direction change cyclically over time. When current is aboutto flow to the inductor, the magnetic field generated by that current cuts across the otherwindings, giving rise to an induced voltage and thus preventing any changes in the current level.If the current is about to rise suddenly, an electromotive force is generated in the oppositedirection to the current--that is, in the direction in which the current is reduced--thus preventingany increase in the current. Conversely, if the current is about to drop, an electromotive force isgenerated in the direction in which the current is increased.These effects of the induced voltage are produced even when the direction in which the current isflowing is reversed. Before overcoming the induced voltage that is attempting to block thecurrent, the direction of the current is reversed so that there is no flow of current.The current level remains unchanged when DC (direct current) flows to the inductor so noinduced voltage is produced, and it is possible to consider that a shorted state results. In otherwords, the inductor is a component that allows DC, but not AC, to flow through it.Summary1. The inductor stores electrical energy in the form of magnetic energy.2. The inductor does not allow AC to flow through it, but does allow DC to flow through it.3K Hinds 2012
To understand how an inductor can work in a circuit, this figure is helpful:What you see here is a cell, a light bulb, a coil of wire around a piece of iron (yellow) and aswitch. The coil of wire is an inductor.If you were to take the inductor out of this circuit, what you would have is a normal flashlight.You close the switch and the bulb lights up. With the inductor in the circuit as shown, thebehavior is completely different.The light bulb behaves like a resistor (the resistance creates heat to make the filament in thebulb glow). The wire in the coil has much lower resistance (it's just wire), so what you wouldexpect when you turn on the switch is for the bulb to glow very dimly. Most of the currentshould follow the low-resistance path through the loop. What happens instead is that when youclose the switch, the bulb burns brightly and then gets dimmer. When you open the switch, thebulb burns very brightly and then quickly goes out.The reason for this strange behavior is the inductor. When current first starts flowing in the coil,the coil wants to build up a magnetic field. While the field is building, the coil inhibits the flowof current. Once the field is built, current can flow normally through the wire. When the switchgets opened, the magnetic field around the coil keeps current flowing in the coil until the fieldcollapses. This current keeps the bulb lit for a period of time even though the switch is open. Inother words, an inductor can store energy in its magnetic field, and an inductor tends to resistany change in the amount of current flowing through it.HenryThis ability of an inductor to resist changes in current and which also relates current, with itsmagnetic field, as a constant of proportionality is called Inductance which is given the symbol Lwith units of Henry, (H) after Joseph Henry.4K Hinds 2012
Because the Henry is a relatively large unit of inductance in its own right, we use smaller valuesfor our inductors (milli Henry, micro Henry and nano Henry).Inductors or coils are very common in electrical circuits and there are many factors whichdetermine the inductance of a coil such as the shape of the coil, the number of turns of theinsulated wire, the number of layers of wire, the spacing between the turns, the permeability ofthe core material, the size or cross-sectional area of the core etc, to name a few.Inductors in Series – No Mutual inductanceWhen inductors are connected in series, the total inductance is the sum of the individualinductors' inductances.LT L1 L2 LNExample #1Three inductors of 10mH, 40mH and 50mH are connected together in a series combination withno mutual inductance between them. Calculate the total inductance of the series combination.Inductors in Series –Mutual inductanceWhen inductors are connected together in series so that the magnetic field of one links with theother; this is referred to as mutual inductance. The effect of mutual inductance either increases ordecreases the total inductance depending upon the amount of magnetic coupling. The effect ofthis mutual inductance depends upon the distance apart of the coils and their orientation to eachother.Mutually connected inductors in series can be classed as either "Aiding" or "Opposing" the totalinductance. If the magnetic flux produced by the current flows through the coils in the same5K Hinds 2012
direction then the coils are said to be Cumulatively Coupled (diagram A). If the current flowsthrough the coils in opposite directions then the coils are said to be Differentially Coupled(diagram B).Diagram AFor Cumulative Coupling, The Total Inductance isgiven by:LT L1 L2 2MWhere M refers to Mutual InductanceDiagram BFor Differential Coupling, The Total Inductance isgiven by:LT L1 L2 - 2MWhere M refers to Mutual InductanceExample #2Two inductors of 10mH respectively are connected together in a series combination so that theirmagnetic fields aid each other giving cumulative coupling. Their mutual inductance is given as5mH. Calculate the total inductance of the series combination.Example #3Two coils connected in series have a self-inductance of 20mH and 60mH respectively. The totalinductance of the combination was found to be 100mH. Determine the amount of mutualinductance that exists between the two coils assuming that they are aiding each other.6K Hinds 2012
Inductors in ParallelInductors are said to be connected together in "Parallel" when both of their terminals arerespectively connected to each terminal of the other inductor or inductors. The voltage dropacross all of the inductors in parallel will be the same. Then, Inductors in Parallel have aCommon Voltage across them and in our example below the voltage across the inductors isgiven as:VL1 VL2 VL3 VAB .etcIn the following circuit the inductors L1, L2 and L3 are all connected together in parallel betweenthe two points A and B.Example No1Three inductors of 60mH, 120mH and 75mH are connected together in a parallel combinationwith no mutual inductance between them. Calculate the total inductance of the parallelcombination.7K Hinds 2012
Mutually Coupled Inductors in ParallelWhen inductors are connected together in parallel so that the magnetic field of one links with theother, the effect of mutual inductance either increases or decreases the total inductancedepending upon the amount of magnetic coupling that exists between the coils.Mutually connected inductors in parallel can be classed as either "aiding" or "opposing" the totalinductance with parallel aiding connected coils increasing the total equivalent inductance andparallel opposing coils decreasing the total equivalent inductance compared to coils that havezero mutual inductance.Mutual coupled parallel coils can be shown as either connected in an aiding or opposingconfiguration by the use of polarity dots or polarity markers as shown below.Parallel Aiding InductorsThe voltage across the two parallel aiding inductors above must be equal since they are inparallel so the two currents, i1 and i2 must vary so that the voltage across them stays the same.Then the total inductance, LT for two parallel aiding inductors is given as:Where: 2M represents the influence of coil L 1 on L 2 and likewise coil L 2 on L 1.If the two inductances are equal and the magnetic coupling is perfect such as in a toroidal circuit,then the equivalent inductance of the two inductors in parallel is L as LT L1 L2 M.8K Hinds 2012
However, if the mutual inductance between them is zero, the equivalent inductance would beL 2 the same as for two self-induced inductors in parallel.If one of the two coils was reversed with respect to the other, we would then have two parallelopposing inductors and the mutual inductance, M that exists between the two coils will have acancelling effect on each coil instead of an aiding effect as shown below.Parallel Opposing InductorsThen the total inductance, LT for two parallel opposing inductors is given as This time, if the two inductances are equal in value and the magnetic coupling is perfect betweenthem, the equivalent inductance and also the self-induced emf across the inductors will be zero asthe two inductors cancel each other out. This is because as the two currents, i1 and i2 flowthrough each inductor in-turn, the total mutual flux generated between them is zero because thetwo flux's produced by each inductor are both equal in magnitude but in opposite directions.Then the two coils effectively become a short circuit to the flow of current in the circuit so theequivalent inductance, LT becomes equal to ( L M ) 2.Example No2Two inductors whose self-inductances are of 75mH and 55mH respectively are connectedtogether in parallel aiding. Their mutual inductance is given as 22.5mH. Calculate the totalinductance of the parallel combination.9K Hinds 2012
Example No3Calculate the equivalent inductance of the following inductive circuit.Calculate the first inductor branch, LACalculate the second inductor branch, LBCalculate the equivalent circuit inductance, LEQThen the equivalent inductance is 15mH.10K Hinds 2012
Energy Stored in an InductorEnergy stored in an inductor is given by the formula:Time Constant of an InductorWhen a current is applied to an inductor it takes some time for the current to reach its maximumvalue, after which it will remain in a "steady state" until some other event causes the input tochange. The time taken for the current to rise to its steady state value (5τ) in an LR circuitdepends on the time constant τ. Similar to Capacitors; τ represents the time taken for the inductorto charge to 63.2% of its final value.The resistance (R) - This is the total circuit resistanceThe inductance of L – This is simply the equivalent Inductance.In a circuit which contains inductance (L), as well as resistance (R), such as the one shown inFig. .4.1, when the switch is closed the current does not rise immediately to its steady state valuebut rises in EXPONENTIAL fashion. This is due to the fact that a BACK EMF is createdby the change in current flow through the inductor. This back EMF has an amplitude which isproportional to the RATE OFCHANGE of current (the faster the rate of change, the greater theback EMF) and a polarity which opposes the change in current in the inductor that caused itinitially. The back EMF is produced because the changing current in the inductor causes achanging magnetic field around it and the changing magnetic field causes, in turn, an EMF to beinduced back into the inductor. This process is called SELF INDUCTION.11K Hinds 2012
Voltage across an InductorLooking at the graph above, which shows the voltage (VL) across the inductor (L) we can seethat at switch on, the voltage immediately rises to a maximum value. This is because a voltage isbeing applied to the circuit and little or no current is flowing because L is effectively (for a veryshort time) a very high resistance due to the back EMF effect. The full supply EMF is thereforedeveloped across the inductor. As current begins to flow through L however, the voltage VLdecreases until a point is reached where the whole of the battery voltage is being developedacross the resistor R and the voltage or potential difference (pd) across L is zero. When thecurrent is switched off, the rapidly collapsing magnetic field around the inductor produces alarge spike of induced current through the inductor in the opposite direction to the current thatwas flowing before switch off. These rapid changes in current as the switch opens can causevery large voltage spikes, which can lead to arcing at the switch contacts, as the large voltagejumps the gap between the contacts. The spikes can also damage other components in a circuit,especially semiconductors. Care must be taken to prevent these spikes that can occur in anycircuit containing inductors. In some circuits however, where high voltage pulses are required,this effect can also be used to advantage.VL LI12K Hinds 2012
Inductors in Series – No Mutual inductance When inductors are connected in series, the total inductance is the sum of the individual inductors' inductances. L T L 1 L 2 L N Example #1 Three inductors of 10mH, 40mH and 50mH are connected together in a series
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Mutually coupled inductors in series Consider there are two inductors L1 and L2 in series, which are magnetically coupled and have a mutual inductance M. The magnetic field of the two inductors could be aiding or opposing each other, depending on their orientation (fig 6.1). a) b) Fig. 6.1. Mutually cou
SMD Inductors Metal Composite Power Inductors MPXV Automotive Grade Part Number System MPX 1 D0520 L 1R5 Series Version Size Code Inductor Inductance Code µH MPXV 1 D0520 5x5x2.0 mm D0530 5x5x3.0 mm D0618 6x6x1.8 mm D0624 6x6x2.4 mm D0630 6x6x3.0 mm D0650 6x6x5.0 mm D
DP Series Power Inductors provide an excellent, low cost alternative to conventional chokes or inductors. Used in EMI filtering and energy storage, these compact, low radiation inductors a
Inductors in series add like resistors in series. Note the total inductance is greater than the individual inductances. Two inductors in parallel: I V I1 L1 I2 L2 Since the inductors are in
2.3.1 Series Inductors Inductors connected in series are connected along a single path, so the same current flows through all of the components. Figure 2.5 is the connection for series inductors. Total inductance (L T) for a series circuit is the sum of all values of inductance in the circuit. L1 L
Inductors LL and LS have been implemented as bond wire inductors. In this design we have modeled bond wire inductors with an inductance of 1 nH/mm, a series resistance of 0.5 Ω/mm, and we have also accounted for pad capacitances of 100 fF at each bond pad. Bond wire inductors are a
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