Today we are going to explore the use of the Inductor. This is a continuation from the series of articles on alternating current. An inductor is a component that can resist changes in AC current, and store energy in a magnetic field from a current that passes through it. A changing current (AC) causes a changing magnetic field which induces a voltage that opposes the current produced by the magnetic field. This is known as the inductance. One could think of an inductor as an AC resistor. But first of all, what is an inductor comprised of?
In simple terms an inductor is a coil of wire, wrapped around a core. The core forms a support for the coil of wire – such as ceramic cores, or in some cases can affect the properties of the magnetic field depending on the chemical composition of the core. These may include cores formed from ferrite (usually zinc and manganese, or zinc and nickel) or powdered iron (which has a tiny air gap allowing the core to store a higher level of magnetic flux (the measure of magnetic field strength)– allowing a higher level of DC current to flow through before becoming saturated.
So, the amount of inductance is influenced by several factors – the core material (as above), the size and shape of the core, as well as the number of turns of wire in the coil and its shape. The unit of inductance is the henry (H), however common values are usually in the millihenry (mH) or microhenry (uH) range.
Furthermore, there is an amount of DC resistance due to the properties of the coil wire, however this is usually negligible and kept to a minimum. For example, looking at a data sheet for a typical line of inductors – inductors.pdf – the DC resistance of a 10uH inductor is a maximum of 0.05 ohms. With inductors of higher values, the DC resistance will need to be taken account of. But more about that later.
However this may also be used:
And here is a variety of inductors in the flesh:
radial ferrite core, generally for PCB use, handles around 1.5 amperes
radial leaded, very low resistance, handles around 2.5 amperes
ferrite core, convenient for through-hole PCB
toroidal – handles large currents ~10 amperes depending on model
surface-mount, can still handle around 500 mA
All of the pictured inductors have an inductance of 10 uH. Now let’s examine how inductors work with alternating current. Consider the following circuit:
Just like capacitors in AC circuits, an inductor has a calculable reactance. The formula for the reactance (X, in ohms) of an inductor is:
where f is the frequency of the AC and L is the value of the inductor in Henries (remember that 1uH is 10 to the power of -6). The formula to calculate the impedance of the above circuit is:
where Z is in ohms. And finally, the formula for AC Vout is
The formula for DC Vout is the usual voltage dividing formula. In this case, as we consider the inductor to not have any resistance, DC Vout = DC Vin.
So, let’s work through an example. Our DC Vin is 12 volts, with a 2V peak to peak AC signal, at a frequency of 20 kHz. The resistor R has a value of 1 kilo ohm, and the inductor L is 10 millihenries (0.01 H). A quick check of the data sheet shows that the 10 mH inductor has a resistance that cannot be ignored – 37.4 ohms. So this must be taken into account when calculating the DC Vout. Therefore we can consider the inductor to be a 37.4 ohm resistor when calculating the DC Vout, which gives us a result of 11.56 volts DC. Substituting the other values gives us a reduced AC signal voltage of 1.24 volts peak to peak.
Another interesting fact is that there is a relationship between AC Vout and the frequency of the AC signal. In the video below, I have used a 10k ohm resistor and a 10 uH inductor in the circuit described above. The frequency counter is measuring the frequency of AC Vin, and the multimeter is measuring the AC Vout:
This is an interesting relationship and demonstrates how an inductor can resist alternating current, depending on the frequency.
Thus ends our introduction to the inductor. We will continue with the inductor in the near future. I hope you understood and can apply what we have discussed today. As always, thank you for reading and I look forward to your comments and so on. Furthermore, don’t be shy in pointing out errors or places that could use improvement, you can either leave a comment below or email me – john at tronixstuff dot com.
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