Introduction
In this installment we examine inductors (also called coils) and their behavior in DC circuits. We’ll look at what they are, what they do, and how they respond in both steady state and transient conditions (i.e. a state change). In addition to the theory, we’ll spend some time in the lab looking at real-world inductor response as well as practical applications.
You can either read the text or watch the video. But will get the most out of the lesson if you do both. You’ll find the lab segments in the video. Let’s get started.
What is an Inductor
Like a capacitor, inductors store energy. But unlike capacitors that store energy as an electric field, inductors store their energy as a magnetic field.
If we pass a current through an inductor we induce a magnetic field in the coil. The coil will store that energy until the current is turned off. Once the current is gone, or diminished, the magnetic field collapses and the coil returns the stored energy.
We can use an inductor’s ability to create a magnetic field to perform a variety of electromagnetic-driven mechanical functions. A few examples include retracting or engaging a door lock, launching a pinball, turning a motor armature, or operating a relay.
In addition, we can use the inductor’s energy storage and return capability to great advantage in our electronic circuits. Boost Converters, which are used to increase a DC voltage, say from a 9V battery at the input to the 100V or more needed to drive a vacuum fluorescent display, use an inductor’s ability to store and return energy to “boost” the voltage. In fact, older CRT-based monitors and TVs used a flyback circuit (based on a set of coils) to generate up to 25,000V DC from a 120V input supply.
Likewise, if we pass an inductor through a magnetic field or subject an inductor to a changing magnetic field we induce a current in the inductor. The larger the coil and the larger the magnetic field the greater the current.
This is how generators are made. A series of coils (also called windings) inside the motor (usually wrapped around an armature) are placed between a set of strong magnets. When the armature is turned, the coils cross (or cut through) the magnetic lines of flux which induces a current in the coil. Large currents (think power generating stations) can be created simply by passing large coils through the magnetic fields generated by huge magnets.
In addition, we can use this same ability to detect changes in a magnetic field to determine where a stud is behind a wall (stud finder), or if there is metal in the ground (metal detector), or to transfer energy from one coil to another coil in close proximity (transformer or wireless charger).
Inductor Behavior in a DC Circuit
As seen below, inductors, like capacitors, can use a variety of core materials to change the properties and effectiveness of the coil. The coils ability to store magnetic energy is called inductance and is measured in Henry’s. In most cases we talk in terms of micro-Henry’s or uH.
While capacitors resist changes in voltage (the voltage across a capacitor can’t change instantaneously), inductors resist changes in current (the current through an inductor can’t change instantaneously).
Let’s look at how an inductor behaves in a simple circuit. The circuit below shows a single resistor (R) in series with an inductor (L). Both components are connected to a battery with a switch.
Before we close the switch the current through the circuit and the voltage across both R and L are equal to zero. Let’s close the switch and see what happens.
Since the current through an inductor cannot change instantaneously, the current through the circuit remains at zero. That means that at the exact instant when the switch first closes, which we will call t0, the current through the resistor (R) is zero. Ohms law tells us that the voltage across a resistor V = I x R. And if I is zero then there is no voltage drop across the resistor. But Kirchhoff’s Voltage Law states that the sum of the voltages around a closed loop must equal zero. So the voltage from the battery (V) must appear across the inductor (L). At the exact instant the switch is closed all of the voltage appears across the inductor.
Immediately after the switch closes, a current begins to flow in the circuit. The rate of charge is given by the formula t = L/R. Like with capacitors, the rate of charge is such that the current reaches approximately 2/3 or 66% of it’s final value after 1t – Remember Tau from our capacitor lesson? Well here it is again. The current will continue to approach its final value getting 66% closer for each t that passes. So after 2t the current is at 66% plus 66% of the remaining 34%. I = 66% + (66%x34%) = 66% + 22% = 88%. In theory, this continues for infinity. However, for practical purposes, and engineering sanity, we consider the current to reach it’s final value in 5t. This is called the transient response. It is what happens as the inductor transitions from no current to the final current (in this case given by I = V/R.
Once the current has reached it’s final value and the inductor has finished charging it behaves like an ordinary wire and we assume the resistance to be zero. This is called the steady state response.
Let’s plug in some values and look at an example.
In the example above we assume a perfect inductor, that is the inductor itself has zero resistance. In reality, the wire has a small resistance but in most cases we can ignore it. The current will continue to increase getting approximately 66% closer to the final value after each time period, t. After 5t periods (50 seconds), the current is at 99.99% of the final value (5A) and we assume the inductor is fully energized.
If we instantaneously flip the switch to the discharge position, as shown below, the magnetic field surrounding the inductor (L) begins to collapse and the inductor will return its energy. The inductor becomes a voltage source for the rest of the circuit. And since the current in an inductor can’t change instantaneously, but the voltage can, the polarity of the inductor reverses. The voltage across the inductor (at the exact instant of change) becomes 5V in the opposite direction from when it was charging. Remember, the current is still 5A and Ohm’s Law still holds true. Kirchhoff’s Voltage Law tells us this has to be true.
The inductor will continue to discharge until the current reaches zero.
Inductive Transient Spikes
Now here is where inductors in DC circuits get really interesting…If we quickly open the switch and leave it as an open circuit after the inductor has been energized and the magnetic field has formed, the magnetic field collapses releasing the stored energy back into the inductor and the inductor becomes a voltage source for the circuit.
The inductor still needs to discharge it’s energy. However, once we open the switch and have an open circuit R becomes very large (in theory infinite). The voltage across the inductor will continue to rise until it gets high enough to jump (or arc) across the switch contacts (30kV/cm in dry air). This is called a transient spike or inductive spike.
Protecting Against Inductive Transient Spikes
If the switch is a transistor or other semiconductor device, the arc will jump across the junction likely destroying it. When I was in my first year of college I built a relay controller board. I hadn’t learned about inductor transient spikes yet so I didn’t understand why the transistors I used to control the relay coils (inductors) had to be replaced almost every time I used it.
Inductive spikes ruin electronics all the time. Luckily there is a simple solution to the problem. We can place a protection diode (also called a flyback diode) across the coil as shown below. When the switch is connected to the battery, the diode is reverse biased so the current flows through the inductor as intended. But when the switch opens (creating an open circuit) and the voltage across the inductor reverses, the current has an easy path through the diode so that the inductor can release its stored energy harmlessly.
Harnessing the Power of Transient Spikes
While the transient response of the inductor can be destructive, as discussed above, we can also use it to our advantage. DC Boost Converters work by charging an inductor and then use diodes to direct the energy to a storage device. A capacitor is used to store the energy released by the inductor and then that stored energy is drawn off as needed.
In the above circuit the MOSFET plays the part of the switch which is continually opened and closed by a series of pulses. This causes the coil to charge and discharge. When the switch is in the on state current flows through the inductor and it charges storing the energy in a magnetic field.
When the switch is in the off state the magnetic field collapses. The current through the inductor can’t change instantaneously so it continues to flow in the same direction (left to right in the figure above). The inductor immediately switches polarity and gives its stored energy back to the circuit.
When that happens, the input voltage source and the inductor, which is now also acting as a voltage source, are in series and based on Kirchhoff’s Voltage Law, the two sources add, doubling the input voltage at the diode. The diode (D1) directs the discharge energy into a capacitor (C1). As a result, the voltage across the capacitor is almost double what the DC input is providing (double minus a small drop across the diode). The capacitor charges (over a short time) to the higher voltage.
The frequency of the pulses is set so that the capacitor doesn’t have time to discharge before it gets the next “boost” of energy thereby holding the output steady at the new voltage. And just like that, 5V can be boosted to 10V.
I hope you enjoyed that and learned something about inductors and their behavior in DC circuits. If you did, then how about a thumbs up and a share. And smash that subscribe button so you won’t miss any new content.
Until next time, cheers!
Dominick
