## Inductors Basics

Describing basic functionality of the inductors and how they are treated when connected in series or in parallel.

What is an inductor? How does it work? And how we handle inductors when they are connected in series or in parallel? Here are the answers.

An inductor is an electric device capable of storing energy in the form of a magnetic or electromagnetic field.

In its basic form, an inductor can be made of a single loop of wire, or several loops (solenoid). These loops can be arranged in air or on a ferromagnetic core.

When an inductor is connected to a battery, a current starts flowing in the circuit. The current that flows inside the inductor generates a magnetic field, like the one that would be generated by an actual magnet. This field stores an amount of energy, the same way an electric field does.

If the battery is suddenly disconnected, the energy that was accumulated in the inductor must be somehow released. but the energy cannot be released instantaneously, it needs to be released a little bit at a time. And since the energy depends on the current flowing in the inductor, the inductor tries to keep the it running, even if the battery is no more connected. To do so, it uses the energy stored into the magnetic field to generate a voltage at its terminals to keep the current going.

However, since the inductor is now connected nowhere, current cannot flow, unless the voltage is so high that the current can flow in the thin air. And that is exactly what happens: the voltage increases so much that there is a sudden discharge of current through the air, in the form of a spark, that dissipates all the energy that was stored in the inductor. This spark is the one you may sometimes notice when opening a switch that is powering a lamp or a motor, or when you pull the plug from a device that was working using a considerable amount of current.

Similarly to the case where the current is suddenly removed, an inductor generates a voltage also when the current is just changed in intensity. In this case, the voltage is created to react to the change in current, trying to keep it to the same value, so the energy can be conserved.

In both cases, the amount of voltage is proportional to the change in current (ΔI) and inversely proportional to the amount of time in which the current changes (Δt). In other words, the faster the current change, the higher is the voltage.

For a specific inductor, the ratio between the change of current and the interval in which that happens equals the voltage generated by the inductor divided by a constant that depends on the physics dimensions of the inductor. Such constant is called inductance, represented with the letter L, and can be calculated with the following experimental formula:

where:

μ = permeability of the material inside the coil

N = number of turns making the coil

A = area of the cross section of the coil

l = length of the coil

L is measured in Henry.

μ is the product of the permeability of the void (or air) and the relative permeability of the material:

The voltage at the terminals of the inductor is therefore calculated as:

We can now calculate the energy stored in the magnetic field of an inductor as the integral of the power, which is obtained multiplying the voltage at the inductor and the current that flows through it:

which, considering the value of the voltage previously calculated, can be solved as follows:

where I is the current flowing through the inductor at the time the energy is calculated.

When choosing an inductor for a circuit, the following parameters must be considered:

• the value of the inductance in Henry

• the max current the inductor can sustain; failure to specify that could cause the inductor to overheat, since the wire could be too thin to deal with the required current;

• the max voltage that can be applied to the inductor; an excessive voltage on the inductor could cause sparks due to insufficient insulation of the wire.

## Inductors In Series

Let’s consider a series of inductors of different inductance values and let’s calculate the equivalent inductance.

All the inductors, being in series, are traversed by the same current. And since each inductor has its own inductance value, each one will store a different amount of energy:

The total energy stored in the inductors is therefore:

So, the equivalent inductance is clearly:

which we can generalize as:

## Inductors In Parallel

In the case of inductors in parallel, they are all subject to the same voltage and are traversed by a different current:

From these equations we can find the currents by integration:

The total amount of current is therefore:

So we can say that the equivalent inductance of a parallel of inductors can be determined through the formula:

or, more in general:

All the formulas presented here are very general and can be applied to both DC and AC circuits. Note, however, that since AC circuits have a variable voltage and current, the application of the formulas in AC is a little more challenging then in DC. But this is a story for another time.

## A Tester For Zener Diodes

Zener diodes are used for several purposes, from providing a reference voltage, to protecting sensitive circuits from being destroyed by the wrong input.

Today, I will show you how these diodes work and how to build a simple circuit to measure their most important characteristic, the reverse breakdown voltage. To know more on this topic, please watch the companion video posted on YouTube.

A zener diode looks like a regular diode and actually behaves as such when directly biased (positive voltage on the anode).

However, when inversely biased (negative voltage on the anode), a zener diode behaves in a completely different way.

Let’s take a look at its characteristic I-V diagram:

You can see that in the region of direct (or forward) bias, the zener behaves just like any diode. It also seems like in the inverse bias it behaves like a regular diode.  However, there is a big difference between the two.

For a regular diode, the reverse breakdown voltage is very high, in the order of 100V or more, sometimes much more. Such high that you never think at it when you use regular diodes, and you assume that with inverse bias the diode just does not conduct electric current.

For a zener diode, instead, the reverse breakdown voltage is low, in the order of one or two digit volts. Therefore, it is very easy in an electronic circuit to bring this kind of diode to reach the condition when it will start conducing electric current even if inversely polarized.

We actually exploit this behaviour to create reference voltages, or to provide a protection against unwanted voltages at the input of certain circuits, or a ton of other things.

The behaviour of a diode depends in fact upon the way it was fabricated, and in particular upon how it was doped. Regular diodes are lightly doped, while zener diodes are heavily doped. Depending on the amount of doping on both the P and the N side of the junction, the reverse breakdown voltage changes. That way, manufacturers can create zener diodes within a large range of breakdown voltages.

Problem is, manufacturers often don’t put the value of the breakdown voltage on the body of the components. Instead, they put some internal code or, sometimes, nothing at all.

So, if you had a number of such diodes on your workbench, how to distinguish them from one another?

Meet the zener tester.

It is a device that allows you to measure the reverse breakdown voltage, so you know if the diode works and what that voltage is.

How such a tester works? From the I-V diagram above, you can see that the characteristic of the zener diode is an almost vertical line when polarized in the reverse bias region. For any current value in that vertical line, the voltage is always the same and corresponds to the breakdown voltage. So, if we circulate a current at any point of that vertical line, we can measure at the terminals of that diode its breakdown voltage.

The zener tester I’m showing you today does just that: forces a current into the zener diode so we can measure the value of the breakdown voltage. We choose this current in such a way that it is high enough to stay away from the point where the characteristic is not linear, but low enough to avoid dissipating inside the diode a power that the diode itself cannot handle.

The following link allows you to download an archive containing the schematic of such device, along with the OpenSCAD code to 3D print the box for the device.

zener_diodes_tester_files

In the schematic you’ll see that I used a ready-made boost converter and a digital voltmeter. Here are the links to the store where I bought them. Of course you are free to use any other equivalent component. It will work as well.

BOOST CONVERTER

DIGITAL VOLTMETER

Please make sure to watch the YouTube video that completes the information I provided in this post. Between the two, you should have a complete view of the design of the device and should be able to build it.

Happy experiments!

## Behind The Scenes Of The Theremin Design

How I design my electronic circuits and prepare the videos to show them to you.

Did you ever ask yourself where I get the schematics of the Theremin circuits and other gadgets that I present on my YouTube videos? The answer is simple: I do some research on books, on specialized magazines and on the Internet. I see solutions created by other people, if any, and then I think about what would better work for my case. Sometimes it ends up to be a modification of something that somebody else did, maybe for a totally different purpose. Sometimes, I just use the general idea to create something different, new, my own design that is more appropriate for my needs.

Either way, I usually build a number of prototypes of what I need, then I take some measurements in lab, then I start making further modifications to my original design, until I obtain exactly what I am looking for.

Also, more often than not, I figure that the circuit I am testing is too sensitive to certain parameters of the circuit itself. Maybe is a capacitor which value needs to be adjusted a little bit, or a connection between two or more components that causes issues because of capacitive or inductive coupling with other components. That is when I try to change my design to reduce such sensitivities, so that the circuit can be assembled by anyone with the exact same results as mine. And this is what is called engineerization, or adjusting the design for mass production.

And sometimes, to do so, it is not enough to test the single circuit. Instead, I need to connect the circuit with other pieces that have to work together with it, and see if further unwanted interactions happen, so that I can eliminate them or, at least, reduce them so that they become negligible.

Sometimes this process goes fast, sometimes takes a long time. And that’s why my videos are not published at fixed intervals. Unfortunately, since this is done only as a hobby, I don’t always have enough time to dedicate to my project, so days go by until, finally, I am done. Then I finalize my schematics, I build the last prototype and the final product and, in the process, I also record all these activities so I can end up making a video out of them.

Then the video editing process starts and, once the video is finally ready, I release it on YouTube for you to watch it.

One day I will be able to do this full time. Who knows, maybe when I retire. Or, maybe, if you all give me a hand, this could become my new full time job (donations, donations, donations). We’ll see.