## A Few Words On DC And AC: What Exactly Are They?

A few disorganized concepts about direct and alternate current.

There are two main variations of the electrical current: the Direct Current, or DC, and the Alternate Current, or AC. But what does that mean?

The DC is the one you obtain when you power a device using batteries, for example. Batteries provide what is called Direct Voltage and that generates a Direct Current once applied to an electric circuit. If we draw a diagram of the voltage and, correspondingly, the current that flows in a circuit powered with DC, here is what we obtain:

This diagram basically tells us that the value of the voltage, and of the current, does not change over time. We usually define the current as flowing from the positive to the negative pole of the battery and that flow never changes over time.

The AC works like the DC, going from the positive to the negative voltage. The difference is that the voltage keeps switching: positive becomes negative and then becomes positive again, and so forth. And so the current keeps changing its direction accordingly.

Also, the AC does not change suddenly back and forth, but it does that progressively, following a shape called sine wave. All electrical energy distributed in our homes has this shape.

In USA, the AC current changes direction 120 times per second, which means that in one second there are 60 full periods of the sine wave. We say that the frequency of the current is 60 Hertz, abbreviated 60 Hz.

In Europe, 50 Hz is used instead. Other parts of the world either use one or the other.

The AC voltage is the one created in the power plants and provided, for example, at the wall outlets in your house by the energy service provider.

The voltage at the outlet is not constant as the one in the batteries. Instead, it changes continuously following the shape of a sine wave. Because of that, the polarity at each electrode of the outlet changes over time from positive to negative and vice versa, following the shape of the sine wave.

So, when we connect a device to the electric outlet, the current that will flow through that device will be an AC current as well.

The sinusoidal shape of the AC voltage depends on the way the electricity is generated. In the power plants, there are devices called alternators, a much bigger version of those that you can find inside your car to recharge its battery, or on a bike, to provide electricity to turn on the lights at night.

Depending on the power plant, a different kind of energy is used to put in motion the alternator. It could be fossil fuel or nuclear energy that heat a reservoir of water and create the steam that makes the alternator rotate. Or it could be the rotation of a propeller-like device that is put in motion by the wind.

Whatever is the source of the mechanical energy, the alternator converts that energy in electrical energy. But, since the rotation translates into a sine wave when described on a Cartesian reference system, the resulting electrical energy acquires that shape too.

But, why do we need both forms of voltage, DC and AC?

First of all, DC voltage is necessary to power up any electronic device, from your TV to your smartphone or radio or computer.

AC voltage, from the electrical engineering perspective, is used to transmit the electrical energy from the places where it is created to the places where it is used.

Back to the time where the first experiments of electricity transmission were conducted, there was a famous diatribe between Thomas Edison and Nikola Tesla.

Edison believed that the safest way to transmit electricity was to do that with cables powered with DC current.

Tesla argued that it was better to use AC current because it allowed much less waste of energy during the transportation, thanks to the fact that it is easier to convert the voltage from a low value to a higher one and vice versa, when using AC. And it is also very simple to convert the AC into DC when DC is needed, through a process called rectification.

As history tells us, Tesla won that battle, rightfully. And so, today, AC is used to bring the electrical energy to our homes from the power plants.

## 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!