By now you have hopefully learned that the voltage induced in a coil is proportionate to the change of the flux threading through that coil. We will now see that this is the cornerstone operating principle for another electromagnetic device called the transformer. We start out with a coil wrapped around a magnetic core as shown here. You will then energize this coil here with a low frequency sinus little voltage source like around, I don’t know say 50 or 60 Hertz. We now repeat Faraday’s relationship here but what we would really like to know is what is the flux that is generated by this voltage. If we rewrite Faraday’s law in its integral form, we see that the flux is proportional to the integration of the voltage wave form. Since the voltage wave form is a sine wave, this implies that the flux wave form will also be sine little, and will lag the voltage wave form by 90 degrees. Now, it’s very important to remember that it’s the voltage wave form not the current in the coil that determines the shape of the flux wave form. In turn the flux wave form drives the shape of the current wave form. But how can we determine the current wave form from the flux wave form? Well, recall from earlier equations, that the current in a coil is proportional to the magnetic field intensity and that the flux is equal to the flux density times the cross sectional area of the magnetic material.

So, for a given magnetic material with a given shape and specified historicist curve we can rescale the axis using these relationships to create a modified historicist curve with flux and current as the new axis as shown here. This is the diagram that we need to relate the flux and the current. So, every value on the flux wave form will map to a unique value of current. Then you know whether the flux is increasing or decreasing. For this particular magnetic material, notice that the peaks of the flux wave form correspond to areas of magnetic saturation on the historicist curve? This means that small incremental changes in flux result in large changes of current to support that flux and the current wave form will be very spiky at its peaks. Since this is the current necessary to support the flux in the core. It is referred to as the magnetizing current of the transformer and will generally lag the voltage wave form by 90 degrees.

Next, let’s introduce the second coil with N2 number of turns wrapped around the same magnetic material. So mean leakage flux is zero, this means that all of the flux which is threading through the first coil is also threading through the second coil. By applying Faraday’s law to this second coil, we can define the voltage that is generated by this coil. If we relate this equation to Faraday’s equation for the first coil, we see that the voltage ratio between the two coils is simply the ratio of the turns fridge coil. In other words, if you want to step up transformer, the second coil called the secondary should have a lot more turns on it than the first coil which is called the primary. Now, let’s connect the load up to the secondary coil which results in current flowing in that coil. By again using the modified historicist curve for this magnetic material we see that this current will attempt to set up its own flux in the core. But wait a minute, didn’t we say earlier that the flux is strictly defined by the voltage source connected to the primary. So what gives? Well, assuming that the impedance of the primary voltage source is sufficiently low, the flux won’t change. Instead, a new current is induced in the primary coil to counteract the flux effect of the current in the secondary coil.

This is the mechanism by which the transformer primary knows that there is current flowing in the secondary circuit. In a similar way that we calculated the voltage ratio between the primary and the secondary we can also relate the primary current to the secondary current. And once again we see that it boils down to simply the ratio of the number of turns between the two coils. When the transformer is operating at full load capacity, we find that the magnetizing current is usually much smaller than this reflected current vice of one in the primary circuit. Nonetheless the magnetizing current does exist regardless of whether a load is present or not in the secondary circuit and it must be taken into consideration when calculating the transformers’ operating efficiency.

No discussion on magnetics would be complete without considering the topic of inductance. As we have already established if we take a coil and inject current into the coil, a magnetic field will be formed. One useful measure of a coil is to determine how much flux will be generated by the coil for a given amount of current. This measure is referred to as inductance. Inductance is measured in henries which is named after the American scientist Joseph Henry who discovered electromagnetic induction at about the same time that Michael Faraday was conducting his magnetic experiments. Using the top equation, we can also derive a very useful relationship between inductance, voltage and current. Recall that the voltage across the coil will be equal to the change in flux linking that coil per change in time which is the famous deflux DT expression. Using the top equation to define flux linkage as the product of inductance and current and substituting this product for flux linkage in the bottom equation, we end up with this expression. If we assume that the inductance is fixed, in other words a linear circuit, then we can pull L out of this expression as a constant which leaves us with L, DI, DT.

In other words, an inductor can only generate voltage across its terminals if the current is changing with respect to time. If the current is constant, the inductor voltage will be zero. It’s also interesting to note that the polarity of the generated voltage will be in such a way as to oppose the change of current. In other words, an inductor protects its current flowing through it just like a mother protects her child and will generate whatever voltages necessary to keep that current at it present value.

We have already established that wires conducting current generate a circular magnetic field at right angles to the wire as shown here. But what do you think would happen if we put 2 wires next to each other with the same current flowing through them but in opposite directions? To make this more interesting, let’s assume that the current is alternating in a sinus little fashion. Let’s take a look at the following simulation to see what this might look like.

Here you can see the magnetic field expanding and collapsing as the current rises to its peak value and then returns to zero. Also as the current alternates, the polarity of the net magnetic field reverses from north to south over and over. So at best we have created a pulsating magnetic field. Now you may want to grab hold of something as this next animation has been known to induce extremic sidemen’s in certain individuals. At least it did for me. What do you think would happen if we make three loops of wire oriented them to 120 degrees with respect to each other and then we pass AC current wave forms through each wire which are out of phase with each other by a 120 degrees. Are you ready? Isn’t this incredible? This is the epiphany that Nicola Tesla had in 1882 when he invented the AC induction motor although his motor involved only 2 phases instead of 3. But for the first time, a motor can now be built that created rotation without a physical mechanism being required such as a commutator or brushes. Also notice that we can easily reverse the direction of rotation by simply swapping the current in 2 of the coils as shown here. We will explore this effect further in a later tutorial on AC motors. But for now I just wanted to give you a little taste of some of the exciting topics to come.

Well that’s it today for our study on magnetic fields. I hope you find this tutorial useful as it prepares you for future topics we will be talking about later in this tutorial series. I am Dave Wilson and thanks for joining on this little stroll through magnetic fields and I hope to see you in other tutorials from freescale Semiconductor.

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