Hello everyone, welcome to the course on magnetics for power electronic converters. In this course, you will learn how to analyze and design magnetic components. That is inductors and transformers that go into your power converters. You may ask why we have a separate course on magnetics when we don't have separate courses on the other components that go into a power converter, such as semiconductor devices or capacitors. Is there something special about magnetic devices? Yes, there is. Unlike other components, that you will buy off the shelf, and simply need to understand how to read the data sheets. In the case of magnetic devices, it is very rare that you will find something suitable for your specific [INAUDIBLE] electronic application. In general, you will be designing and fabricating your own magnetic devices for your power electronic converter. Inductors and transformers are typically also the largest component in a power converter. You can see this in this example shown here, this 550 watt DC/DC converter uses three inductors and one transformer. As you can see more than half of the board area and most of the volume is consumed by the magnetic components. Shown below this converter is another 550 watt dc-dc converter that is designed for the same specifications and has almost the same performance but has a much smaller size. The reduction in size in the second dc-dc converter is achieved by combining three inductors of the original converter into a single magnetic structure. And the magnetic devices are further optimized to reduce the size further. The result is that the second converter with the optimized magnetics is 20 times smaller than the original one. Hence, learning how to design magnetics well is an important skill for all power electronic professionals. Inductors and transformers are typically made by winding a wire around a magnetic core while from a circuit perspective, you may only be interested in the terminal behavior of a magnetic device. That is the relationship between its terminal voltages and currents. In order to analyze a magnetic device, we must look at the electric and magnetic fields associated with the device. In this lesson, we will cover the basics of electric and magnetic fields as they relate to magnetic devices. Since magnetic devices store energy in the form of magnetic fields, the most important quantities will be those related to the magnetic fields in the devices. Two of the magnetic field quantities that we will repeatedly encounter are shown here. The first one is B Which stands for magnetic flux density. This is measured in tesla. For which we will also use the symbol T. The other important quantity is H, which stands for magnetic field intensity, and is measured in amps per meter We will often shorten its name and simply call it as magnetic field. As we will soon see magnetic field can be directly related to the terminal currents of our magnetic device through Ampere's law. Also, as we will see the magnetic flux density can be related to the terminal voltages of the device through Faraday's Law. And finally, the magnetic flux density B is related to the magnetic field through the characteristics of the magnetic material used in the core. To fully understand these relationships, let's look at the laws that govern electromagnetic fields. The laws that govern electric and magnetic fields are consolidated together as Maxwell's Equations. These comprise four separate equations, each with its own name. The first one is Ampere's Law. Then we have the Magnetic Flux Continuity condition. Then we have Faraday's Law and finally we have Gauss's Law. Most of these laws are named after the person who discovered them. In addition to these four equations, we also have equations that describe how some of the field quantities are related to one another. These two equations essentially encompass the material properties. In addition to the two magnetic field quantities that we looked at earlier, B and H, these equations utilize a number of other electromagnetic quantities. So let's review some of these other key electromagnetic quantities. The first one is E which stands for electric field, or electric field intensity. Electric field is measured in volts per meter. If we integrate electric field over some part, we get the voltage across that part. If the electric field is aligned with our pot then the voltage is simply equal to the electric field times the length of the pot. Another quantity that related to electric field is D which stands for Electric Flux density. D is measured in coulombs per meter squared. D and E are related to one another through the permittivity of the material in which the fields exist. You can think of D as a dual of B, the magnetic flux density and you can think of E, the electric field intensity as the dual of H. The magnetic field intensity B and H are related to one another through mu which is the permeability of the material in which they exist. The tube of voltage for magnetic fields is a quantity known as MMF which stands for magneto motive force. The unit of magneto motive force are amp turns or simply amps as turns is a unit less quantity We will understand what terms me in a later lesson. Another quantity that is used in Maxwell's equations is current density, J. You can find J by dividing the total current going through some surface by the area of that surface. The units of J are clearly amps per meters squared. Another quantity that is used in Maxwell's equations is which is the charge density This is measured simply in coulombs per meter cubed. The final quantity that is going to be important to us is the total flux or the total magnetic flux, phi. This is the total magnetic flux passing through some surface. And it is related to the magnetic flux density B through the area of that surface. Essentially, the total flux is the flux density times the area of that surface. Hence, you can also think of total flux being analogous to total current while the flux density B being analogous to the current density J. Now we've covered all the quantities of interest so we can start to explore Maxwell's equations. The first equation Ampere's Law Simply describes how the magnetic field is related to the current and the electric field in the system. Specifically, it states that if we integrate the magnetic field over a closed part L Then the integral is equal to the total current that passes through this loop plus the rate of change of the total electric flux that passes through this loop. Which is essentially the displacement current passing through this loop. Now in most magnetic devices, we can ignore the displacement current term. This approximation is known as the magnetoquasistatic or the MQS Approximation. For all the devices that we will cover in this course, and probably all the devices that you will ever encounter, we can make the MQS approximation. In this case, Ampere's Law simply reduces to the left-hand side being equal to the first term of the right hand side. The second of Maxwell’s equations, which is the Magnetic Flux Continuity equation, simply states that the net total flux going into some closed surface must be equal to zero, ie, the total flux going into some closed surface must equal the total flux exiting that closed surface. This makes sense, since there are no magnetic monopoles. The next equation, Faraday's law is a dual of Ampere's law and simply states that the integral of electric field over some closed path l is equal to the negative of the rate of change of the total flux going through that closed path, or loop. The last of Maxwell's Equations, Gauss's Law, is the dual of the magnetic flux continuity condition. And it states that the total electric flux coming out of some closed surface must equal the total charge contained inside that closed surface. Since we don't expect any stored charge in our magnetic devices, we will not need to use Gauss's Law. Next, let's explore the relationship between B and H in more detail. As stated earlier, the relationship between the magnetic flux density B and the magnetic field H depends on the properties of the material in which these fields are present. In free space or air the relationship between B and H is linear. In that case, B simply given by new binds H. When new the slope of this line is the permeability of free space. The value of mu ought is four pi ten to the minus seven Henries per meter and it is a universal constant. The relationship between B and H in a magnetic material is not so simple. Here, we can see the relationship between B and H for an example magnetic material as you can see this curve is non linear. As the value of h increases the slope between b and h decreases, also notice that this curve is multi valued. The value of d depends on whether h is increasing or whether h is decreasing. The fact that the slope of this curve is decreasing corresponding to a decrease of the permeability of this material, with increasing H, is referred to as saturation. And the multi-valued nature of this curve is known as hysteresis. Saturation and hysteresis can both be explained by the fact that magnetic materials comprise magnetic domains. These magnetic domains are like tiny magnets that produce magnetic flux and can also rotate. When no external magnetic field is applied to the material, magnetic domains are aligned randomly. Therefore, they produce no net magnetic flux. However, when an external magnetic field is applied to the material, the magnetic domains start to rotate and align themselves with the external field, hence amplifying the magnetic flux density in the material. However, when the applied magnetic field is so large that all the magnetic domains have already rotated. Then any further increase in H will only result in B increasing by mu 0 times the increase in H. Hence, the slope of the B- H curve once it hits saturation, it's going to reduce to simply mu not. The reason for the hysteresis in the B-H curve is due to the energy needed to rotate the magnetic domains. We will explore this further in a later lesson. For the purpose of analysis of magnetic devices, we can use approximations to the actual vh curve of the magnetic material. In a simple model we can ignore both hysteresis and saturation and simply model B being equal to the permeability mu times H. Often, the permeability is expressed in term of a relative permeability times the permeability of free space. For magnetic materials commonly used in power converters, the relative permeability ranges between 1000 and 100000. That means the permeability of magnetic materials is three to five orders of magnitude larger than the permeability of free space. To have a more accurate representation between B and H we could also include in our model the effect of saturation. We can do that by defining a saturation flux density, B(sat), which defines the limit of B, after which the slope of the curve changes from mu to mu(naught). The value of saturation flux density, B(sat), ranges between 0.3 tesla and two tesla for the magnetic materials commonly employed in power converters. Magnetic cores made from iron alloys, such as silicon steel, have the higher saturation flux densities. On the other hand, ferrite, which is used in high switching frequency power converters, have the lowest saturation flux density. Finally, before concluding this lesson, let's summarize the main magnetic field quantities that we will be using extensively in this course. Also listed in this table are the SI units for these quantities. The four key quantities that we will use extensively are the magnetic field and density H. The magnetic flux density B. The magnetic flux V. The magneto motive force or MMF written as script f. Note that the total magnetic flux has its own unit called weber, hence you can also write tesla, the units of magnetic flux density, as webers per meters squared. While tesla is the SI or NKS unit For magnetic flux density, some data sheets will also provide this information in terms of Gauss, which is the GCS unit for B. Note that 1 Tesla is equal to 10,000 Gauss. With this introduction, you're now ready to take on the scores and learn how to analyze and design magnetic devices which we will start to do from the next lesson. Welcome on board, I look forward to helping you succeed.