Welcome back to the course on Magnetics for Power Electronic Converters. In this and the next lesson, we will learn how to design magnetic devices. A typical magnetic device looks like as shown here. It comprises a core, which is typically in two parts that come together to form the magnetic device. The winding goes inside the core. Where it is typically wound on what's called a bobbin. And then this bobbin fits into the center post of the core. Once the bobbin is wound, the three parts, the two core house, and the bobbin come together to form a single structure, and are held together by a couple of clips. So when you're designing a magnetic device, such as an inductor or transformer, what you have to do is select, first of all, the core that you're going to use. Now cores come in different shapes and different sizes, but what's most important is going to be the size of the core. The shape will have some impact on your design. But those impacts can be considered second order. There are a number of dimensions that can be used to describe the size of the core. But the most important parameter that we will use, is the core cross sectional area for the shape of the core shown here. The core cross sectional area is really the cross sectional area of the center post of this core. Since the winding is wound around the bobbin and the bobbin sits around the center post, the flux is generated so that it flows vertically through the center post and then returns from the site post returning it off equally through each of the site post so the cross sectional area is really a cross sectional area of the center post which is equal to the sum of the cross sectional areas of the two site posts. Other core dimensions that we will find useful in the design of the magnetic structure include the window area associated with this core, which is really the area of the gap to which the winding can be wound. Another dimension that is going to be important is what's known as the mean length of turn. This is essentially the average length of a single turn of the winding as it goes around the center post. Apart from selecting the size of the core to use in the design other things that need to be specified as part of the design are the number of turns of wire to be wound, and then also the size of the wire to be used in the winding. And finally, if there is an air gap in the structure, then the length of that air gap also needs to be specified as part of the design. Instead of four key outcomes of any magnetic device design. The core, the number of turns of wire, the wire size and the air gap in case there is an air gap. In terms of how to go about designing a magnetic device there is no single best design procedure. How do you choose to design the magnetic device depends partly on what it is that you want to minimize or optimize. Typically, you're trying to minimize losses but size is also often quite important and there's a trade off between minimize in size and minimize in losses. Quite often, you may have an upper limit on size and within that constraint, you want to minimize losses. On the other hand, you may have a loss budget and you're trying to minimize the size, while making sure that the losses do not exceed the loss budget for your magnetic device. The design procedure to follow also depends on the type of magnetic device. There are a number of magnetic devices that are used in falcon orders. We are familiar with the filter inductor which is probably the most common type of magnetic device used in falcon orders. Filter inductors are used in all PWM type of converters. In addition to filter inductors, there are also AC inductors. These are typically used in resident converters. Inductors in PWM converters which have large ripple current can also be treated like AC inductors. For example, inductors that are used in BWM converters operating in DCM mode, look very similar to AC inductors. In addition to inductors, power converters also use transformers. Transformers are very commonly used whenever an isolation Barrier is required. However they are also very useful where large change in voltage is required. Another magnetic device that is often found in power converters are coupled inductors. Coupled inductors are magnetic devices in which multiple inductors have been wound on a single core. In some converter structures, when designed properly, coupled inductors can be of great advantage for example they can be used to minimize the ripple in one of the inductors through a technique known as ripple steering. In addition to conventional transformers in which current is flowing through two or more of its windings there are flyback transformers that are used in electronic converters. A flyback transformer, while it is called a transformer, is more like two inductors, both on a single cord. In a flyback converter which uses a flyback transformer, current flows through the primary winding through half of the time period, and stores energy in the air gap of the transformer. In the second period of the converter operation, the energy stored in the air gap is released through the secondary winding to the output side of the converter. Hence, unlike a conventional transformer, in which current is flowing through both the primary winding and the secondary winding of the transformer at the same time. In a flyback transformer current is either flowing through the primary winding, or it is flowing through the secondary winding but not in both the windings at the same time. Hence the design of the flyback transformer is quite different from the design of a conventional transformer. Given the differences between these devices, it is difficult to generalize the design procedure for all of these devices into one or two design procedures. However, we can categorize the design procedure for magnetic devices based on a few different aspects. One thing that differentiates the different design procedures is how the maximum flux density in the core is determined. There are two things that can limit the maximum flux density in the core. The first is the saturation flux density of the core material. The second is the losses in the core. In the case of some of these magnetic devices, core losses are not very large. In that case, maximum flux density in the core is not constrained by core losses, but rather by core saturation. In other cases, core losses are very large and you cannot afford to have very flux densities so you're not very limited by core saturation but you're instead limited by core losses. Another design aspect that differentiates how these different magnetic devices are designed Is really whether they have an air gap or not. Magnet devices that are required to store energy have an air gap while devices that do not require energy storage, such as a transformer, will not have an air gap. Depending on the type of constraints imposed on the design one can come up with design procedures that do not require iteration. However, these design procedures do not necessarily yield the optimum design. To get an optimum magnetic design, you will invariably have to iterate your design. However it is still useful to look at some of these non-iterative design procedures as they yield design equations that provide insight into how the different parameters affect the overall design. We will develop one such design procedure later in this course. But first, let's look at the kind of constraints that are imposed on some of these magnetic devices. In particular, we look at the filter inductor, the AC inductor, and the conventional transformer. The filter inductor is one of the most common magnetic components in a power converter. Here, you can see it being used. In a buck converter operating in continuous conduction mode. In a CCM buck converter the function of this inductor is to minimize the output current triple. Here you can see the typical wave form for a filter inductor. Delta IL Is the average to peak current ripple in this inductor. Typically, delta IL will be much smaller than the average current I through the inductor. Since delta IL is small, the AC component of the inductor current is small. Because of that the ac winding losses in the inductor are small. That is to say that skin and proximity effect do not substantially increase the losses in the winding beyond the dc losses. Also, because delta IL is small the radiation in the magnetic field inside the core is small. It is easy to show that the magnetic field inside the core is directly proportional to the current that's flowing in the winding. The expression given here for the magnetic field in the core can be derived simply by considering a magnetic circuit model for the core. Here Rc is the reluctance of the core. And Rg is the reluctance associated with the air gap? LC is the length of the core and N is the number of domes of the winding on this one. Since the medic field, H, and the core is directly proportional to the I and the winding and the radiation Ni is small. And the radiation in the magnetic field of the core is also small. You can see this pictorially here on the B-H loop. The delta Hc is a small radiation in the magnetic field H. As a result of the small variation in current delta IL. So the B-H loop or which the flux changes in the core is really quite small and the area enclosed in it is small. Hence the core losses associated with this B-H loop are small. Hence the coil losses in a filter inductor are also very small. Therefore, in the design of a filter inductor, we can ignore core losses as well as winding ac losses and really only concentrate on dc losses in the winding. Since the core losses are small, the flux density in a filter inductor is not constrained by core losses, instead it will be constrained simply by saturation. What this means is that we don't want to allow the maximum value of the flux density B to ever exceed B sat in our design. In fact, we would like to leave some margin and operate D below that. Finally, since a filter inductor has to store energy, we will need to employ an air gap in our design. The design constraints on an AC inductor are quite different from those on a filter inductor. AC inductor are commonly used in converters, known as the resonant converters. These converters transfer energy from input to output in the form of AC wave forms, they for the currents through the inductors has large AC content, the wave formed do not have to be sinusoidal but they have large ripple, PWM converters that have large ripple in their inductors, can also be treated like AC inductors. A good example of that would be Peter Gram converters operating in the discontinuous conduction mode. In the case of a PWM converter operating in DCM The current through the inductor would also have a dc component in addition to the large ac component. Due to the large ac component in the inductor current, both the core loss and the ac winding loss cannot be neglected in the design of an ac conductor. You can see that pictorially here in this BH diagram because the inductor current this varying by a substantial amount the magnetic field in the core is also varying by a proportionately large amount. So in this case the BH loop that's formed Is really spanning a much larger fraction of the total B-H loop of this core. Therefore, in order to limit the core losses in this inductor, the flux swing will have to be substantially limited, so that the B-H loop that's actually formed is Is much smaller, resulting in smaller core losses. Therefore in the design of an ac inductor, the maximum flux density in the core is not limited by the saturation flux density. But instead limited to a much smaller value by the core losses. Hence the flux density design constraint on an AC inductor is quite different from that of a filter inductor. I would just like a filter inductor since this inductor also needs to store energy. You will need to employ an air gap in this inductor as well. Finally, let's look at the design constraints associated with a conventional transformer. The magnetic field in the core of a transformer is directly proportional to the current flowing through the magnetizing inductance of the transformer. In fact using a magnetic socket model, it is easy to show that the magnetic field inside the core of the transformer is given by this expression. Here i mu one is the magnetizing current of the transformer. Or the current through the magnetizing inductance of the transformer reflected on the primary side. N1 is the number of terms on the primary and lc is the length of the core. The shape of i mu 1 can be determined simply from the fact that v1, that is the voltage on the primary terminals of the transformer, is equal to l mu one times d i mu one d t. And therefore, i mu one is simply equal to 1 over i mu 1, the integral of dt. Assuming that is some rectangular rear voltage that supplied to the primary of this transformer, as would be the case in a full bridge type can order, than i mu 1 Is simply going to look triangular, and its amplitude would be proportional to the area under the v1 curve. During the time that v1 is positive, the current mu 1 will ramp up and when v1 is negative, i mu one will ramp down, hence i mu one will have a large ac content, as a result the B-H loop produced in the case of a transformer will enclose a large area unless the fluxswing is limited to well below The saturation level of the material. So just like in the ac inductor, the core losses and the ac winding losses in the transformer will also be significant. Therefore the flux density in the case of the transformer will again be constrained by the need to limit core losses. However unlike the ac inductor, the transformer is not required to store any energy, so we don't need to employ any air gap in the design of the transformer. Now that we have a high level view of the type of thinking that goes into the design of a magnetic device we can go into the details of a specific magnetic device and see how that gets done.
