We've discussed basic magnetics and we've also modeled the different types of losses in magnetic elements, including AC core loss, DC copper loss, and AC copper loss. Next we're going to talk about how to design inductors and transformers. We'll discuss some of the classic processes used to design inductors and transformers. Which are based on certain assumptions about which losses are dominant and what the key constraints are, really we should think of these as first pass designs. That still need to be further optimized after all the losses have been modeled. Really, there are many different types of magnetic devices that operate with different constraints. So I'm going to talk about a few of those right now. And their constraints arise from which losses usually are dominant, and also on things such as whether they have an air gap or not. Whether the flux density is chosen to simply avoid saturation, or whether it's something to be chosen to optimize loss. The first example is a filter inductor that has small ripple, such as the filter inductor and the buck converter that we talked about at the very beginning of this specialization. So, for example, in a continuous conduction mode buck converter, the inductor Is there to simply filter the switching harmonics. And we talked about inductors running in continuous conduction mode that have small inductor current ripple such as this. So the current waveform is dominated by its DC component and it has small ripple delta I. On the B-H loop of the inductor core material, we know from ampere's law that H is proportional to the winding current with some formula like this. If the current has small ripple, then H has small ripple as well. There'll be an average value of H that is proportional to the DC component of the current. And then there'll be some ripple superimposed that is proportional to the current ripple delta I. And on the B-H loop, we go around what's called a minor loop, a small B-H loop whose area is proportional to the ripple. In such a case, we expect the core loss to be small because it's proportional to the area of the B-H loop, which also is small. On the other hand, we've already discussed filter inductors and why we add air gaps to them. We'll generally use an air gap, so that the inductor does not saturate at its maximum current. So to design a filter inductor will have a structure such as this, with a core a winding in an air gap, it will have a magnetic circuit model such as this. We expect the core loss to be small. Also since the inductor current ripple is small, we don't expect to have much proximity loss just because the AC component of current is small. And so we expect the loss to be dominated by what's left, which is just the DC copper loss. The DC component of current put through the DC resistance of the wire. The other constraint in this case is that we don't want the inductor to saturate at its peak current. So we choose the air gap, and the operating flux density to be less than the value that saturates the inductor with some suitable margin. Another design choice is the selection of the core material. We could use a lower frequency core material. In this case, if the core loss indeed is small and a lower frequency core material may come with a higher saturation flux density, which would be an advantage in this case. Another type of inductor is an AC inductor. And here's an example of what we call a tank inductor, in which there's a resonant LC circuit whose voltage and current wave forms have large AC components. In fact, when the L is in series with the C there is no DC component, and all of the current is AC. So we think of this kind of inductor, an AC inductor as having large ripple and in this case no DC. If we sketch the B-H loop for this case, again H is proportional to current. So with large variations and current to go positive and negative, the B-H loop will have large positive and negative variations in proportion. We have a large area of our B-H loop, so there'll be significant core loss. With a large AC magnitude of current, there'll be significant skin and proximity loss as well. So we have to account for all of the AC losses in designing such an inductor. We'll still want to use an air gap to prevent saturation of the core. But we may need to reduce the flux density below saturation in order to reduce the core loss and we'll have to do a lot of work to minimize the proximity loss. Generally we'll want to use a high frequency material such as ferrite that can operate with large flux swings while maintaining sufficiently low core loss. A third type of magnetic device is a transformer, here's a conventional transformer as we've discussed in the past. Where here I've drawn it as an ideal transformer in parallel with the magnetizing inductance. In the transformer the magnetizing current ICBM is proportional to H and the core. Here's the primary voltage waveform, let's switch to like we might find in some kind of switching converter. When the voltage is positive, the magnetizing current increases, which makes us go up the B-H loop with increasing H. When the voltage is negative, the magnetizing current decreases, which makes us go down the B-H loop. In this example, As I've drawn it, there's a large area of B-H loop and so we may have significant core loss and we need to include that in our design as a constraint. On the other hand, we're not worried about saturation of the transformer, at least not by current. If you recall current is not what saturates transformers, It's too many volts seconds. So, current that goes in the primary we hope comes out the secondary and doesn't flow through the magnetizing inductance and therefore it doesn't cause saturation. So in a conventional transformer, the core loss is significant. We have large AC currents flowing in the windings, so copper loss, and AC copper, or proximity loss are usually important. We won't employ an air gap. The air gap simply reduces the value of magnetizing inductance but doesn't really add any benefit. Often we'll choose a reduced flux density to reduce the core loss in the constraint in the transformer design, then is reducing core loss rather than preventing saturation. And because core loss is significant, we may need to use a high frequency ferrite type material. Here's another device that looks at first like a transformer, but I would prefer to call it a coupled inductor. It's really two filter inductors that are wind on the same core. Here's an example with a two output forward converter. We're going to be talking about examples like this in more detail in upcoming weeks. This is a forward converter that has two outputs with two transformer secondaries and two inductors. There's a trick that you can actually wind the two inductors on the same core. You can design them to have DC with small ripple. In this case this two whining inductor needs an air gap to prevent saturation. If the ripples are smaller then the B-H loop is small. The B-H loop, H is proportional to the sum of the amp terms of the windings. And so we can design this a lot like an inductor with an air gap, but we have more than one winding which we need to account for. Yet another example is a discontinuous mode flyback transformer. This is also a two winding transformer except that really works like an inductor not a transformer. In this continuous mode the ripple is large, so we'll have primary current that ramps up to a large value and then turns off when the transistor turns off secondary current then flows out the diode. Also with large ripple and then we have a discontinuous interval at the end. The magnetizing current is the sum of the AMP turns of these two primary and secondary windings. This is proportional to the H in the core. So our B-H loop, generally is something with a large area that starts at zero, goes up to a peak and comes back down to zero like this. With large ripple, the core loss is significant. With large current ripple in the windings, the AC copper losses are significant, there's also a significant DC component. We need to worry about the peak flux density to not saturate the core so we need to use an air gap, but we need to control the core loss as well. We have to use a high frequency core material. Flyback transformer can be pretty challenging to design because all of the losses are significant and have to be controlled and modeled. So in the upcoming lectures now we're going to talk about how to design these different kinds of magnetic devices. We're going to start with classic design procedures, which really are first pass designs that make a lot of simplifying assumptions. Once we have a first pass design, then we're in a pretty good place where we can model all of the losses and try to refine our design to optimize the element.