For this Capstone design project, you will specify and design your own magnetics for your power converter. And you will simulate the magnetics in LTpsice. So the purpose of this lecture is to illustrate what is expected and how to do this. In the magnetic stimulations of the previous courses in this specialization we used the standard linear inductor model. Which doesn't saturate and you simply specify the value of the inductance. LTspice has a more complex model as well in which you can specify parameters about the course size as well as about the BH loop of the core material. And LTspice then will model saturation and hysteresis. So what we're expecting you to do for this project is to design your magnetics as in correspide of the specialization. And then enter your design into LTspice, so that the simulations of the magnetics are more realistic. Here on the first slide is an illustration of a generic BH loop. With the parameters that LTspice uses explicitly identified. So this is a BH loop that has history so sand saturation and LTspice requires parameters entered for the saturation flux density B sub S shown here. What's called the core u sub force, H sub C is a measure of the BH loop. And for what's called the rim flux density B sub R. And with those three parameters, LTspice will fit a BH loop model. To the given numerical values. So we have to enter these three things into our inductor model in LTspice. In addition there's four other things that we need to tell LTspice that relate to the geometry of the inductor core which are shown here. So A is the core cross sectional area. L sub m is the magnetic path length of the core. So if we have some core that looks like this then L sub M is the distance around the core like that. L sub G is the gap length. And N is the number of turns of the winding. Okay, so these are the things that you work out when you do the inductor design and they're the things that we enter into LTspice. Now these are the names given by LTspice, so A is the core cross-sectional area and so on. The dimensions are all in ks units so you have to convert to meters for the cross-sectional area and so on. There is a link here to a wiki on the LTspice site that gives more data. Our information about this model. But this is what you need to know. So instead of entering the value of the inductance in Henry's in LTspice. We enter all seven of these parameters in some form such as hc equals whatever it is and so on. So, here is an example, Ferroxcube 3F3 material, this is fairly well known and widely used material, core material. Here are its published B-H characteristics. They look a little funny because the horizontal scale changes right there, so that they can give me a more accurate plot at large values of H, of how it saturates. But the remnant flux is the flux where B is to equal to, or where H was equal to zero, so it's this value. The H sub C is the value of H when B is zero, so that's right here. And the saturation flux density is up here, and this saturation flux density depends on temperature. So, what we're going to use in this class is to take the saturation flux density to be 0.33 Tesla, which is where we are when the core is hot. So for your designs, we will use expecutees, these values and assume that everybody is designing with this 3F3 material. So you need to say B sub R is .12 tesla. H sub C is 12 amps per meter. And B sub S is .0.33 tesla. So, here's an example. This is the buck converter that was used as a simulation example at the beginning of the very first course in this specialization. So, I had a buck converter here with a linear inductor. It was a 40 inductor, no saturation was modeled during steady state. The peak current in the inductor which is shown here in red was somewhere between two and a half and three amps right there. And there was a turn on tangent where the inductor current got all the way up to a peak value between seven and eight amps. Okay, we did include a series resistance of 0.1 ohm or 100 miliohms in the simulation model. And these were the wave forms that we got in that lecture. So let's now design an inductor and simulate it as I'm expecting you to do in this course. So, we can use the case of GE design method from course five. We will take that the inductance a low current will be 40 microhenrys. The maximum current that we expect to operate at will be three amps. We will design for a flux density of .25 T when the current is three amps. And so we will have to have a larger current before we'll reach saturation. We'll design for a DC winding resistance of 50m. This gives about .5 W loss at three amps. And we'll choose a fill factor for our line of 0.5 as is typical. So here's the calculation for K sub G, it turns out that we need a core with having a K sub G of at least 1.59 times ten to the minus third centimeters to the fifth power. So what we will do is look on the list of available cores to pick a core that is at least this large. For this course, we have included a list of magnetic ferrite cores, they're standard core shapes, in a document called Appendix D. So for the design, for your designs you're allowed to use any core that you find in this appendix. So there are different core shapes pot cores EE cores and so one. For example we might choose to use an EE core. This column, second column is a list of a geometrical constance K sub G and units of centimeters to the fifth. And the EE16 on this list is the smallest EE core that has a large enough K sub G, greater than 1.59 times ten to the minus three. So let's pick that one. Okay, I will also point out while we're here that this Appendix D document also has a wire gauge. So American Wire Gauge table. That this standard round copper wire sizes along with their wire cross section area which is the bare area in the second column. So, when you design your inductor you can select a wire off of this list as well. Okay. So, we'll choose an EE16 core from that list. Here are the parameters from that Appendix D table. And with those parameters we can plug in the gauging design method to calculate the gap length. The number of turns, the wire gauge. So I need a wire bare area at least this much, which on the wire table is 22 gauge wire. And we can calculate what the DC resistance will be for our inductor winding 45 milliohms and include that in our LTspice model. We can draw a magnetic circuit model for our inductor in the usual way within MMF source equal to the amp turns of the winding. A core reluctant and an elegant reluctantance. This and the flux takes the place of the current through the loop. We can generally make the approximation that the core reluctance is much smaller than the gap reluctant and ignore it. And the express the amp turns of MMF of the winding as equal to the flux times the reluctance of the gap. Okay, finally we can for total flux express this as flux density B times the cross sectional area Ac. And for reluctance of the gap we can write that as the gap length divided by. Munoz times the air cross sectional area of the core or the gap. And the cross-sectional areas cancel out. Finally now, we can solve for b and if we do that then we get this expression shown here. Okay, so, to enter this model into LTspice, here's what we do. For our linear inductor we enter the inductor name, the nodes that it's connected to and just the value in henry's for the inductor. This is for the Netlist version, and for a non-linear model that includes this BH loop. And with its histories of saturation what you enter instead of the value is the seven parameters that we've now worked out and we don't give the value in microhenries. So basically where you would have entered the inductance the seven parameters. In this schematic capture version that probably all of you are using LTspice. [COUGH] Where you would enter the inductor value, you can enter the seven parameters. Or if you control right click on the inductor, it will give you additional spiceline entries and you can enter this things there. Either way will work. So here is a simulation now. Of the turn on transient when we put this saturating inductor model for L1. So the top trace here is the original trace that we had with a linear inductor. And you can see that we reach our peak current at between eight and ten amps. And the bottom trace is what we get with the saturating inductor. And you can see that when we get to around four amps the inductor saturates and all the sudden the current gets huge. So, the peak inductor current during the startup trangent is actually off scale on this plot. If you zoom back, you can see that it's about 75 amps. And it's limited just by the resistance of the wire and the resistance of the. Here's a magnified view during the turn on transient. The one of the ringings that happens while the current is settling down. And you can see that when we have currents below four amps the inductor has linear ripple. It doesn't saturate and it looks like the inductance is essentially constant. Recall that the slope of the inductor current is the applied voltage divided by the inductance. So if we have constant inductance and constant applied voltage, we get a constant slope. When the current gets larger and we start to saturate then what happens is that the inductance gets small as we approach the knee of the BH loop curve. And the slope gets large as a result. So, the current will increase very quickly as the inductor starts to saturate. So what we would like to do is to make sure that this doesn't happen. In practice when the inductor saturates, we get large currents that may blow up our. We can also plot the flux density, B(t). We use the formula that I derived on an earlier slide relating the flux density B to the winding current. So B is this collection of constants, mu zero n over the gap length, times the current. So what we can do is plug in the values of those constants. And for this design, this collection of constants turns out to be 1/12 Teslas per Amp. So B of t is equal to 1/12 times the i of t. And to get spice to plot this, what we can do is to enter a formula. So when we have the waveform plotted, we can right-click on this label and it will let us enter a formula there. So we can take i of the inductor current and divide by 12 and what we will get is a plot of b(t). So you can see that what our saturation flux density was point .33 Tesla, or 330 millitesla. And you can see that when the current gets close to that saturation value, the slope starts to change and we start to saturate. So this is a nice way you can check your designs and check your simulation to see what's going on inside the core. So you will be expected to design the inductors of whichever converter you choose. And to simulate them in LTspice using the saturating inductor BH loop model within spice.