I have to take issue with your statement that inductance varies with frequency. Inductance is a function of the materials and the construction, the same as resistance or capacitance. Inductive reactance is, of course, frequency dependant On 24 Mar 2016 18:51, "Byron Jeff" wrote: > This is going to be long. So I'll start with the core question for anyone > who finds this TL;DR. > > If you had to choose a single toroidal core for winding inductors for > one-off buck regulators with switching frequency range of 40-200 kHz, > amperage range for 0.5 - 10A, and Vin to Vout range of 3 to 35V, what siz= e > and material type of core would you choose? > > Power inductors and cores are an elusive subject for a hobbyist such as > myself. Unlike resistors, capacitors, and transistors, the sorts of > parameters and measurements for them are not necessarily commonplace. Als= o > often the use is with a prepackaged switching regulator where the > applications engineer for the part specifies a single or small range of > inductors that works for that application. > > My interest is rolling switching regulators with DIY extremely small volu= me > (one or two) projects. Some I want to do with discrete control using op > amps. Others I'd like to integrate with PIC firmware for additional > functionality. > > As a hobbyist often the design process is a bit less precise than the one= s > that a design engineer uses. As a simple analogy consider the lighting of > an LED. An applications engineer designing for thousands or millions of > units would go through a painstaking process of working through the desig= n > parameters, such as light output and required viewing angle, along with > cost to precisely specify a particular LED. Then given the LED parameters > such as forward drop voltage and maximum current, would then compute the > required resistance and wattage for the resistor. > > A hobbyist on the other hand would just pull an LED from the junkbox and = a > resistor that causes the LED to light up. If that happened to by a 470 oh= m > 1/2 watt resistor, then so be it. > > Now of course there are limits to the utility of that approach. Someone > picking a 470k resistor would not get the expected results. OTOH if the > input voltage is 48V, then the standard hobbyist approach would end up > smoking both the resistor and the LED. So a basic understanding of the > relationship of current drop across a resistance using V=3DIR and power u= sing > P=3DVI are helpful in understanding the basic parameters to getting the j= ob > done. > > Now a buck regulator isn't really a complicated circuit. The basic idea i= s > to use PWM to chop the input voltage generate an average output voltage. > Then an inductor and a capacitor are used to smooth the generated voltage > and current ripple that is generated by the chopping of the input. > Specifically the inductor is used to regulate the rate of change in curre= nt > for the circuit. So when the input voltage is switched in, the current > rises linearly, and correspondingly when the input voltage is removed, th= e > current drops linearly also. The average current around that ripple curre= nt > is the current for the regulator. > > Now the amount of change in the ripple current depends on two parameters: > the inductance of inductor and the switching frequency. Specifically the > relationship of inductance, output voltage, switching frequency, and ripp= le > current is: > > L =3D Vout / (f * Iripple) > > Where L is inductance, Vout is the output voltage, f is the switching > frequency, and Iripple is the amount of current ripple at the given > frequency. > > Now there are a couple of more useful formulas. First maps the chopping o= f > the input voltage to generate the output voltage. It's a linear > relationship of the duty cycle: > > DC =3D Vout / Vin > > And finally in order for the inductor to operate with continuous operatio= n, > the ripple current cannot exceed the output current. Usually the rule of > thumb is that the ripple current should be 25 to 30 percent of the output > current: > > RF =3D Iripple/Iout > > where RF is the ripple factor. > > OK so as an example my first project is a lead acid battery charger for 3= 5 > Ahr 12V power wheelchair battery. As with most lead acids that are sealed= , > the maximum current should limited to about 1/3 the AHr rating, which is = a > shade over 10A. The input is from a salvaged UPS transformer that generat= es > about 27 VDC. So with a charging output voltage/current of 14.4V at 10 am= ps > we get: > > Vout=3D14.4V > Vin=3D27V > DC=3D14.4/27 -> 53% > RF=3D0.3 > IRipple=3D10A*0.3 -> 3A > > This leaves two parameters unspecified, the switching frequency and the > inductance. These two are inversely proportional, so the faster you switc= h, > the smaller the inductor (and inductance) can be. > > Now this leads us down the rabbit hole on several fronts as there are > competing goals. Before I get to them, we need to have a discussion about > inductor construction. Anyone who would like to clarify any of this pleas= e > feel free. > > The basics of inductors is that it is a coil of wire that generates a > magnetic field. My hobbyist understanding is the amount of magnetic energ= y > that can be contained depends both on the number of turns in the coil and > also in the material that the coil is wrapped around. > > The best discussion that I've seen so far analogizes magnetic flux with > current. Just as resistors uses materials that resist the flow of current= , > there are materials that resist the flow of magnetic flux. This is known = as > reluctance. From my reading the inverse of this property is known as > permeability. > > The upshot is just as you would not expect to be able to transfer a lot o= f > energy across an insulator, that it's difficult to move magnetic flux > across materials with low permeability. Air is pretty much the worst. So = if > you wind a coil around air, the inductance will be small. > > So cores are used to lower the reluctance and allow a larger amount of > magnetic flux to flow, which raises the inductance. > > The second parameter is physical size. Simply put the more area a coil > encloses, the higher the inductance. > > However, inductance is frequency dependant. The higher the frequency you > change electrical flow across an inductor, the lower the inductance value= .. > > Finally just as a resistor heats up as you pass current across it, an > inductor heats up as it manages its magnetic field. This is known as a co= re > loss. It is both frequency and size dependant. > > Finally the last parameter is known as saturation. This is the point when > amount of magnetic flux maxes out in the inductor. Any more energy doesn'= t > get converted to magnetic flux. This causes the current to shoot through > the roof. > > So this is why choosing an inductor core is challenging. You need the rig= ht > material to get the right inductance. You need a material that doesn't ha= ve > too much of a core loss at the given frequency. You need a size that will > keep the inductor cool enough. And finally you need a material that doesn= 't > saturate at either the average nor peak current you plan to use the core > in. > > So back to the problem. Given the values we've seen so far, let's attempt > to keep the switching fequency to a moderate 100khz. This gives us the > following calculation: > > L =3D 14.4/(100000 * 3) -> 48 uH > > Now the next parameter is the number of turns to generate that inductance= .. > This is specified for cores using the value Al. Al is given in two forms: > inductance/1000 turns or inductance/(turns squared). I used the latter wi= th > the values from here: http://www.micrometals.com/pcparts/pc_l.pdf for som= e > micrometal iron powder cores. So for example the 2 inch core T184-52 has > Al =3D 159.0 nH/N^2 where: > > L =3D N^2 * Al > > So the number of turns is the square root of L/Al: > > sqrt(0.000048/0.000000159) -> sqrt(301.8) -> 17.3 > > Only full turns count. So 17 turns would be > 17^2 * 0.000000159 -> 45.9 uH > while 18 turns is: > 18^2 * 0.000000159 -> 51.h uH > > Note that in each case the impact since the L, f, and Vout are all fixed > would be a change in the ripple current and ripple factor. Since the 30% > ripple fact is a rule of thumb, a bit of error one way or the other won't > kill the project. > > OK, so this is where I get lost hence my original question. The reason fo= r > the wide range of current values and switching frequencies is so that the > inductance and ripple current can be adjusted to match the particular > project. Higher frequencies allow for smaller ripple currents, which > facilitates lower output currents. For example if the output current is 0= ..5 > amps, then at a 30% ripple factor the ripple current has to be 150 mA. Bu= t > if the other parameters (Vout, f, L) are fixed, there is no way to genera= te > that ripple current at 100 Khz. So you have to change the frequency. But > then that impacts the core losses, which changes the heating profile of t= he > core. > > So is there a core that will stay cool enough, not saturate, and can > generate the inductance I need across the range of frequencies and curren= ts > to do low voltage buck regulators? Right now it looks like using somethin= g > like an iron core type #52 in a large enough size (hence my T184-52 > example) may be able to pull it off since it's good up to about 250 Khz. > > Any suggestions? > > Thanks. > > BAJ > > -- > Byron A. Jeff > Associate Professor: Department of Computer Science and Information > Technology > College of Information and Mathematical Sciences > Clayton State University > http://faculty.clayton.edu/bjeff > -- > http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive > View/change your membership options at > http://mailman.mit.edu/mailman/listinfo/piclist > -- http://www.piclist.com/techref/piclist PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .