# I found an outstanding coil/transformer reference.



## ga2500ev (Apr 20, 2008)

This transformer/coil tutorial is the best that I've found on the net so far. Talks about the process of selecting cores and winding coils and transformers in plain language. With this I think I can finally start working on the magnetics I need for chargers, DC/DC converters, and other power electronics.

Thought others would be interested.

ga2500ev


----------



## major (Apr 4, 2008)

ga2500ev said:


> This transformer/coil tutorial is the best that I've found on the net so far. Talks about the process of selecting cores and winding coils and transformers in plain language.
> 
> Thought others would be interested.


Took a cursory read through it. Looks good  But I didn't see Q mentioned at all 

Thanks.


----------



## ga2500ev (Apr 20, 2008)

*Re: (inductor question) was: I found an outstanding coil/transformer reference.*

I'm just trying to fill the black hole in my power electronics knowledge. I'm coming to an understanding of why of all the major components in power electronics:

switches
caps
diodes
sensors
control systems (generally microcontrollers)
fuses
batteries

that inductors are the most crucial element, and yet the least understood. With virtually all of the other items on the list, specifications are generally fairly clear, and more importantly it's possible to get a standard part COTS given those specifications. With inductors, neither are true. The document above does give some better indication of how to specify what type of magnetics one needs. But the practice of it isn't straightforward.

Let me give an example. I'd like to build a DC/DC converter that accepts input from a nominal 72-156V pack and can deliver 40A of continuous current at 14V with 5% ripple current maximum. Now I think we all know that we can use a buck, forward, or flyback converter. For simplicity of the exercise let's use a buck configuration (though in reality because of wanted isolation properties, a flyback would be a better choice). So one digs up the hundreds of sites of discussion of buck converters and come up with a diagram similar to this one:










from this page. The specifications of the other items are not too terribly complicated in terms of probably one or two 200V mosfets in a TO247 package that can handle the current, a 50A ultra fast recovery diode with 200 PIV, and a collection of low ESR caps for both the input and the output sides, Throw in a fuse and either a microcontroller or dedicated switching regulator for the control with a 50A hall effect current sensor and a precision resistor voltage divider for the output voltage sensing and you're pretty much set... except for the inductor. As specified on the page:



> The main question when designing a converter is what sort of inductor should be used. In most designs the input voltage, output voltage and load current are all dictated by the requirements of the design, whereas, the Inductance and ripple current are the only free parameters. It can be seen form Equation 1, that the inductance is inversely proportional to the ripple current. In other words, if you want to reduce the ripple, then use a larger inductor. Thus, in practice a ripple current is decided upon which will give a reasonable inductance.
> 
> There are tradeoffs with low and high ripple current. Large ripple current means that the peak current is ipk greater, and the greater likelihood of saturation of the inductor, and more stress on the transistor.
> 
> So when choosing an inductor make sure that the saturation current of the inductor is greater than ipk. Likewise, the transistor should be able to handle peak current greater than ipk. The inductor should also be chosen such that the it can handle the appropriate rms current.


and this is where the confusion begins. While it's possible to compute the appropriate inductance in Henries using the ripple current, and that an inductor is little more than some type of wire wrapped around some type of core, frankly trying to figure out all the parameters is like taking a walk through NerdLand:

What impact does the switching frequency have upon the inductor? Rule of thumb is higher frequency means smaller inductors. But what's the actual relationship?

What type of core? There are laminated sheets in EI and EE configurations. There are toroids. They can be made of ferrite or powdered iron. They have different permeabilities based on the type of material. Each impacts saturation current (which I finally figured out is the current at which the core is no longer effective and it's just like air, significantly lowering the effective inductance and spiking the switching current) and the number of turns of wire required to get the needed inductance.

What type of wire? Thin magnetic wire? Regular insulated wire? Regular uninsulated wire? Copper tape? What type of current can each hold?

Is it possible to get an inductor off the shelf? Or pull one from common switching equipment (dead PC power supplies). How does one know if it can do the job? How does one measure the inductance, saturation voltage, and current carrying capabilities of an unknown inductor anyway? To answer my own question a quick GoogleNator pulled up this DIY inductance meter that explains how to do it.

BTW major mentions Q. I know that it's a factor that is related to the resonance properties of an inductor. I'm pretty sure he didn't mention it in this particular tutorial because its focus is on the specification of inductors for converters of the type we are discussing, not tank circuits. So from my limited understanding of everything, Q doesn't have a significant impact on the design parameters of an inductor used in a converter circuit, where the energy storage and transferrance properties of the inductor are the critical need.

Like I said... black hole.

I'm determined to build my own power electronics. The initial page is an attempt to begin to bridge the virtually complete gap in my understanding of not how inductors work, but in how to pick the right one. In an ideal world, it would be



> Go and get a couple of different sizes of Amidon 43 material toroids from here. Use the Al value to determine the number of turns you need. Use formula X to compute the inductance you need based on the ripple current, formula Y to compute the number of turns, and formula Z to compute the saturation current. Ipeak is this for this inductor in this circuit. If you use G gauge wire, then it can carry current up to A amps. Good luck.


Every attempt to find this straightforward method has been a fail so far. Every page that attempts to describe how to do it wanders off into the weeds. Even the first page that I specified started well in terms of Webers and Tesla computations, But the further down it went, the more complicated it became.

At this point I feel I'm OK with computing the inductance in Henries for a circuit based on switching frequency, duty cycle, and ripple current. I understand how Al is used to generate the number of turns. I feel I'm still missing how to compute the saturation current and the ampacity of the wire required. I can see in the 10kW charger page that JackBauer isn't using 10,8, or 6 gauge wire in his inductors, even though the charger is carrying 50+ amps of current. Why is that?

Resistors are driven by V=IR and caps work on the RC constant, and ESR for heat and ripple current. They are somewhat easy to specify. What is the simple formula for inductors when it comes both to their usage in power switching circuits and their physical formulation from a core and wire?

No one dips their own resistors. No one picks cans, electrolyte, and aluminum foil to roll their own caps. No one builds their own lithium batteries (at least not yet). But inductors are a different breed. You either wind your own or know how to test ones that others have wound for an application. I'd really like to understand how to do that. BTW the original author I talked about does have a Practical Transformer Winding tutorial that discusses some of these issues.

Thanks for any assistance you can offer...


ga2500ev


----------



## ga2500ev (Apr 20, 2008)

*Re: (inductor question) was: I found an outstanding coil/transformer reference.*

I guess I'll follow up my own post. I'm wondering if it's possible to work backwards from the inductor to the switching frequency based on the allowable ripple current. It looks like the magic formula I've been looking for is actually specified. It's the relationship of voltage, ripple current, and the PWM Ton pulse time:

L = V * Ton / Iripple

and the converse

Iripple = V * Ton / L

Finally the computation we need is Ton:

Ton = Iripple * L / V

Now the post above specifies that of these that the Iripple and L are the free parameters. I see it differently. What I want to do is fix L, iRipple, and V and then figure out the switching frequency necessary to make it work. Just for reference I'm working with a Microchip SMPS presentation that I found online. I also figured out that since there's such a wide range of V for my example, I've decided to specify a maximum ripple current at the highest input voltage. So I need 5% ripple of 40 A, which is 2A at 144V max input voltage.

Now on to the inductor. They are fixable. The peak current is twice the average current, so we need 80A. Now I have a question here. When the amperage is specified for an inductor, that has to be the amperage of the output circuit right? Since the inductor is in the loop, there is an average of 40A @ 14V running though the inductor. For example I found this inductor at Digikey. 1.5 microhenries @ 83A. So let's plug in the numbers.

Ton = 2A * 0.0000015 H / 144V = 20.8 nS

Houston I think we have a problem... Ton also has to be related to the duty cycle, which is related to the relationship of the input/output voltages:

D = Vout / Vin

Ton = D/f = Vout/ (Vin * f)

f = Vout / (Vin * Ton)

f = 14/(144 * 20.8 ns) = 4.67 Mhz

This is clearly not working. I either have to up the ripple, or raise the inductance. So say I wanted to keep the ripple current the same and limit the switching frequency to 100 khz, with the 1/46 the speed above. I'd have to raise the inductance 46 times from 1.5 uH to 70 uH. So let's look for that...
Parametric search locates this inductor but it's specified at 3A.

So what is it that I'm missing? Obviously people are building high current circuits using inductors. They are not operating in the Mhz switching frequency.

The only good thing that I've seen so far is that these inductors are not too terribly expensive. But other than that, I'm just pretty confused as to how it actually really works.

Adding another reference for specifying inductors in power switching circuits.
ga2500ev


----------



## ga2500ev (Apr 20, 2008)

*Re: (inductor question) was: I found an outstanding coil/transformer reference.*

I think I may have stumbled into a better computation for computing L. Start with:

L = Vin * Ton / Iripple

and

Ton = (Vout / (f * Vin))

So substituting the Vin's cancel out and you're left with:

L = Vout / (f * Iripple)

I like this one better because while Vout is fixed generally, that tuning can happen by changing the frequency or the allowable Iripple. Also F and L (or Iripple and L) can be swapped if the inductor is fixed.

Useful formula.

ga2500ev


----------

