# Is it good to have many, few turns in an inductor?

#### Glebiys

##### Newbie level 6
Hi,

I'm selecting ferrite core to create a resonant inductor in an LLC converter.

Required parameters of the inductor:
1) Inductance - 18.2uH
2) Max current - 13A (3.3kW)
3) Frequency range(min-max) - 100-400kHz

I'm only now dealing closely with the construction of inductors.

After studying some information, I realized:
- The ferrite parameters indicate the value of the inductance per turn (AL), through it you can find out the final inductance: L = AL * N^2.

Since the inductor must be designed for high power and I have not yet quite accurately determined the method for calculating the overall power - I chose the PQ5050 (N87) ferrite, where the inductance of one turn is 6500nH. Based on the formula above and the required inductance, I got a value of 1.67 turns.

This confused me, since powerful inductors usually have many turns.

Ok, I thought it was due to the high cost of such ferrite and started looking for ferrites with lower AL values already having an air gap.

AL:
1) 1uH = 4.26 turns
2) 700nH = 5.09 turns
3) 100nH = 13.49 turns

Something is closer, but still it seems to me that something is wrong.

I found a similar powerful inductor. The diagram shows that it is big dimensional and there are many turns.

Question: Would a large number of turns on an inductor be better than a smaller number?
Or am I doing something wrong?

I have not seen powerful inductors with 1-2 turns.

Thank you!

#### barry

If you want a larger number of turns, then you'll need a different core. You've got three things you can control, pick two.

" Would a large number of turns on an inductor be better than a smaller number?" How do you define "better"?

You also need to consider DC current capacity, which will determine minimum wire size, and, thus, overall inductor size.

Glebiys

### Glebiys

Points: 2

#### KlausST

##### Super Moderator
Staff member
Hi,
How do you define "better"?
Cheaper, nicer, better availability..

It is 13A..thus one kind of "better" may be low loss. Shorter wires have less power dissipation at same diameter.

Klaus

Glebiys

### Glebiys

Points: 2

#### FvM

##### Super Moderator
Staff member
For an AC inductor of given core cross section, frequency, voltage and maximal core flux determine the minimal number of turns. The air gap is varied to adjust the inductance.

For > 100 kHz, the core flux has to be reduced according to the loss characteristic. You should also consider winding skin effect and e.g. use litz wire.

Glebiys

### Glebiys

Points: 2

#### Easy peasy

18.2uH, 13A ( peak ? - peak is the parameter you need to know )

energy - 1/2 L I^2 = size of inductor, at 400kHz you can have only 30-40mT peak else the core losses will be too great.

at 100kHz you can come up to 80mT, so if the applied volts / current to the inductor go down with freq you can incorporate this into the design ( as the flux will also drop with freq in that case )

All the energy is stored in the gap as energy = 1/2 B^2 Vol-core / Uo.Ur as Ur is high the energy stored in the core is low

for an air gap all the energy is in the gap = 0.5 B^2 Ae. Lg / Uo ( Uo = 4. pi E-7 )

Also at 400kHz you will need fine gauge litz wire ( 44 AWG ) else the skin & proximity effect will be too great ...

happy designing ...

Glebiys

### Glebiys

Points: 2

#### Glebiys

##### Newbie level 6
@barry , @KlausST , @FvM , @Easy peasy ,

Sorry to answer a little late. During this time, I additionally studied everything about inductors and began to better understand some of the details.

For this, I chose a ferrite of size RM14 with an air gap of 1 mm. Its clearance and area can provide non-saturation operation up to 27A (300mT) (approx.). Yes, my peak current - 13A.

B65887E0250A041

#### Easy peasy

Respectfully:

300mT @ 400 or even 100kHz will cook your core and the fringing B field near the air gap will cook your wire - build, test and try not to burn your fingers too much - happy designing ...
--- Updated ---

Can you get 3C96 material ( or even better 3C98 ) ? if an H bridge consider 2 chokes - one going to each totem pole - this has big RFI advantages too ... ( each choke then Lr/2 but same Ipk ) - also 40mT peak @ 400kHz is about state of the art unless you have significant cooling available ...

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Glebiys

### Glebiys

Points: 2

#### Glebiys

##### Newbie level 6
@Easy peasy, Thank you!

At the moment, I was planning to use only one inductor.

There is a more powerful (ETD)
B66367G2000X187

Approximately 9.8 turns and a maximum saturation current of 48A.

The only thing is that in its datasheet the AL and ue values are indicated only for half of the core (this is visible due to the g parameter in the dimensional drawing). It turns out that as soon as I connect the two parts of the core, the gap will double, and the resulting values AL, ue will change accordingly.

I searched for more details but couldn't find it.
As the gap increases - AL and ue has fall, there will be more turns.

At the same time, RM14, which I chose earlier - the datasheet indicates AL and ue, calculated for the final gap of the assembled core.

Is it possible to calculate the final values of AL and ue from the data of this core?

#### Easy peasy

AL = Uo. Ae / ( lg ) in nH / T^2 - for any gapped core with gap > 1mm

( however Bpk / dt = V / ( N. Ae ) where V = ave applied volts over dt )

Also - for the air gap in the core - the rest of the core can be ignored - Bpk = Ipk . N . Uo . /Lg Lg = gap

so for a given Ipk in the ckt, Bpk should be < 50mT for an AC choke at 100 - 400kHz ( even lower is good )

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Glebiys

### Glebiys

Points: 2

#### c_mitra

I have not seen powerful inductors with 1-2 turns.

Let us begin at the beginning.

Inductance depends on the core (permeability) and the number of turns. Not on the current or size. Basically a geometry effect.

When you specify the current, you need to ensure that the core does not saturate. In other words, higher current means higher core size (to keep the flux density low or within limits).

When you specify the frequency, you are concerned about the losses. Both core losses and winding losses. The loss is related to the area of the hysteresis loop. Higher frequency gets you proportionately higher losses. Also skin effect on the winding wires contribute to the losses.

So where we begin?

Begins with the wire size. 13A, 400 kHz, 1 uH. It may be wise to select Litz wire.

Select the core according to the power required.

Gapped core provides higher reluctance. Reduces chances of saturation of the core. But comes at a cost. manufactured cores comes with fixed gaps and they provide reliability and reproducibility.

Estimate losses. . Calculations may become iterative. So repeat the same calculations for lower losses with a new core.

Glebiys

### Glebiys

Points: 2

#### FvM

##### Super Moderator
Staff member
Approximately 9.8 turns and a maximum saturation current of 48A.

The only thing is that in its datasheet the AL and ue values are indicated only for half of the core (this is visible due to the g parameter in the dimensional drawing). It turns out that as soon as I connect the two parts of the core, the gap will double, and the resulting values AL, ue will change accordingly.

I searched for more details but couldn't find it.
As the gap increases - AL and ue has fall, there will be more turns.
The datasheet values are for a total air gap of 2 mm. If you want Al of 188 nH/n², you can either use two B66367G1000X187 parts or a combination of B66367G0000X187 and B66367G2000X187. If you want a lower Al value, the air gap has to be recalculated considering fringing fields. There are calculation tools like Ferroxcube SFDT or Epcos/TDK MDT. MDT claims to get correct values up to 3.5 mm air gap. A large air gap causes however excessive winding losses, even with litz wire.

Z

#### zenerbjt

##### Guest
Yes the AL value for a gapped core is for one gapped core half , fitted to an ungapped core half.

By the way...make life easy for yourself and use an offtheshelf gap size.....otherwise it costs much to get the ungapped cores grinded down......(if you do get them grinded, then you simply have to specify your desired AL value and they will put the necessary gap in there for you....they won't even let you specify a gap size...[unless you really scream and scream])
But yes you do have to know roughly how big the gap will be because too big a gap is a problem with leakage flux (fringing flux).

The magnetic design tool software that FvM tells about is the one i uses for the TDK cores (search under EPCOS for it). Its good for getting gap sizes……in fact, if you scale by the same ratios, you can also use it for the ferroxcube cores as they are the same size and shape.

In theory you can use reluctance equation to calculate your AL value for a core with a given gap…..but in practice, its not accurate and so you need the Magnetic design software tool.

But as said, don’t use a custom gap, use an offtheshelf gapped core…and use two inductors if need be, as Easy Peasy said.

*********************************************
If it helps, rather than remembering too may equations.........think of Amperes Law [N.I=H.dl], Faradays Law V = N.d(phi)/dt, Lenz’s Law V = L.di/dt
And common equations like

B = uo.ur.H; B=(phi)/A where phi = flux in webers

L = (N^2)/Reluctance

N.I = Flux.Reluctance

Reluctance = (Path Length in magnetic material) / [uo.ur.A]

Eg reluctance of gap = [gap length]/[uo.ur.A]

Where u0 = 8.854e-12 and ur for air is 1 and A = core cross sectional area

From the above common equations, you can figure out your Flux density etc.
If you want a feast of equations for SMPS…then here you are…

https://massey276.wixsite.com/maths
*********************************************************************************

By the way. You need to get the Watts/Volume vs Flux density graph for your core so that you can calculate the core loss. This graph will have lines drawn on it for various frequencies.

And by the way, we got some great ferrite cores from a place in China. I think (not too sure) it was called “Pairui” or “Fuantronics”, but I’m not too sure.

BTW, here is a nice course on SMPS with stuff on LLC

**********************
Regarding heating of a resonant inductor in an LLC….i once took apart a 3Kw EV charger (from a reputable company) with a 3Kw LLC inside it. They were using a well coupled transformer and external resonant inductor and even an extra external magnetising inductor aswell. The core for the resonant inductor was the same core as the LLC transformer core (probably because it was same height and could be gap padded to the metal case top). It was a PQ40/40 or PQ5050. What surprised me was that it was also gap-padded to a aluminium heat sink (gap pad thickness approx. 5mm). The aluminium heatsink was a kind of a “tombstone” (50mm*40mm*5mm thick) on the PCB alongside the resonant inductor. The PQ4040 is quite an open core, and so I was surprised to see they’d put a metal heatsink so close to it..and alongside the “Open” bit of the core…as you’d have thought it could have interfered with the flux around the PQ4040 resonant inductor.
***********************
By the way, I thinks its already been said above…with an LLC, you wont need to worry about 400kHz….as you will be in very light load if the frequency goes that high.
With most LLC controllers, you can set a maximum frequency above which you will not go....and if the load goes that light, it just goes into burst mode

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#### mtwieg

Stop worrying so much about AL and saturation and focus more on core loss and winding loss. Those are going to be your bottlenecks. But unfortunately they're trickier to model (especially winding loss).

I'd recommend looking at Wurth's REDEXPERT tool. It's a convenient way of estimating losses and temperature rise for all of their power inductors. You may actually find something that suits your needs. If not, it will give you an idea of what sort of size inductor you'll need.

Z

#### zenerbjt

##### Guest
Here is the Epcos (TDK) magnetic design tool

..you can use it to find the AL value for a given gap size.
--- Updated ---

I put PQ5050 in to it, with N87 core material, and it shows the Core loss per volume of core at the chosen frequency. Just note that the B value is the peak value, not the peak to peak value. In fact, at 100kHz, N87 material....the core loss is 23.4W/m^3....thats with a peak sinusoidal B of 50mT and at 25degC. Interestingly, at 100degC, the core loss goes down to 7.4W/m^3, which shows that core loss will not give a thermal runaway situation.

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#### Easy peasy

7.4W/m^3 = 7.4mW / cm^3 which is very low - are you sure you got the units right? kW/m^3 perhaps ... (?)

zenerbjt

Z
Points: 2

#### FvM

##### Super Moderator
Staff member
It's 10³ kW/m³ = W/cm³

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#### Easy peasy

24kW / m^3 = 24mW / cm^3 at 400kHz the loss will be raised by F^2.4 or 28 times

so 672 mW / cc

100mT pk & 300kHz = 390mW / cc & 500kHz, 50mT = 215mW/cc a PQ50 has 37.6cc giving

14.7 & 8.1 watts respectively for the total core losses - however these are best case with sinusoidal flux and applied volts - losses are higher for more aggressive edged drive volts ...

#### Easy peasy

Oops, from above " 7.4W/m^3 " actually = 7.7 uW / cm^3 which is why I was confused about the result being low ...

it is actually 7.4 W / cm^3 ( CC ) - but beware real world losses ...

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