# Ferrite Core Size Selection Method

#### sabu31

##### Full Member level 4 Hi All,

I am having a confusion regarding the method used for selection of core size for high frequency converters. I know there is Area Product Method and Core Geometry Method.
I studied core Geometry method presented in both mentioned in Transformer and Inductor Design Handbook by Col. McLyman and Another Presented in Fundamentals of Power Electronics by Erickon and Maksimovic.

In First method its using formula for Kg(electrical)= Energy^/(Ke*Alpha)
where
Ke=0.145*(output power )*(Bm)^2*10^-4
Alpha is regulation in %

In second method
Kg=(Rho*Lm^2*Im,max^2*Irms_tot^2*10^8)/(Bm^2*Pcu*Ku)
where

Pcu is copper loss
Bm is max flux density
Ku is winding utilization factor
Irms
Im is peak magnetising current
Lm is primary inductance
But both these valuations are giving different values of core geometry. Based on Geometrical size we are getting

Kg=(Core Cross Section)^2*(Winding Area)/(MLT) (Based on Erickson Formula)
Kg=(Core Cross Section)^2*(Winding Area)*Ku/(MLT)

However, despite the only difference in them being Ku. The calculated values of Kg requirement (based on electrical condition) is different from Kg (based on core specifications). From my calculation Erickson Kg method is giving values close to whats required and can be applied using manufacturer core specification datasheet. From Col. McLyman method I have to depend upon tables givnen in the book.

a ) Is there any thing missing in my understanding, why this difference is arising and whats correlation between them.
b) Secondly, in TI app note they are using Area Product Method .Using a definition given as

AP= (LmIscspk*Ifl/(Bm*Ku*J*10^-4))^4/3

There is another formula
Ap=2*Energy10^4/(Bm*J*Ku)

Which is more accurate or commonly used.

c) Which is the method commonly used by magnetics designers (Area Product or Core Geometry. And whats relating all different formulae

#### wwfeldman there is a fairly large tolerance in magnetics because of the tolerances of core
material properties, different wire gauges, winding patterns, insulation, etc etc

if you picked a core according to Area Product Method and another core according to
the Core Geometry Method, there is some fair certainty that both will work.

if you can, build both and test both
then choose which you like better

do this a few times, and you'll develop your own skills and preferences,
because that's the real difference between the methods.

#### Akanimo Hi,

The kg value that you calculate is the minimum Kg value required for your design. After you have calculated your Kg value, you need to select a core with Kg value higher than that which you have calculated. In fact, the immediately bigger core with lowest cost and board space should is the best choice.

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This is a first pass design that you initially use an arbitrarily estimated Rdc value. You are supposed to calculate the actual Rdc that you obtain as a result of your initial estimate of Rdc and then iterate. It is important to iterate to obtain an optimized Kg value. If you select an initial Rdc that is too low relative to the actual Rdc value, then your resulting Kg will be too large. On the other hand, if your initial Rdc estimate is too high, then your Kg will be too small and so your magnetics will saturate.

If you want to use the first pass Kg value, then use a small Rdc value. Sometimes however, this is an expensive choice to make.

#### Akanimo Hi,

The kg value that you calculate is the minimum Kg value required for your design. After you have calculated your Kg value, you need to select a core with Kg value higher than that which you have calculated. In fact, the immediately bigger core with lowest cost and board space should is the best choice.

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This is a first pass design that you initially use an arbitrarily estimated Rdc value. You are supposed to calculate the actual Rdc that you obtain as a result of your initial estimate of Rdc and then iterate. It is important to iterate to obtain an optimized Kg value. If you select an initial Rdc that is too low relative to the actual Rdc value, then your resulting Kg will be too large. On the other hand, if your initial Rdc estimate is too high, then your Kg will be too small and so your magnetics will saturate.

If you want to use the first pass Kg value, then use a small Rdc value. Sometimes however, this is an expensive choice to make.
I noticed that I was mentioning Rdc throughout. I mixed up Kg design methods for the inductor and the flyback transformer designs.

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See this document for a simple lab to gain a good insight for the Kg method.

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Hi All,
...
However, despite the only difference in them being Ku. The calculated values of Kg requirement (based on electrical condition) is different from Kg (based on core specifications). From my calculation Erickson Kg method is giving values close to whats required and can be applied using manufacturer core specification datasheet. From Col. McLyman method I have to depend upon tables givnen in the book.

a ) Is there any thing missing in my understanding, why this difference is arising and whats correlation between them.
There are a few differences other than Ku. From the two Kg methods, notice that the McLyman method uses (Ipk^2)^2 and the Erickson method uses Ipk^2*Itot^2.

Just write them out and you'd spot the difference.

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#### Easy peasy All methods end up being iterative - as judgement is needed as to freq and Bpk, and cooling available ....

At 100kHz, a Bpk of 100mT ( each way ) is a good starting point, depending on the ferrite ( or other ) you have in mind

Knowing the max volts on a wdg you can calc the turns, for a given core size you can then work out the wdg area avail to pri & sec etc, & length of wire,

then knowing the rms currents, you can work out the resistive losses ( pri & sec) this would give for the length of wire calc, just using P= Irms^2 . Rdc ( 25 deg C )

if the losses are too high - you need to migrate to a larger core

then - if you have the training you can consider the Rac ( skin effect ) in the wires you might choose to use in the Tx, and you will get higher losses again - in the wire.

and so on ... Rdc ( and Rac ) is 30% higher at 100 deg C for example ...

then there is proximity loss in the wdgs, due to wdg layout, and so on ...

#### sabu31

##### Full Member level 4 I noticed that I was mentioning Rdc throughout. I mixed up Kg design methods for the inductor and the flyback transformer designs.

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See this document for a simple lab to gain a good insight for the Kg method.

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There are a few differences other than Ku. From the two Kg methods, notice that the McLyman method uses (Ipk^2)^2 and the Erickson method uses Ipk^2*Itot^2.

Just write them out and you'd spot the difference.
Thanks Akanimo for the reply. I will explain my self clear with an example from infineon design

I will make my self clear through an example
Using Infineon Application Design for a DCM Flyback. I am using the calculated values in the design note
Vout 12V, fsw=65kHz, Po=25W. The values calculated are L=407uH, Ip_pk=1.53A, Ip_rms=0.58A, Is_rms=3.9 A ,Bm=0.3T Ku=0.3(Assumption), Alpha=2% (Pcu/Po*100) (Assumption)

Using Handbook method I am getting the following

E=0.5*L*Ip_pk^2, we obtain E=0.00047 Ws

Ke=0.145*Po*Bm^2*10^-4, we obtain Ke=0.000016 (I am not clear what 0.145 factor is about)

Kg(calculated)=E^2/Ke*Alpha= 0.0067 cm5

In Design note they have used E20/10/6(EF20)

Ae(cm2) Aw(cm2) MLT (cm) Ap (cm4) Kg(cm5)
EE20 0.321 0.34 4.12 0.10914 0.002551

The core geometry for this from the core and bobbin specification is 0.00255 cm5
[using formula based on core specification mentioned in handbook Kg= (Winding Area * Cross-Section ^2*Ku)/MLT]
As per handbook this core is not suitable

Now in in Method Mentioned in Erickson
Using Pcu=0.5W (0.5/25*100) (So that Alpha=2, and loss component is similar in both methods)
Rho=1.724*10^-6Ohm-cm
The Required Core Geometry based on power requirement using formula Kg=Rho*L^2*Ip_pk^2*Ip_rms^2*10^8/(Pcu*Ku*Bm^2)
The value obtained is 0.00749cm5
The calculated Core Geometry based on specifications Is = Winding Area * Cross-Section ^2)/MLT]
Kg=0.0085cm5 which shows the core is able to meet the requirements.

Now both the books are very well accepted. So what is wrong in my understanding of the method for calculation for core geometry using Handbook method. I like handbook method since it uses skin effect and fringing effect etc. However, I am not able to apply to data sheets of manufacturers. So what should be corrected in my assumptions/calculations.

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Thanks Easy Peasy for the reply. However, I wanted to know regarding core geometry calculations difference in method by Mc Lyman and Erickson. Which method do you use.

#### Easy peasy The methods are in fact exactly the same with some fudge factors built in for wdg fill factor for the "formula" approach, same as my method, except with my method you get to see exactly what you are doing, step by step, the formula approach leaves one in the dark a bit ...

In the real word core sizes and bobbin wdg sizes are stepped - so it makes a lot of sense to "get a feel" for the design by iteration ...

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formula's often a assume a current density that is not practical for high freq litz ...

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also - you should really use SI units ...

• sabu31

### sabu31

points: 2

#### sabu31

##### Full Member level 4 As I have to give design outside for fabrication. Trial process would require more time. So thought of having a generalized formula which can be applied to datasheet.

• Easy peasy

### Easy peasy

points: 2

#### Easy peasy " trial " process can be done with paper, pencil & calculator, iterating on paper gets you a lot closer to a real transformer that won't overheat ...

#### Akanimo I use AP for DCM and Kg method in Erickson's book for CCM. I do not have issues when I use them. I have not used the Kg method in McLyman's book before. However, I am going to look at everything together and come back with findings.