How to calculate Toroidal Core Maximum VA capacity

[SanPhysics]

Hello San,
If I already have the transformer ready then how can I calculate the effective area Ac of the core?
My core Dimension are OD=80mm, ID=46mm H=30mm, 100VA
VA=5.0*J*Bm*f*Ac min*ID²*10-7

Hello Jimmy Lalani
Actual bare core dimension required for calculation, is your provided sizes are bare core or after transformer winding completed.please clarify.or proved primary and secondary VA rating.

 

[Jimmy Lalani]

Hello San,
The transformer winding is already completed.

 

[Jimmy Lalani]

try this approach

volts per turn is a good measure

e = n dΦ/dt
if Φ = A sin(100πt)
dΦ/dt = 100πAcos(100t)

so e = n_turns X 100πA cos(100t)
you know n = 755
and e = 230√2 cos(100t)

so A = 230√2cos(100t) / (755 X 100πcos(100t))
A = .00137 Webers

did i make any arithmetic mistakes? Took me several tries to get same answer twice in a row.. darn that Windows calculatordivide Webers by area of core in square meters to get Teslas

volts per turn divided by ω gets magnitude of flux,

0..305 / 100π = .000971 Weber RMS flux, which is .00137 peak, divide them by area of core to get flux density

volts per turn at your line frequency is a handy thing to know about a core.

Now - what do you get for your flux density ?

Hello Hardy Sir,
I was just going through the conversation for calculating Maximum VA capacity. I found this conversation. In this you have taken e=230sqrt(2) cos(100t). I am a bit confused. Normally we take e=Em sinwt. Then why is it so here? Sorry , if it seems a stupid question to ask.

Jimmy Lalani

 

[jim hardy]

. I found this conversation. In this you have taken e=230sqrt(2) cos(100t). I am a bit confused. Normally we take e=Em sinwt. Then why is it so here?

That was just an example of starting with an assumed flux instead of an assumed voltage.
Flux and voltage have a derivative relationship, do they not ? One can ssume any flux one wants and voltage will be its derivative . I started with sine because its derivative has same sign. And san said he has 230 volts RMS.(not peak) where he is.

 

[Jimmy Lalani]

Hello Hardy Sir,
Thank you very much. Now it is crystal clear in my mind.
However, if I assume Bm in order to calculate various parameters of transformer at the very begining, then later do I again have to find the new value? I asked few people and they said that my be I have to iterate until I get a suitable or final value? I could not understand what they meant? Can you please help me.

 

[jim hardy]

However, if I assume Bm in order to calculate various parameters of transformer at the very begining, then later do I again have to find the new value? I asked few people and they said that my be I have to iterate until I get a suitable or final value? I could not understand what they meant?

I don't know why they said that.

If you make a good guess at how much flux density your core will happily accommodate, then the magnetizing current required to produce it will be reasonable. For that reason you need to be aware of you core's flux capability when you choose your operating flux density.
Since cores are available in discrete sizes and number of turns is an integer, you may have to adjust your Bm slightly to get your desired voltage with a standard size core .

Here's an example from the internet, worked out by what appears to be a methodical student with a lot of common sense and a good "Do It Yourself" mindset:
:
:http://engineerexperiences.com/design-calculations.html

1. Core Calculations:
Calculate area of core (central limb) by using following formula:

Ai= area of core
F= operating frequency
Bm= magnetic flux
Te= turns per volts
(for derivation of this formula Click Here)
Assumptions:
So, we know the frequency of the power system. We need magnetic flux and turns per volts. For designing a small transformer magnetic flux is averagely taken as 1 to 1.2.
By putting values we will get the area of core.
Current density of copper wire is taken as 2.2 A / mm2 to 2.4 A/ mm2 (approximately).
So, putting values
F= 50 hz
Bm = 1.2 wb/m2
Te = 4 (turns per volts)

As, we are going to design a practical transformer so we must consider the core available in market. The standard Bobbins available in market practically is 1”x1”, 1.25”x1.5”, 1.5”x1.5” and so on. We took nearest core area available to our calculation. We took bobbin of 2.25 inch2 (1.5”x1.5”) or 0.00145161 meter square. We have the core area. We can calculate turns per volts using this area by following:
Putting f=50 hz; Bm = 1.2 wb/(m^2); Ai= 0.001451 m^2, we got:

here he shows pictures of the transformer he built and it's a pretty nice job...
http://engineerexperiences.com/hardware-design-.html

 

[Daniman]

I don't know why they said that.

If you make a good guess at how much flux density your core will happily accommodate, then the magnetizing current required to produce it will be reasonable. For that reason you need to be aware of you core's flux capability when you choose your operating flux density.
Since cores are available in discrete sizes and number of turns is an integer, you may have to adjust your Bm slightly to get your desired voltage with a standard size core .

Here's an example from the internet, worked out by what appears to be a methodical student with a lot of common sense and a good "Do It Yourself" mindset:
:
:http://engineerexperiences.com/design-calculations.html
here he shows pictures of the transformer he built and it's a pretty nice job...
http://engineerexperiences.com/hardware-design-.html

Why did he take the value of turns per volts=4.

 

[Tom.G]

Unfortunately Jim Hardy is now deceased, so he won't be answering.

I haven't been following the thread, but just from reading the last post it seems the calculation used an iterative approach; that is, take a guess at the unknowns, work the formulas, and see if all the constraints are met.

The 4 Turns-per-Volt ( T_e) was an initial guess (likely based on experience as being 'safe').
This was immediately followed by the calcualtion for the actual Turns-per-Volt which was found to be T_e = 2.6 for that particular core.

Cheers,
Tom