# Derivation of Formula for Calculation of Turns per Volts of Transformer Design

For designing a transformer, we need certain number of turns on each side for a specific rating transformer. Voltages on each side have direct relation with number of turns. So, we are interested in finding voltage per turn and for designing, turns per voltage. This is obtained from basic voltage equation of transformer:

$$E=4.44fB_mA_i$$

This equation is derived from basic equations. Here, we are going to derive this.

As we know that emf induced is given by rate of change of flux:

$$e=N\frac{d\phi}{dt}$$

RMS value is linked with $$\sqrt{2}$$ with peak value i.e. $$e=\sqrt{2} E$$. So, putting this we get:

$$E=\frac {N}{ \sqrt {2} } \frac {d \phi }{dt}$$

$$\phi (t) = AB\sin(\omega t)$$

Taking derivative w.r.t t of above equation

$$\frac{d \phi (t)}{dt} =\omega AB \cos (\omega t)$$

for Maximum flux linkage

$$\frac{d \phi (t)}{dt}=2 \pi f A B_m$$

And we know that $$\omega =2 \pi f $$

$$E= N \frac{2 \pi f AB_m}{\sqrt{2}}$$

This is total emf induced. But we are interested in voltage per turn. So, dividing both sides by total number of turns (N).

$$E_T=4.44fAB_m$$

We are also interested in finding turns per volts So,

$$T_E=\frac{1}{4.44fAB_m}$$

P.S: As for 3 phase transformers, this derivation is different so the factor 4.44 will not present there.

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Ï•(t)=ABsin(Ï‰t)

what is mean by A , B in above equation and how you name them A for area and B for flux density please explain it.

Sir can you please give me link or refer me detail for three phase transformer i have been working on this

i have seen the formula for getting the turns per volt but i still need area and magnetic flux density to calculate that how do i find those

how we can find out diameter of winding conductor in transformer

Diameter of winding conductor is measured by micro-meter screw gauge. The readings are then compared with standard table to check other specifications of conductor.

for turns ratio turns ratio = 1000000000*E/FAP4.44

F=Frequency

A= area of core

P=flux density

E=pressure

Are you trying to tell something or asking something ? Please explain so you can be entertained.

Regards

pls explain how you did this:

from dÏ•(t)dt=Ï‰ABcos(Ï‰t) how did u get to dÏ•(t)dt=2Ï€fABm. what happened to coswt

thanks

As we are taking maximum flux so this factor is taken as 1.

At max em produce at at=90 so cos90= 1

Sry wt=0 so cos0=1

Sure you can design transformer in Excel, there are no issue

Could you please enlighten us how you could design a transformer using Excel ??

Sir,

We design the power transformer but some transformer doing more hamming issue (noise issue) and we also design toroide choke but its burn after 1to 2 year we trying to find root causes but i cant find proper solution.

Humming sound in transformer is due to loosely bounded core strips. Make it tighter (do it by hammering). Further use varnish after completion.

Burning may be due to overloading or due to poorly designed core.

Can you please provide some information about calculation of parameters of Toroid/ Ring Transformer as I am doing my Thesis in it.

Thanks in advance.

i am doing a design of distribution transformer . working with my excel sheets doing the calculations ., & produce a best design for my company.

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