# 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

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

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

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.

For calculations and complete step by step hardware design and implementation of small transformer (Click Here)

## 19 thoughts on “Turns per Volts Derivation Transformer Design”

1. subaiyyal Bin Sabir says:

ϕ(t)=ABsin(ωt)
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.

2. subaiyyal Bin Sabir says:

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

3. kudzai mataya says:

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

4. subhan says:

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.

5. 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

6. Bobby says:

pls explain how you did this:
from dϕ(t)dt=ωABcos(ωt) how did u get to dϕ(t)dt=2πfABm. what happened to coswt
thanks

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

2. Eshan says:

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

1. Eshan says:

Sry wt=0 so cos0=1

7. SUDARSHAN says:

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

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

8. SUDARSHAN says:

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.

9. Jimmy Lalani says:

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