Turns per Volts Derivation Transformer Design

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:


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:


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).


We are also interested in finding turns per volts So,


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


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Asad Ullah

I am MSc Electrical Scholar under a fellowship program. Working with Modeling and Simulation software related to my field are my activities in leisure.

14 thoughts to “Turns per Volts Derivation Transformer Design”

  1. 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

    1. 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.

  2. 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

  3. 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.

    1. 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.

  4. 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.

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

    1. Thank you for visiting our website.
      It's not clear to me either you are asking some help or providing feedback. Please elaborate your comments.

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