# Transformer Design Turns per Volts

In previous article, we derived a formula for turns per volts of transformer winding for transformer design. That formula has core area involved in it. Now, we are going to derive a formula for transformer design turns per volts according to transformer ratings and depending upon type of transformer and magnetic flux required.

(In transformer design article, turns per volts are calculated using $B_m$ and area of core and we took some parameters constant and some assumption for designing small transformers.)

$Q = {VI}\times{10^{-3}} $ Q in kVA

$E_t=4.44f \phi$$

$E_t= 4.44fB_mA_i$

So, $Q=4.44f \phi I N\times 10^{-3} $

As, ratio of cross sectional area of core and cross sectional area of winding is constant So,

$\frac{A_i}{A_c} = Constant$

$\frac{\phi \sigma}{B_m IN}$

$\Rightarrow \gamma = \frac{\phi}{IN}$

Now,

$E_t=4.44f\sqrt{\frac{Q \gamma \times 10^3}{4.44 f}}$

$E_t=\sqrt{4.44 f Q \gamma\times 10^3}$ (Q is in kVA)

**$E_t=K_t\sqrt{Q}$ **

where, $K_t=\sqrt{4.44 f \gamma\times 10^3}$

Value of $K_t$ depends upon:

- Type of Transformer (Core or Shall Type).
- Material Employed in Construction
- Choice of electric and magnetic cooling of transformer

Value of $$K_t$$ greater for shall type as that of Core type transformer of same ratings because shell type need greater magnetic material.

For different type of transformer, depending upon $\phi $ and other requirements, following table is developed:

Type of Transformer Value of $K_t$3-$\phi$ Shell Type 1.3 3-$\phi$ Core Type 0.6~0.7 3-$\phi$ Core Type (Distribution) 0.45 1-$\phi$ Shell Type 1~1.2 1-$\phi$ Core Type 0.75~0.85

By using this Table and formula $$E_t=K_t\sqrt{Q}$$ we can estimate voltage per turn and by taking its inverse we can calculate turns per volts for designing transformer.

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So if E (Volt per turn) is proportional to root of Q (power Rating) it means, that If I want to rewind new transformer with higher power, let’s say 2 times (1kVA become 2kVA) using the same core I can reduce the winding number of turns by 0.88 times? With of course I must using conductor with 2 times of the original size both primary and secondary (cause of the current).

Where is the formula for calculating turn per volt?

This article was written to give explanation related to turns per volt value taken in transformer design calculation in http://engineerexperiences.com/design-calculations.html

As you can see end conclusion give you a table and a two constants. one constant Kt is derived and Q is your power ratings. if you put value of Kt (derived above) you can get the whole formula.