Design of transformer core

Core design fixes the net iron area, the shape of the limb section, the stampings, and the yoke, so that the flux $\phi_m$ is carried at the chosen flux density with low loss and low cost.

1. Net iron area

From $E_t = K\sqrt{Q}$:

$$\phi_m = \frac{E_t}{4.44f},\qquad A_i = \frac{\phi_m}{B_m}$$

$B_m$ is chosen according to the steel: about 1.1–1.45 Wb/m² for hot-rolled, 1.35–1.75 Wb/m² for CRGO.

2. Shape of limb section

Windings are circular, so the limb is made stepped to fill the circle of diameter $d$:

(stacking factor 0.9). More steps use the circle better and shorten the mean turn, but increase labour. Square and cruciform cores are used for small transformers; 3 to 7 steps for large ones.

3. Stampings and stacking

• Thin silicon-steel laminations (0.35 mm or less), insulated by varnish or oxide, to reduce eddy loss.
• Stacking factor (net/gross area) ≈ 0.9.
• Joints are staggered (overlapped) or mitred at 45° (for CRGO) to reduce reluctance and loss at the corners.
• Large cores have cooling ducts between packets.

4. Yoke

• With hot-rolled steel, yoke area is made 15–20% larger than limb area to lower yoke flux density, loss and magnetising current.
• Yoke is usually rectangular: depth $D_y = a$, height $H_y = A_{gy}/D_y$.
• With CRGO, yoke area is equal to limb area (stepped yoke).

5. Window

The output equation gives the window area, $A_w = Q/(2.22 \text{ or } 3.33\,fB_m\delta K_wA_i\times10^{-3})$, with $H_w/W_w$ = 2 to 4. The core frame then follows: $D = d + W_w$, $H = H_w + 2H_y$, $W = 2D + a$ (3-phase) or $D + a$ (1-phase).