--- title: "Design of transformer core" subject: "Electric Machine Design" chapter: 3 key: "semester_5/electric_machine_design:transformer-core-design" source: https://www.bctengineer.com/q/semester_5/electric_machine_design/transformer-core-design site: BCT Engineering --- # Design of transformer core Electric Machine Design · Chapter 3: Transformer Design - Asked in: 2073 Chaitra, 6 marks - Video: [Module 3 Design of transformer Design of core](https://www.youtube.com/watch?v=pHtw-yBnQ_Y) — ANAND MELINAMANI - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/electric_machine_design/transformer-core-design - Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machine_design/chapter-3 ## Question Discuss in brief about the design of core of transformer. ## Short answer Core design fixes net iron area Ai = φm/Bm with φm = Et/(4.44f). Limb is stepped to fill the circular winding; stacking factor ≈0.9; yoke area 15–20% larger than limb for hot-rolled steel. Window area derived from output equation. ## Answer 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 $d$: | Core section | Net area $A_i$ | Largest stamping $a$ | |---|---|---| | Square | $0.45d^2$ | $0.71d$ | | Cruciform (2-step) | $0.56d^2$ | $0.85d$ | | 3-stepped | $0.60d^2$ | $0.90d$ | | 4-stepped | $0.62d^2$ | $0.93d$ | (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). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The net iron area is found from: A. Ai = Bm / phi_m B. Ai = Et Bm C. Ai = Q / f D. Ai = phi_m / Bm Answer: D. phi_m = Et/(4.44 f), Ai = phi_m/Bm. (Key point: Net area) 2. Why is the limb made stepped? A. To fill the circular winding space better B. To reduce stacking C. To increase eddy loss D. To save oil Answer: A. Windings are circular. (Key point: Stepped limb) 3. With hot-rolled steel, yoke area is: A. Equal to limb B. 15-20% larger than limb C. Half the limb D. Double the limb Answer: B. This lowers yoke flux density, loss and magnetising current. (Key point: Yoke area) 4. Why are laminations thin and insulated? A. To increase hysteresis B. To raise stacking factor above 1 C. To reduce eddy loss D. To reduce window Answer: C. Thin insulated laminations limit eddy currents. (Key point: Joints) ## Related in Electric Machine Design - [Core type versus shell type transformer](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Acore-vs-shell-transformer) — Electric Machine Design, chapter 3, asked 3× - [Leakage reactance of core type transformer](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Aleakage-reactance-core-type) — Electric Machine Design, chapter 3, asked 3× - [Requirements of transformer core material](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Atransformer-core-material-requirements) — Electric Machine Design, chapter 1 - [Per unit resistance drop of core type transformer](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Aper-unit-resistance-drop) — Electric Machine Design, chapter 3 - [Core, turns and conductors of 5 kVA transformer](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adesign-5kva-single-phase-core) — Electric Machine Design, chapter 3 - [Design: 100 kVA single phase, square core](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adesign-100kva-single-phase-square) — Electric Machine Design, chapter 3 ## Related in other subjects - [Transformer no-load and load operation, constant core flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aideal-transformer-noload-load-constant-flux) — Electrical Machines I, chapter 2, asked 5× - [T/F: rural design, transformer size first](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-rural-transformer-size-first) — Transmission and Distribution System Design, chapter 7 - [Design: 550 m head plant, transformer quotation](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2077-550m-quotation) — Power Plant Design, chapter 4, asked 3× - [T/F: urban design, transformer location first](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-urban-transformer-location-first) — Transmission and Distribution System Design, chapter 7