---
title: "Choice of flux density in transformer design"
subject: "Electric Machine Design"
chapter: 3
key: "semester_5/electric_machine_design:transformer-flux-density-choice"
source: https://www.bctengineer.com/q/semester_5/electric_machine_design/transformer-flux-density-choice
site: BCT Engineering
---

# Choice of flux density in transformer design

Electric Machine Design · Chapter 3: Transformer Design

- Asked in: 2073 Shrawan, 4 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machine_design/transformer-flux-density-choice
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machine_design/chapter-3

## Question

How is the flux density in the design of transformer chosen?

## Short answer

Flux density is chosen high to reduce core size, but limited by iron loss, magnetizing current, noise and steel grade. Distribution transformers use 1.35–1.55 T (CRGO) or 1.1–1.35 T (hot‑rolled) for high all‑day efficiency; power transformers can use up to 1.75 T with CRGO.

## Answer

The maximum flux density $B_m$ in the core is chosen as high as possible to reduce the size and cost of the core, but it is limited by iron loss, magnetising current, noise and the type of steel.

#### Factors deciding $B_m$
1. **Core loss and efficiency:** hysteresis loss ∝ $B_m^{1.6}$ and eddy loss ∝ $B_m^2$. Higher $B_m$ means more iron loss and lower all-day efficiency.
2. **Magnetising current:** near the knee of the B–H curve the mmf rises sharply, so $I_0$ and its harmonics increase.
3. **Type of transformer:** distribution transformers are energised 24 h, so a lower $B_m$ is used to keep iron loss low. Power transformers can use higher values.
4. **Grade of steel:** cold-rolled grain-oriented (CRGO) steel has low loss and high permeability along the grain, so it allows higher $B_m$ than hot-rolled steel.
5. **Over-voltage and frequency:** margin is kept so the core does not saturate at overvoltage or reduced frequency.
6. **Noise:** magnetostriction hum increases with $B_m$.

#### Usual values
| Steel / transformer | $B_m$ (Wb/m²) |
|---|---|
| Hot-rolled silicon steel, distribution | 1.1–1.35 |
| Hot-rolled, power transformer | 1.25–1.45 |
| CRGO, distribution | 1.35–1.55 |
| CRGO, power transformer | 1.55–1.75 |

So $B_m$ is a compromise between a small core (high $B_m$) and low iron loss, low no-load current and low noise (low $B_m$).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Higher Bm leads to:
   A. Lower iron loss
   B. Higher iron loss and magnetising current
   C. No change
   D. Lower noise
   Answer: B. Hysteresis ~ Bm^1.6 and eddy ~ Bm^2. (Key point: Iron loss dependence)

2. Why is a lower Bm used in distribution transformers?
   A. They are larger
   B. They use air cooling
   C. They are energised 24 h so iron loss must be low
   D. They have higher voltage
   Answer: C. Low iron loss improves all-day efficiency. (Key point: Distribution vs power)

3. CRGO steel compared to hot-rolled allows:
   A. Lower Bm
   B. Higher Bm due to low loss and high permeability
   C. No change
   D. Higher eddy loss
   Answer: B. CRGO has low loss along the grain. (Key point: Steel grade)

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