Transformer Design Reference
Design guidelines, core materials, and selection criteria
Transformer Types
Shell Type
Efficiency Medium-High
Leakage Flux Low
Cost Medium
Core Type
Efficiency High
Leakage Flux Medium
Cost Medium-High
Toroidal
Efficiency Very High
Leakage Flux Very Low
Cost High
Autotransformer
Efficiency High
Size Compact
Isolation None
Core Materials
| Material | Typical Bmax (T) | Frequency Range | Core Loss | Applications |
|---|---|---|---|---|
| Grain-Oriented Silicon Steel | 1.7 - 2.0 | 50 - 60 Hz | Medium | Power distribution, large transformers |
| Non-Oriented Silicon Steel | 1.5 - 1.8 | 50 - 400 Hz | Medium-High | Small power transformers, motors |
| Amorphous Metal | 1.4 - 1.6 | 50 - 20k Hz | Very Low | High-efficiency distribution transformers |
| Manganese-Zinc Ferrite | 0.3 - 0.5 | 10k - 1M Hz | Low at HF | Switch-mode power supplies, RF applications |
| Nickel-Zinc Ferrite | 0.2 - 0.4 | 1M - 100M Hz | Low at VHF | EMI suppression, RF transformers |
| Powdered Iron | 0.5 - 1.0 | 20k - 100k Hz | Medium-High | Inductors, noise filters |
Transformer Design Guidelines
Core Selection
- Select core size based on power rating and frequency
- For power transformers: 1.2-1.7 T flux density
- For high-frequency: 0.2-0.5 T flux density
- Area product method: Ap = Wa × Ac
- Window utilization: 30-45% for small transformers
Wire Selection
- Current density: 2-4 A/mm² for natural cooling
- Primary AWG: selected for full load current
- Secondary AWG: based on output current
- Use Litz wire above 50 kHz to reduce skin effect
- Insulation class determines temperature rating
Loss Minimization
- Core losses: proportional to fnBm
- Copper losses: I²R, use larger wire gauge
- Eddy currents: use laminated or powdered cores
- Hysteresis: use materials with narrow B-H loop
- Balance core and copper losses for optimal efficiency
Thermal Management
- Natural cooling: 10-40°C rise above ambient
- Forced air cooling: allows 2× higher current density
- Oil immersion: for high power density applications
- Surface area to power ratio: ~5-10 cm²/W for natural cooling
- Insulation class determines maximum temperature
Design Formulas
Turns Calculation
N₁ = (V₁ × 10⁸) / (4.44 × f × Bm × Ac)
Where:
N₁ = Number of primary turns
V₁ = Primary voltage
f = Frequency (Hz)
Bm = Flux density (Tesla)
Ac = Core cross-section area (cm²)
Core Area Product
Ap = (S × 10⁴) / (4.44 × f × Bm × J × Ku)
Where:
Ap = Area product (cm⁴)
S = Apparent power (VA)
J = Current density (A/cm²)
Ku = Window utilization factor
Core Loss
Pcore = Kc × fα × Bmβ × Weight
Where:
Pcore = Core loss (W)
Kc = Core loss coefficient
α, β = Steinmetz parameters
Weight = Core weight (kg)
Copper Loss
Pcu = I₁² × R₁ + I₂² × R₂
Where:
Pcu = Copper loss (W)
I₁, I₂ = Primary and secondary currents
R₁, R₂ = Primary and secondary winding resistances