Single-Phase Transformer
Design Calculator
Compute turns ratio, core area, winding data, copper & iron losses, and voltage regulation.
Input Parameters
Primary Voltage (V₁) V
Secondary Voltage (V₂) V
VA Rating VA
Frequency Hz
Core Type
Current Density (J) A/mm²
Winding Resistance — Primary (R₁) Ω
Winding Resistance — Secondary (R₂) Ω
Load Power Factor
Iron Losses (P_fe) W
Turns Ratio (a)
2.09
N₁ / N₂
Efficiency
96.4%
at full load
Core Area (Ac)
12.4
cm²
Regulation
3.2%
at full load
Copper Loss: 23.2 W
Iron Loss: 15.0 W
Total Loss: 38.2 W
Winding & Core Data
| Parameter | Value |
|---|
Three-Phase Transformer
Design Calculator
Star/Delta configurations — per-phase and line quantities, losses, and voltage regulation.
Input Parameters
Primary Line Voltage (VL1) V
Secondary Line Voltage (VL2) V
3-Phase kVA Rating kVA
Frequency Hz
Primary Connection
Secondary Connection
Core Type
Current Density (J) A/mm²
Per-Phase R₁ (referred) Ω
Per-Phase R₂ Ω
Load Power Factor
Iron Losses (total) W
Turns Ratio (a)
—
N₁ / N₂
Efficiency
—
at full load
Core Area (Ac)
—
cm²
Regulation
—
at full load
Cu Loss: — W
Fe Loss: — W
Total: — W
Per-Phase & Line Results
| Parameter | Value |
|---|
Design Formulae Reference
All equations used in the transformer design calculations.
Turns Ratio
a = N₁ / N₂ = V₁ / V₂
N₁ = V₁ / (4.44 × f × Bm × Ac)
N₂ = V₂ / (4.44 × f × Bm × Ac)
N₁ = V₁ / (4.44 × f × Bm × Ac)
N₂ = V₂ / (4.44 × f × Bm × Ac)
where f = frequency (Hz), Bm = max flux density (T), Ac = core cross-section area (m²)
Core Cross-Section Area
Ac = V₁ / (4.44 × f × Bm × N₁) m²
For design: Ac ≈ √(kVA / (2.22 × f × Bm × J × Kw)) m²
For design: Ac ≈ √(kVA / (2.22 × f × Bm × J × Kw)) m²
Kw = window utilisation factor ≈ 0.3–0.4
Winding Currents
I₁ = VA / V₁ (primary)
I₂ = VA / V₂ (secondary)
a_wire = I / J (conductor x-section mm²)
I₂ = VA / V₂ (secondary)
a_wire = I / J (conductor x-section mm²)
Voltage Regulation
%VR = (V_NL − V_FL) / V_FL × 100
Approximate:
%VR ≈ ε_R·cosφ + ε_X·sinφ
where ε_R = (R_eq × I₂) / V₂ × 100
ε_X = (X_eq × I₂) / V₂ × 100
Approximate:
%VR ≈ ε_R·cosφ + ε_X·sinφ
where ε_R = (R_eq × I₂) / V₂ × 100
ε_X = (X_eq × I₂) / V₂ × 100
Losses
P_cu = I₁²R₁ + I₂²R₂ (copper loss)
P_fe = P_h + P_e (iron/core loss)
P_h = hysteresis, P_e = eddy current
P_total = P_cu + P_fe
P_fe = P_h + P_e (iron/core loss)
P_h = hysteresis, P_e = eddy current
P_total = P_cu + P_fe
Efficiency
η = P_out / P_in × 100 %
P_out = VA × cosφ (output power)
P_in = P_out + P_cu + P_fe
Max efficiency when P_cu = P_fe
P_out = VA × cosφ (output power)
P_in = P_out + P_cu + P_fe
Max efficiency when P_cu = P_fe
Three-Phase — Star (Y)
V_phase = V_line / √3
I_phase = I_line
S = √3 × V_L × I_L
I_phase = I_line
S = √3 × V_L × I_L
Three-Phase — Delta (Δ)
V_phase = V_line
I_phase = I_line / √3
S = √3 × V_L × I_L
I_phase = I_line / √3
S = √3 × V_L × I_L
Transformer Design Guide
Step-by-step procedure for transformer design using the output-coefficient method.
Design Procedure
| 01 | Choose core material & determine Bm |
| 02 | Select current density J (A/mm²) |
| 03 | Calculate output coefficient Kva = 4.44 × Bm × J × Kw |
| 04 | Determine core cross-section area Ac |
| 05 | Compute EMF per turn: Et = 4.44 × f × Bm × Ac |
| 06 | Calculate N₁ and N₂ from V₁/Et and V₂/Et |
| 07 | Determine winding currents I₁, I₂ |
| 08 | Calculate conductor cross-sections a₁, a₂ |
| 09 | Compute copper loss, iron loss, regulation, efficiency |
Typical Design Values
| Current density J | 1.5 – 3.5 A/mm² |
| Window util. factor Kw | 0.3 – 0.4 |
| CRGO Bm | 1.5 – 1.7 T |
| Efficiency (large) | 97 – 99 % |
| Regulation (dist.) | 2 – 5 % |
| Stack factor | 0.85 – 0.95 |
Core Material Comparison
| Material | Bm (T) | Loss |
|---|---|---|
| CRGO | 1.6 | Low |
| HRGO | 1.4 | Medium |
| Ferrite | 0.35 | Very Low (HF) |
| Amorphous | 1.5 | Ultra Low |