The transformer for a flyback converter is used as the converters inductor as well as an isolation transformer.

# Variables and acronyms

• Universal constants
• Permittivity of free space (Wb A−1 m−1)
• (Wb A−1 m−1)

• Wire variables:
• , Wire resistivity (Ω-cm)
• , Total RMS winding currents (A)
• , Peak magnetizing current (A)
• , Max RMS current, worst case (A)
• , Allowed copper loss (W)
• , Cross sectional area of wire (cm2)

• Xformer/inductor design parameters
• , turns (turns)
• , Magnetizing inductance (for an xformer) (H)
• , Inductance (H)
• , Winding fill factor (unitless)
• , Core maximum flux density (T)

• Core parameters
• EC35, PQ 20/16, 704, etc, Core type (mm)
• , Geometrical constant (cm5)
• , Geometrical constant (cmx)
• , Cross-sectional area (cm2)
• , Window area (cm2)
• , Mean length per turn (cm)
• , Magnetic path length (cm)
• , or , Air gap length (cm)
• , Permittivity (Wb A−1 m−1)
• , Relative Permittivity (unitless)
Acronyms
• RMS: root-mean-squared - (where denotes the arithmetic mean)
• MLT: mean length turn
• AWG: American wire gauge

# Initial calculations

Variables
• - output voltage [V]
• - input voltage [V]
• - diode voltage drop [V]
• - transistor on voltage [V]
• - turns ratio [unitless]
• - duty cycle [unitless]
Calculate turns ratio

• Diode
• Rectifier:
• Schottky diode:

# Inductance calculations

The inductance of the transformer, , controls the current ripple.

Say you want a current ripple 50% of average current.

Solve for

let

The permittivity of free-space is so much larger than the permittivity the transformer material, that the magnetic path length, , can be estimated to be the air gap length, . so and

Solve for

Minimize total power loss:
Core loss:

The and are in the core material's datasheets

# Core calculations

## Core selection

Variables
• - power loss in the core []
• - saturation flux density []
• - max flux density []
• - change in flux density [], aka
• - winding area []
• - effective cross-setional area of the core []
• - Area Product []
• - window utilization factor, or fill factor [unitless]
• - number of turns on the primary [unitless]
• - number of turns on the secondary [unitless]
• - number of turns on the bias [unitless]
• - permittivity of free space (air) [H/m]

Material specifications
Grade [T] Specific Power Losses @100 °C [W/cm3] Manufacturer
B2 0.36 THOMSON
3C85 0.33 PHILIPS
N67 0.38 EPCOS (ex S+M)
PC30 0.39 TDK
F44 0.4 MMG

Calculate minimal AP needed

[]

• should be less than , to avoid core saturation. for example , then for a conservative calculation use
• Generally and
• Using for off-line power supplies is a good estimate
Calculate minimum number of primary and secondary turns
Calculate actual number of turn on the primary and secondary to be used.
• : Round up to the nearest integer
Calculate air gap

# Current calculations

Variables
• - Ripple current max peak
• - Ripple current min peak
• - pk-pk ripple current
Peak current

DC current

RMS current

AC current