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

Variables and acronyms[edit | edit source]

  • 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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

Core selection[edit | edit source]

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[edit | edit source]

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

DC current

RMS current

AC current


Power Loss[edit | edit source]

References[edit | edit source]

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