Optimize Flyback Magnetics to Empower the PD

Mar 23, 2007 2:58 PM
By John Gallagher, Field Applications Engineer, Pulse Engineering, San Diego

Design Example

For simplicity, the equations will be designed for a PoE input (33 V to 57 V) with a single output (5 V/12 W) switching at 200 kHz. It will be assumed that the primary switch voltage drop (V_S1) is 0.4 V, the secondary switch voltage drop (V_S2) is 0.3 V and that the overall efficiency is 90%. Multiple output applications can use the same design procedure by selecting one of the outputs as the master and combining all of the output power onto this one output. This will allow the selection of the duty cycle, primary inductance, turns ratio, primary peak and root-mean-square (rms) currents. The only difference is in calculating the rms currents on each of the secondary windings. This requires careful attention to the secondary waveforms of each output.

Step One
Select a maximum duty cycle, calculate the resultant turns ratio and analyze the voltage stresses on the primary and secondary switches. If the stresses are too high, the duty cycle can be adjusted and/or the switch ratings can be increased.
Select a duty cycle maximum equal to 45%.
Calculate the turns ratio using Eq. 15 and assuming that t_DEAD=0:

Select the actual turns ratio of N_PRI/N_SEC = 5.
Recalculate the actual duty cycles based on actual turns using Eq. 15:

Analyze the voltage stresses using Eqs. 8 and 17:

Assuming V_LK=0.33V_IN: V_S1=1.3357+5.335=100 V.

Step Two
Calculate the primary inductance at the boundary condition and select inductance for application. If discontinuous, recalculate the actual duty cycles.
Calculate the boundary inductance for discontinuous mode (DCM) using Eq. 33:

Calculate the boundary inductance for continuous mode (CM) using Eq. 34. Assuming that I_OUTMIN = 0.5 3 I_OUTMAX:

Select the inductance for application with a 5% margin:

For DCM operation, the inductance chosen will affect the dead time (t_DEAD) and, therefore, the actual duty cycles.
Recalculate the DCM duty cycle using Eq. 31:

Calculate the off time (D_OFF= t_OFF/T) from Eq. 15:

Step Three
Calculate the worst-case DI, I_PK and I_RMS for each winding.
Calculate the secondary ripple current from Eq. 11.
For DCM:

For CM:

For CM:

Calculate the secondary peak currents (I_PKsec) using Eq. 28.
For DCM: I_PKsec =

For CM:

For CM:

Calculate the secondary rms currents (I_RMSSEC)using Eqs. 22 and 24.
For DCM:
For CM:

For CM:

Calculate the primary peak current (I_PRIPK) using Eq. 9.
For DCM:

For CM:

For CM:

Calculate the primary rms current (I_RMSPRI) using Eqs. 21 and 23.
For DCM:

For DCM:

Note: For CM,
For CM:

For CM:

Typically, it is not the design of the transformer that leads to a nonoptimized flyback design, but rather a failure to calculate the design inputs correctly. Once the primary inductance, primary peak current, turns ratio and primary and secondary rms currents are known, the transformer can be designed following any standard procedure. Typically, a core size is selected and the number of primary turns (to achieve the inductance and peak current without saturating) is calculated.

Knowing the primary turns and the turns ratio sets the secondary turns. To minimize leakage inductance, it is necessary to interleave the primary and secondary windings and keep the windings to one layer per section by choosing the appropriate wire size and number of strands. Once the wire size and strands are selected, the rms currents, along with the core losses, can be used to calculate the total losses in the transformer. If the total losses are too high (due to temperature rise of overall efficiency), it will be necessary to select a larger core size. If the total losses are too low, a smaller core size may be evaluated.

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