Optimize Flyback Magnetics to Empower the PD

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

Critical-Conduction Mode

It should be clear that the boundary between continuous mode and discontinuous mode, also known as the critical-conduction mode (CCM), occurs when the secondary of the transformer delivers all of the stored energy at the end of the switching period T (as shown at the bottom of Fig. 4c). In this case, t_DEAD is equal to zero:

T_ON + T_OFF = T. Or, using Eq. 1, T_OFF = (1 – D) 3 T.

If all of the stored energy is delivered to the output (minus system losses or efficiency), then:

where h equals efficiency.

P_OUT = I_OUT 3 (V_OUT + V_S2).

Simplifying gives: (Eq. 31)

(Eq. 32)

For any given application, there is a primary-winding inductance that will dictate if the transformer operation is discontinuous across the full output-current range (L_PRI < L_CCM), or if it is in discontinuous mode below some minimum output current, and in continuous mode (L_PRI > L_CCM) above this current.

Eq. 31 defines inductance at the CCM for a given duty cycle. Typically, a duty cycle is selected and the turns ratio is then calculated to produce the desired duty cycle. The turns ratio will affect the stresses on the primary and secondary switches. As shown in Eqs. 8 and 17, the turns ratio must be large enough to minimize stress on the S2 and small enough to minimize stress on the S1. This bounds the absolute maximum and minimum turns ratio.

Once the turns ratio is selected, the value of the primary inductance (L_PRI) is chosen to ensure that the transformer always runs in discontinuous mode up to the maximum output (I_OUTMAX) or that it runs in continuous mode down to some minimum output level (I_OUTMIN). As a result, Eq. 31 can be redefined as follows:

For discontinuous mode:

For continuous mode:

(Eq. 34)

It should be noted that in continuous mode, because there is no dead time, the turns ratio alone for a given input and output voltage sets the duty cycle. However, for discontinuous mode operation, the existence of the dead time means that duty cycle is affected by the turns ratio and the primary inductance.

The easiest way to illustrate the use of the previous equation is to run through a quick design example that will also illustrate the differences between the continuous mode and discontinuous mode flybacks.

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