AND8112/D

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4

Re(d) +

t V1(t) u

t I1(t) u

+

2

LP

d(t)

2

TS

(eq. 19)

However, in quasi−resonant converters, the power transfer

can re−arrange equation 9 to reveal

TS + ton

(N

Vg) ) V

V

(eq. 20)

By finally plugging equation 10 and 20 into 19, we obtain

Re(ton) +

2

LP

(V

) N

Vg)

ton

V

(eq. 21)

that Figure 5 portrays:

The average input waveforms of the switch can be modeled via

the above equivalent network.

Figure 5.

The two−port loss−free network where all the input power trans-

forms into output power.

Figure 6.

As reference [1] details, the apparent power consumed by

a 100% efficiency. Therefore, equation 19 can be re−written

by:

t P(t) u+t V1(t) u t I1(t) u+

(eq. 22)

t V2(t) u t I2(t) u+

Re(ton)

Our switch network can thus modeled according to the

so−called loss−free network where all the power developed

across an input resistance transfers to the output without any

loss (Figure 6) [1].

A More Complex Model Including Parasitic Effects

The above simplified model assumes that there are no

transient

times

between

the

conduction

and

demagnetization phases. A more precise modelling

approach requires that the two following delays

are taken into account, as highlighted by Figure 7 and 8:

Figure 7.

and makes the drain sinusoidally ring at the core reset

…

Core Is Reset!

1. At the end of the ON−time, the power switch

opens but the energy transfer to the secondary side

does not start immediately. The primary inductor

switch, charges the surrounding capacitive

Vg )

V

N

(eq. 23)

At that moment, the secondary diode starts to

conduct and current feeds the output capacitor. One

enough to consider that the primary inductor current

Vg )

V

N

(eq. 24)

Dt1 + Ctot

Vg )

V

N

IP

, i.e.: