AND8112 Datasheet, PDF (6/12 Pages) ON Semiconductor – A Quasi-Resonant SPICE Model Eases Feedback Loop Designs

AND8112/D
(eq. 35)
t I1(t) u+ Vg
2
LP
ton2
NJ Nj D_t1 ) D_t2 ) ^ƪ(N
Vg))V^Æ«
V
ton
Similarly to the simplified model analysis, one can note
that the average input current is proportional to the input
voltage. The effective resistance Re is thus: Re(t_on) =
NJ Nj 2 LP
ton²
[(N
D_t1 ) D_t2 )
Vg) ) V]
V
ton
(eq. 36)
It is pleasant to confirm that if D_t1=D_t2=0, the Re(t_on)
expression reduces to equation 21…
Then, the equivalent circuit depicted in Figure 6 and based
on the loss−free resistor Re(t_on) can be applied. To complete
the model, let’s calculate <I_2(t)> by combining equations
(17) where d′ is taken equal to (t_demag/T_S), (13) and (31):
t
I2(t)
u+
1
N
Vg ton
2 LP
ton
TS
N Vg
V
(eq. 37)
Substitution of equation (32) giving T_S into equation (37),
leads to: <I_2(t)> =
Vg ton
2 LP
ton
Vg
D_t1 ) D_t2 ) ^ƪ(N
Vg))V^Æ«
V
ton
V
(eq. 38)
This expression can be simplified as follows: <I_2(t)> =
Vg
Re(ton)
V
Vg
) Vf
+t
I1(t)
u
Vg
V ) Vf
(eq. 39)
The model assumes a 100% efficiency power transfer. To
better stick to reality, the above expression should be
multiplied by the estimated efficiency to obtain the final
<I_2(t)> equation:
t I2(t) u+t I1(t) u
Vg
V ) Vf
eff
(eq. 40)
where eff is the efficiency.
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