AND8112 Datasheet, PDF (7/12 Pages) ON Semiconductor – A Quasi-Resonant SPICE Model Eases Feedback Loop Designs

AND8112/D
The following table summarizes the main equations upon which our model is based:
Delay between the power switch opening and the start of the ener-
gy transfer to secondary side:
D_t1 + LP
Ctot
Vg
)
V
N
Vg @ ton
Delay between the core reset completion and the next turn on of
the power switch (Note 1):
Equivalent input resistance:
Switching Frequency:
D_t2 + p ^ǸLP Ctot
NJ Nj Re(ton)
+
2
LP
ton²
[(N
D_t1 ) D_t2 )
Vg) ) V]
V
ton
fSW
+
D_t1
)
D_t2
1
) ^ƪ(N
Vg))V^Æ«
V
ton
Average input current:
Average output current:
t I1(t) u+ VgńRe(ton)
t
I2(t)
u+
Vg
V
t I1(t) u
eff
NOTE:
: even if the proposed value appears to us as the
optimal one, SMPS designers might make a
different choice for D_t2. That is why, if the model
proposes ^Dt2 ^{+ p ǸLP Ctot} as default
value, you can modify this simulation parameter
to stick to your application in case valley
switching is not considered.
Implementing the SPICE Model with the
Loss−Free Network
As exemplified by Figure 6, the model shall emulate an
input resistor being t_on dependent and then transmit a power
following equation 23. Different ways exist to implement
this topology in Spice. INTUSOFT’s IsSpice authorizes
behavioral resistors, e.g. following any particular ohmic
evolution with time, voltage, current etc. For instance, the
following code would be accepted by the simulator:
R1 1 2 R = 2.0 * v(1)^0.5 + 3.0*v(2)*time + v(2)*sqrt(temp)
Unfortunately, despite its obvious interest, this code is not
very portable and would constrain the model usage to
IsSpice only. Figure 9 offers a more practical association
using behavioral voltage and current sources [2]:
I₁
I₂
The input voltage source being supposed to emulate a
resistance, its expression shall be in the form of:
Et = I₁ x Re where Re is simply equation 22, thus:
Et + I1
2
LP (V ) N
ton V
Vg)
(eq. 41)
where t_on is an input port of the model, imposed by the
control loop. In the final model, this value will be derived
from L_P and the peak current given by the error voltage
divided by R_sense, where V, V_g and N are to be passed or
sensed by the model.
The output current source together with V₂ shall deliver
the output power as imposed by equation 22. Thus, i₂
generation shall follow:
(eq. 42)
I2
+
Rin(eq)
v2
i12 ₊ 2
LP (V ) N
ton V
Vg)
i12
v2
Also, one can introduce the efficiency by simply
multiplying the I₂ current source by {eff}, where eff is a
parameter entered by the user in the model. Hence, I₂ can be
written as:
2
I2 +
LP (V ) N
ton V
Vg)
i12
v2
eff
(eq. 43)
V₁
Et
Gd ^V2
Figure 9. Implementing the DCM Model via Two
Controlled Elements
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