 Semiconductor Components Industries, LLC, 2003
October, 2003 − Rev. 1
1 Publication Order Number:
AND8112/D
AND8112/D
A Quasi-Resonant SPICE
Model Eases Feedback
Loop Designs
Prepared by: Christophe Basso
Prepared by: Joel Turchi
ON Semiconductor
Within the wide family of Switch Mode Power Supplies
(SMPS), the Flyback converters represent the structure of
choice for use in small and medium power applications. For
compact designs and radio−frequency sensitive
applications, e.g. TV sets or set−top boxes, Quasi− Resonant
power supplies start to take a significant market share over
the traditional fixed frequency topology. However, if the
feedback loop control is well understood with this latter, for
instance via a comprehensive literature and SPICE models,
the situation differs for self−oscillating variable switching
frequency structures where no model still exists. This article
will show how a simple large−signal averaged SPICE model
can be derived and used to ease the design work during
stability analysis.
Quasi−Resonant Operation
It is difficult to abruptly dig into the analytical analysis
without giving a basic idea of the operation of a converter
working in Quasi−Resonance (QR). Figure 1 depicts a
typical FLYBACK converter drain−source waveform as you
probably have already observed. When the switch is closed,
the drain−source voltage V
DS
is near 0 V and the input
voltage V
g
appears across the primary inductance L
P
: the
current inside L
P
ramps up with a slope of
S
ON

V
g
L
P
(eq. 1)
When the controller instructs the switch opening, the
drain−source quickly rises and the energy transfer between
primary and secondary takes place: the secondary diode
conducts and the output voltage flies back on the primary
side, over L
P
. This “Flyback” plateau is equal to V
g
+ (V +
V
f
) / N, where N is the secondary to primary turn ratio, V the
output voltage and V
f
the diode forward voltage drop.
During this time, the primary current decreases with a slope
now imposed by the reflected voltage
S
OFF

(V V
f
)
N L
P
(eq. 2)
Figure 2 zooms on the simulated primary current (actually
circulating in the magnetizing inductor), showing how it
moves over one switching cycle.
ON OFF
Figure 1. A Typical FLYBACK Drain−Source
Waveform
Core is Reset
Valleys
V
in
Plateau:
(V
out
+ V
f
)/N
Leakage Inductance
OFF
Figure 2. The Primary Current Ramps Up and Down
to Zero in DCM
ON
0
I
peak
S
on
= V
g
/L
P
I
P
= 0, Reset
S
off
= (V + V
f
) / (L
P
x N)
When the primary current reaches zero, the transformer
core is fully demagnetized: we are in Discontinuous
Conduction Mode (DCM). The primary inductance L
P
together with all the surrounding capacitive elements C
tot
create a LC filter. When the secondary diode stops conducting
at I
P
= 0, the drain branch is left floating since the MOSFET
is already open. As a result, a natural oscillation occurs,
exhibiting the following frequency value:
F
ring

1
2 L
P
C
tot

(eq. 3)
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