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core.  The drain to source voltage V
 across 
TOPSwitch
 is
nearly zero during this interval.  The output diode prevents
current flow in the secondary due to the transformer dot
polarity.  Since the transformer secondary  is isolated from the
output by the reverse biased diode D2, current is supplied to the
output from C1.
The second interval (2) of operation starts when 
TOPSwitch
turns off.  The energy stored in the magnetic field of the
transformer causes the voltage across both the primary and
secondary windings to reverse polarity.  In an ideal circuit the
primary current I
 instantly stops flowing while the secondary
current I
 instantly starts flowing  (it will be shown later how
important it is to consider non-ideal behavior).   The voltage
across the secondary winding is equal to the sum of the output
voltage and diode forward voltage.  The secondary voltage is
“reflected” back through the transformer turns ratio to the
primary winding.  Note that the drain to source voltage across
the 
TOPSwitch
 during this interval of operation is equal to the
sum of the reflected output voltage V
 and the input voltage
V
.  This reflected voltage must be taken into account when
selecting the transformer turns ratio to avoid excessive voltage
stress on 
TOPSwitch
.  The reflected voltage can also be used to
indirectly sense the output voltage of the supply from the
primary side of the transformer through a bias or control
winding referenced to the primary return, making primary side
control of the supply possible.
The energy stored in the primary inductance of the transformer
during the first interval of operation supplies current to the load
circuit during the second interval of operation and replenishes
the charge depleted from output capacitor C1 during the first
and third intervals.
The third interval (3) of operation occurs when the magnetic
field within the core has decayed to zero (I
SEC
 = 0).  No current
flows in the primary or secondary of the transformer (which
defines the discontinuous mode of operation).  Note that the
drain to source voltage across the 
TOPSwitch
 has decayed to the
level of the input voltage.  Since the stored energy of the
transformer has decayed to zero, the output load current is again
supplied by output capacitor  C1.
The energy delivered to the load each cycle by the transformer
is given by
1
2
E
L
I
P
P
=
×
×
×
2
η
thus the output power is defined by
P
L
I
f
O
P
P
S
=
×
×
×
×
1
2
2
η
where f
 is the operating frequency of the power supply, and 
η
is the efficiency.  Substituting the expression of Equation (1) for
I
 (with I
 = 0 and V
 = 0), and defining t
 as D/f
, where
D is the duty cycle, and f
 is the 
TOPSwitch
 operating frequency.
One obtains the expression
P
V
D
L
f
O
IN
2
P
S
=
×
×
×
×
2
2
η
(3)
In a power supply operating in the discontinuous mode, the
controller will adjust the duty cycle of the primary switch  to
deliver enough power to the load to maintain the desired output
voltage.  The duty cycle is a function of both the input voltage
and the output load.
Ideal Model (Continuous Mode)
Refer to Figure 7 for the characteristic waveforms for the
continuous mode of operation.  The reference circuit is the same
as in Figure 6.
The secondary current I
 does not decay completely to zero
as in  the  discontinuous  mode,  so  that  the  third  interval  of
operation  (3) does not exist.  The primary current I
 starts with
a current step equal to the final value of the secondary current
I
  reflected back through the transformer turns ratio.  The
drain to source voltage across 
TOPSwitch
 at the instant of turn
on is also different since the third interval has been eliminated
as previously discussed.  The reflected output voltage state
persists for the balance of the off cycle until 
TOPSwitch
 turns
on again.
In order to maintain a constant output voltage, the amount of
current ramped up in the primary inductance during the on time
must be balanced by the current ramped down during the off
Figure 7.  Ideal Flyback Converter Waveforms - Continuous Mode.
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PI-1736-021496
VIN
VDRAIN
IPRI
ISEC
VIN+VOR
Interval
1
2