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Chapter 10
Off-line converters are derivatives of standard DC-DC converter topologies. For example, the
yback topology, popular for low-power applications (typically 100 W), is really a buck-
boost, with its usual single-winding inductor replaced by an inductor with multiple windings.
Similarly, the forward converter, popular for medium to high powers, is a buck-derived
topology, with the usual inductor ( choke ) supplemented by a transformer. The ﬂ yback
inductor actually behaves both as an inductor and a transformer. It stores magnetic energy as
any inductor would, but it also provides mains isolation (mandated for safety reasons), just
like any transformer would. In the forward converter, the energy storage function is fulﬁ lled
by the choke, whereas its transformer provides the necessary mains isolation.
Because of the similarities between DC-DC converters and off-line converters, most
of the spadework for this chapter is in fact contained in Chapter 3. The basic magnetic
deﬁ nitions have also been presented therein. Therefore, the reader should read that
chapter before attempting this one.
Note that in both the ﬂ yback and the forward converters, the transformer, besides providing
the necessary mains isolation, also provides another very important function—that of a
xed-ratio down-conversion step , determined by the turns ratio of the transformer. The
turns ratio is the number of turns of the input ( primary ) winding, divided by the number
of turns of the output ( “ secondary ” ) winding. The question arises—why do we even
feel the need for a transformer-based step-down conversion stage, when in principle, a
switching converter should by itself have been able to up-convert or down-convert at will?
The reason will become obvious if we carry out a sample calculation; we will then ﬁ nd
that without any additional help, the converter would require impractically low values of
duty cycle to down-convert from such a high input voltage to such a low output. Note that
the worst-case AC mains input (somewhere in the world) can be as high as 270 V. So when
this AC voltage is rectiﬁ ed by a conventional bridge-rectiﬁ er stage, it becomes a DC rail of
almost
2
270 382 V, which is fed to the input of the switching converter stage that
follows. But the corresponding output voltage can be very low (5 V, 3.3 V, or 1.8 V, and so
on), so the required DC transfer ratio ( conversion ratio ) is extremely hard to meet, given
the minimum on-time limitations of any typical converter, especially when switching at
high frequencies. Therefore, in both the ﬂ yback and forward converters, we can intuitively
think of the transformer as performing a rather coarse ﬁ xed-ratio step-down of the input
to a more amenable (lower) value, from which point onwards the converter does the rest
(including the regulation function).
10.1 Flyback Converter Magnetics
10.1.1 Polarity of Windings in a Transformer
In Figure 10.1 , the turns ratio is n n
P
/ n
S
, where n
P
is the number of turns of the
primary winding, and n
S
is the number of turns of the secondary winding. www.newnespress.com
297Off-line Converter Design and Magnetics
We have also placed a dot
on one end of each of the windings. All dotted ends of a
transformer are considered to be mutually equivalent. All non-dotted ends are also
obviously mutually equivalent. That means that when the voltage on a given dotted
end goes high (to whatever value), so does the voltage on the dotted ends of all other
windings. That happens because all windings share the same magnetic core, despite the
fact that they are not physically (galvanically) connected to each other. Similarly, all the
dotted ends also go low at the same time. Clearly, the dots are only an indication of
relative polarity. Therefore, in any given schematic, we can always swap the dotted and
non-dotted ends of the transformer, without changing the schematic in the slightest way.
+
+
V
INR
= − V
IN
/n
V
IN
V
IN
+ V
Z
V
IN
+ V
OR
1D
V
OR
= nV
O
I
LR
= I
L
/n
V
IN
I
LR
I
L
V
Z
C
IN
C
O
I
O
V
O
V
OR
I
LR
=
I
OR
1D
I
L
=
I
O
V
O
V
O
n = n
P
/n
S
0
X
X
n
P
n
S
Current in winding
Voltage at switching node
PRIMARY SIDE
SECONDARY SIDE
0
Figure 10.1 : Voltage and currents in a ﬂ yback

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