Phasing
Since transformers are essentially AC
devices, we need to be aware of the phase relationships
between the primary and secondary circuits. Using our SPICE
example from before, we can plot the waveshapes for the
primary and secondary circuits and see the phase relations
for ourselves:
legend:
*: v(2) Primary voltage
+: v(3,5) Secondary voltage
time v(2)
(*)----------- -10 -5 0 5 10
(+)----------- -10 -5 0 5 10
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
0.000E+00 0.000E+00 . . x . .
1.000E-03 3.675E+00 . . . + * . .
2.000E-03 6.803E+00 . . . . + * .
3.000E-03 9.008E+00 . . . . +* .
4.000E-03 9.955E+00 . . . . x
5.000E-03 9.450E+00 . . . . *+.
6.000E-03 7.672E+00 . . . . * + .
7.000E-03 4.804E+00 . . . *.+ .
8.000E-03 1.245E+00 . . . * + . .
9.000E-03 -2.474E+00 . . * + . . .
1.000E-02 -5.864E+00 . *+ . . .
1.100E-02 -8.390E+00 . *+ . . . .
1.200E-02 -9.779E+00 .x . . . .
1.300E-02 -9.798E+00 +* . . . .
1.400E-02 -8.390E+00 . +* . . . .
1.500E-02 -5.854E+00 . + *. . . .
1.600E-02 -2.479E+00 . . + * . . .
1.700E-02 1.246E+00 . . .+ * . .
1.800E-02 4.795E+00 . . . + *. .
1.900E-02 7.686E+00 . . . . + * .
2.000E-02 9.451E+00 . . . . x .
2.100E-02 9.937E+00 . . . . x
2.200E-02 9.025E+00 . . . . *+ .
2.300E-02 6.802E+00 . . . . *+ .
2.400E-02 3.667E+00 . . . * + . .
2.500E-02 -1.487E-03 . . * + . .
2.600E-02 -3.658E+00 . . * + . . .
2.700E-02 -6.814E+00 . * + . . . .
2.800E-02 -9.026E+00 . *+ . . . .
2.900E-02 -9.917E+00 *+ . . . .
3.000E-02 -9.511E+00 .x . . . .
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
legend:
*: i(v1) Primary current
+: i(vi1) Secondary current
time i(v1)
(*)---------- -2.000E-04 -1.000E-04 0 1.000E-04 2.000E-04
(+)---------- -1.000E-03 -5.000E-04 0 5.000E-04 1.000E-03
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
0.000E+00 0.000E+00 . . x . .
1.000E-03 -2.973E-05 . . + *. . .
2.000E-03 -6.279E-05 . + . * . . .
3.000E-03 -8.772E-05 . + . * . . .
4.000E-03 -1.008E-04 + * . . .
5.000E-03 -9.954E-05 .+ * . . .
6.000E-03 -8.522E-05 . + . * . . .
7.000E-03 -5.919E-05 . +. * . . .
8.000E-03 -2.500E-05 . . + *. . .
9.000E-03 1.212E-05 . . . * + . .
1.000E-02 4.736E-05 . . . * .+ .
1.100E-02 7.521E-05 . . . * . + .
1.200E-02 9.250E-05 . . . *. +.
1.300E-02 9.648E-05 . . . *. +
1.400E-02 8.602E-05 . . . * . + .
1.500E-02 6.362E-05 . . . * . + .
1.600E-02 3.177E-05 . . . * + . .
1.700E-02 -4.998E-06 . . x . .
1.800E-02 -4.136E-05 . . + * . . .
1.900E-02 -7.246E-05 . + . * . . .
2.000E-02 -9.331E-05 . + .* . . .
2.100E-02 -1.019E-04 + * . . .
2.200E-02 -9.651E-05 . + * . . .
2.300E-02 -7.749E-05 . + . * . . .
2.400E-02 -4.842E-05 . . + * . . .
2.500E-02 -1.275E-05 . . x. . .
2.600E-02 2.428E-05 . . . * + . .
2.700E-02 5.761E-05 . . . * .+ .
2.800E-02 8.261E-05 . . . * . + .
2.900E-02 9.514E-05 . . . *. +.
3.000E-02 9.487E-05 . . . *. +.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
It would appear that both voltage and
current for the two transformer windings are in phase with
each other, at least for our resistive load. This is simple
enough, but it would be nice to know which way we
should connect a transformer in order to ensure the proper
phase relationships be kept. After all, a transformer is
nothing more than a set of magnetically-linked inductors,
and inductors don't usually come with polarity markings of
any kind. If we were to look at an unmarked transformer, we
would have no way of knowing which way to hook it up to a
circuit to get in-phase (or 180o out-of-phase)
voltage and current:
Since this is a practical concern,
transformer manufacturers have come up with a sort of
polarity marking standard to denote phase relationships. It
is called the dot convention, and is nothing more
than a dot placed next to each corresponding leg of a
transformer winding:
Typically, the transformer will come with
some kind of schematic diagram labeling the wire leads for
primary and secondary windings. On the diagram will be a
pair of dots similar to what is seen above. Sometimes dots
will be omitted, but when "H" and "X" labels are used to
label transformer winding wires, the subscript numbers are
supposed to represent winding polarity. The "1" wires (H1
and X1) represent where the polarity-marking dots
would normally be placed.
The similar placement of these dots next to
the top ends of the primary and secondary windings tells us
that whatever instantaneous voltage polarity seen across the
primary winding will be the same as that across the
secondary winding. In other words, the phase shift from
primary to secondary will be zero degrees.
On the other hand, if the dots on each
winding of the transformer do not match up, the phase
shift will be 180o between primary and secondary,
like this:
Of course, the dot convention only tells you
which end of each winding is which, relative to the other
winding(s). If you want to reverse the phase relationship
yourself, all you have to do is swap the winding connections
like this:
-
REVIEW:
-
The phase relationships for voltage and
current between primary and secondary circuits of a
transformer are direct: ideally, zero phase shift.
-
The dot convention is a type of
polarity marking for transformer windings showing which
end of the winding is which, relative to the other
windings.
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