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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