On Sat, 17 Mar 2018 12:44:53 +0000, Roger Hayter wrote:

Johnny B Good wrote:

====snip====


I can imagine the need for a 10A rated 240v supply which would require
a
400VA auto transformer in this case (40v difference at 10A) which could
easily weigh some 16 to 20 Lbs. Just as you described, not a
lightweight item. :-)

My knowledge of transformer theory was never very clear, but why is it
not rated for the total output, which might well be something like 10A
at 200v, 2000VA?


The main advantage of an auto-transformer over a conventional one with
isolated primary and secondary windings is that you only need to rate it
for the VA difference between input and output voltages.

The easiest way to explain this is to consider the equivalent derived
from, in this case, a 40v 10A rated secondary output 240v mains
transformer where the secondary winding is wired in series opposing to
the 240v live connection (voltage buck configuration) so as to provide
the required 200vac. Since the 40v 10A secondary is merely handling its
rated current and the mains live connection can handle whatever a 13A
fused outlet can supply from a ring main socket, the 240v primary is only
handling the 400VA load it is already rated for (its secondary winding is
only handling an opposing 40v at 10A leaving the mains to directly supply
a 240v 10A loading).

A purpose designed auto-transformer in this case would consist of a
single winding designed with appropriate tapping points of a common
neutral (0v reference end), 200v and a 240v tapping points (with possibly
other tap voltages such as 210, 220, 230 and 250 volts). Normal practice
when winding such auto-transformers is to use appropriate gauges of wire
between each tapping point to ensure that whichever way such a
transformer is used, no more copper than is actually required at the
maximum VA rating is used.

In the case of Andrew's 240v to 200v autotransformer (assumed to have a
400VA rating), the section between the hot end of the 200v winding (200v
tap) and the 240v tap (the mains input side) will have thicker gauge wire
designed for the 10A load (less the portion of current supplied by the
200v winding section to the load) whilst the 0 to 200 volt winding will
be specified to handle a maximum current calculated from the sum voltages
of the 40v winding and itself which works out at a mere 1.67A which means
the 200 to 240v section only has to handle a mere 8.33A.

If we use the same auto-transformer to step up a 200v supply to 240v at
the same 400VA load, those current ratings remain unchanged and this
remains true even if we use the "240v tap" for the neutral connection so
that we can provide a non-isolated 40v at 10A from the "200v tap" with
the "0v tap" connected to the incoming 240v mains live.

Another example of this principle is to take a 120VA split primary
240/120v mains transformer with any arbitrary low voltage secondary
winding(s) which will remain unused in this case and use it as a 240VA
auto-transformer to step up a 120v supply to 240v or to step down from
240 to 120v by simply connecting the split primaries in series phase
aiding as per the requirement to provide the secondary voltages from a
240v supply. The connection between the split primaries becomes our 120v
tapping point which can be used either as the input or the output,
depending on whether we're stepping the voltage up or down respectively.

In this example case, the 240VA auto-transformer rating arises out of
the fact that each of the 120v windings is supplying 1A each to the load
when used to step down the voltage. When used to step up the voltage, the
required 2A at 120v is now split equally between the two windings, 1A to
supply the 0 to 120v winding[1] and the remaining 1A becoming the load
current via the other 120 to 240v winding to supply the load with 1A at
240v (240VA total output).

The difference between a conventional fully isolated voltage transformer
and and an autotransformer is that the VA rating in the former case has
to be at least that of the load whilst that of the latter merely has to
handle the VA difference between the input and output voltages. If you
only had to step up to 240v at 10A from a 230v supply, the VA rating
required of the auto-transformer would only need to be 100VA rather than
the former case of stepping 200v to 240v at 10A which requires a rating
of 400VA. A fully isolated transformer would, in this case, need to be
rated at the full 2.4KVA rating of the load.

[1] The reason for this portion of the winding requiring 1A is that the
1A load on the other winding is simply the result of a one to one voltage
transformation to a secondary that happens to be connected series aiding
to the incoming 120v mains so as to supply a 240v 1A load.

--
Johnny B Good