[Amps] HV transformer and Variac

[Manfred Mornhinweg]

Just a little more trivia on the comparison between transformers and 
autotransformers:

Let's consider an autotransformer with the tap at the center. Assume we are 
applying 240V input, and get 120V output (minus losses), at 10A.

You can see this as 5A of current flowing from the input through the upper half 
winding and into the output, with another 5A being induced in the lower half 
winding and also flowing into the output. So you get 10A output current. The 
energy extracted from the upper half is put into the lower half. So you can see 
the autotransformer as a plain 1:1 transformer, with 120V input, 120V output, 5A 
load current.  In fact the entire design of the autotransformer, in terms of 
core size and shape, number of turns, and wire size, can be exactly the same as 
a 120V to 120V, 5A, isolation transformer. Just connect the two windings of that 
600VA isolation transformer in series, and you get a 1200VA autotransformer, at 
the cost of losing the isolation.

In other words, a 2:1 ratio autotransformer saves half the iron, copper, and 
power loss, compared to a full transformer of the same output rating.

As the ratio deviates from 2:1 (or 1:2, doesn't matter), the savings tend to 
diminish, ultimately asymptotically approaching the same ratio of iron, copper, 
power and loss of a full transformer.

Applying this to an autotransformer used in such a way that the output tap is 
closer to the input end than to the common end, the lower voltage you have to 
consider is that between the input and output, not across the input nor the output.

To make this clear, should anyone have doubts: When you use an autotransformer 
to reduce 240V to 230V, the efficiency will be almost the same as if you use a 
plain 240 to 10V transformer to do that job. But for such a ratio you should use 
an autotransformer that has the 10V winding made with much thicker wire than the 
230V winding! If you use the same wire thickness throughout, such as is done 
with a VARIAC, the safe output current will be severely limited by the wire size 
of this short section, and that means that the core and the big lower chunk of 
the winding will be severely underutilized. In turn that causes a higher loss 
than using a transformer optimized for that task.

In short, when the task is lowering the voltage by a small amount, an optimized 
autotransformer is most efficient, a plain transformer with separate secondary 
comes as a close second, while a variac is far less efficient. Instead for a 2:1 
ratio, the optimized autotransformer and the Variac are just as efficient, while 
the transformer with separate windings has twice the size, weight, cost, and 
loss. "Efficiency" in this context means not just output power per input power, 
but also output power per cost, size and weight!

The above analysis is a bit simplistic, because it doesn't consider the effects 
of the special construction needed for a Variac with a circularly moving carbon 
tap, and doesn't fully consider voltage drop, magnetizing current, etc, but at 
least it should illustrate the principles.

Manfred

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