Will the transformer's output be phase shifted with respect to its input?
And here was me thinking the question was what is quoted above
Perhaps your memory was in context of 3 phase AC power transformers. The following is something I found while googling the topic:
Detla-Wye transformers appear to have very large (30 degree) phase shifts simply because of the difference in connection between primary and secondary. Through suitable interconnection of different secondary coils from a three phase primary (you may need more than three secondaries, and they may have different numbers of turns) you could get any phase shift desired. For example, special transformers are sometimes used to generate 18 phases on the secondary, each with its own phase displacement, in order to feed rectifiers and get smoother DC.
But the original question really speaks to phase shift in a single phase transformer. An ideal single phase transformer doesn't produce any phase shift; the output signal is a perfect in phase copy of the input signal. Real transformers have numerous non-idea features, and will produce a small phase shift. This can be minimized but not eliminated, by using more expensive construction techniques. It becomes an engineering problem to select a transformer with sufficiently small phase shift and distortion for any given application.