Delta - Wye Transformer Question on the 480/277v Setup as Opposed to 120/208v

Hi all,

I'm having trouble understanding the differences in setup between the Delta/Wye used for a 120/208v arrangement compared to the 277/480v arrangement. In particular, I'm looking at it with 2400v being applied to the primary windings.

If 2400v is applied to each coil on the Delta side of the transformer, the line to line voltage is clearly 2400v on the primary side since the coil is connected between phases. Because the secondary coils on the Wye side are each connected from the phase to neutral(lets assume grounded neutral), the secondary voltage, 120v for example, should appear across the coil from phase to neutral, making each phase voltage 120v and the line to line voltage 208v. This much I understand.

The 277/480v on a Delta-Wye transformer has a 277v phase voltage and a 480v line to line voltage. Let's still say we have 2400v line to line on the Delta primary side like before. I'm having trouble comprehending how the voltage across the primary winding(2400v) transforms into 277v across the secondary winding(phase to neutral), considering 277v is not a scalar from 2400v. 480v is a scalar of 2400v, but that voltage is the line to line voltage in a 277/480v system.

In the first scenario, 120v, the scalar multiple of 2400v appears as the phase voltage. In the second scenario, 480v, the scalar multiple of 2400v appears as the line to line voltage. As far as I know, the Delta-Wye transformers are used in the same way in each case.

What is the difference in implementing 120/208v compared to 277/480v to obtain the different voltage ratios? Or is there a mistake I'm making in my reasoning?

Thanks in advance, and I appreciate any insight anyone can offer!