Power Transformer: 110V and 220V input, with two 15V outputs 180 degrees out of phase
Using a centre-tapped primary usually means that you de-rate the transformer to half power.



Figure 1. Series and parallel connections for split-winding transformer. Image source: Electro-Dan. The linked article discusses torroidal transformers but the principle is the same for standard transformers.

Instead, the common approach due to its flexibility is to use a transformer with two 110 V primaries and two equal secondaries. The primaries can then be wired in series for 220 V operation and parallel for 110 V. Similarly, the secondaries can be wired in parallel for high current or series for higher voltage. The series connection point is, in effect, the secondary centre-tap.



Figure 2. For switching primary voltage by the user you would add a voltage selector switch. Source: Modulus Amplification.