For the Logic Power supply I want to convert AC 120/240V to 24/15/5/3.3 VDC. I am wondering what is the best topology to do this. Currently I am using a power transformer to convert down to 24vac rectify and tap off of that. Is there a way to reduce/remove the power transformer? Should I change to a flyback style of converter? I need about 5-10 Watts DC power total.
If you do not care about power factor (means no need of power factor correction), then indeed a possible solution is to use the transformer, rectify it and tap-off the rectified voltage. However, already here, you would not have stabilized DC-voltage without any linear regulators or switched regulators, i.e. you would have voltage ripples which could deteriorate the performance of your logic circuit.
Other possibility is to use active rectifier (i.e. not using diodes, but using active transistors). You could modulate the switching patterns of the transistors to get the necessary main DC voltage, which you process further with switched or linear regulator to generate different DC voltages for you logics. With the active rectifier, you would be able to perform power factor correction. The better your power factor is, the more active power you get at reduced reactive power.
Generally with such low power the normal 50Hz/60Hz transformer does not show the best efficiency because the internal power losses due to magnetizing current are not so negligible compared with the Whole power involved. In addition once you rectify 24 Vac you get 24*1.414 Vdc and therefore you need a regulator to get stable 24 Vdc.
If you use a typical analog solution you don't get more than 50% of efficiency. I think the flyback solution is the best and the simplest, you can get more isolated DC voltages regulating only one of them.
Using a typical boost controller you can get also a flyback PFC avoiding the bulk capacitor after the bridge rectifier. In this way the 4 diodes have less losses because the input current is almost sinusoidal and not a triangle like with the classical rectification (that means less rms).
Disadvantage of the flyback PFC is that the power transformer has more losses because the rms current is greater than the classical solution where the flyback stage is supplied with the rectified main voltage (around 330 Vdc).