Sub response down to 20 Hz is not just about power, but more about design of the speaker and cabinet. Buying a 300 watt amplifier in a subwoofer doesn't mean it will go down to 20 Hz for example. If you have a limited budget you can still get a good subwoofer at HSU and AVS-123. The compromise made is you only get frequency response to about 25 Hz in your price range, but these companies publish real specifications for their subwoofers. You can study their subs and see how much you have to spend to get 20 Hz. Response to 25 Hz covers most music except deep notes of a pipe organ. Response below 25 Hz is mostly for dramatic special effects in movie soundtracks and special effects can go lower than 20 Hz.