How important is the power supply in power amps?
The power supply converts the incoming AC line into the necessary DC voltages for the amplifier. It is especially important that adequate short-term current reserves be available from the power supply when musical peaks demand that large currents be delivered to the loudspeaker. Most amplifier power supplies are unregulated, so their voltage will fluctuate by some amount in accordance with the current demands of the output stage. Their outputs will also contain some AC "ripple" as a result of the rectification process. It is the job of the large filter capacitors to minimize this ripple and provide good short-term high-current capability. The larger the cap, the better this is done. Well-designed power amplifiers are fairly immune to ripple on the power supply and voltage fluctuations, with the exception that these imperfections come directly into play when the amplifier clips, since the power supply rail voltage sets the maximum achievable output before clipping. Power supplies with higher ripple will tend to sound worse when they clip, because the instantaneous clipping power tends to be modulated by the 120 Hz ripple on the power supply. Power supplies with larger power transformers and larger amounts of filter capacitance will help an amplifier sound better. Put simply, the power supply is important to the extent that it avoids being under-sized.
If capacitors act as a power supply reservoir for an amp, will power cords, receptacles, dedicated lines, or power conditioners really do anything since they are before the caps? Is there science behind this?
The amplifier power supply draws almost all of its current from the AC line only during the short time interval at the top and bottom of the sine wave when the rectifiers are conducting. This time interval may only be 10% of the total cycle. An amplifier drawing an average of 200 Watts from the 120V line, or about 1.7 amps average, will actually be pulling that current in 0.8 ms bursts on the order of 11.8 amps twice each cycle. This means we'd like to keep the TOTAL AC line resistance low, not just that of a six-foot power cord. It is not unusual in a house with 14 AWG Romex to see an AC line impedance of as much as an ohm at the outlet. Try it yourself and plug a 1200 Watt hair dryer into your outlet and measure how much the line voltage drops under this "10 Amp" load. Thus, when your amp demands a burst of 12 Amps from a nominal 120V line with an impedance of one ohm, you'll lose about 12 volts at the peak, or about 10% of your supply voltage. Since power goes as the square of voltage, the peak output power capability of your amp will drop 20% as compared to a perfect 120V line voltage source. This sounds bad, but the simplest cure is to use a slightly larger power amplifier in the first place. Better house wiring, and maybe a dedicated 10 AWG line to a 20-Amp breaker will help a lot – much more than an expensive 6-ft beefy boutique power cord. If the power supply is well-designed, fancy power cords, outlets and power conditioners shouldn't matter much. Spend $2.50 on the Home Depot outlet rather than 49 cents, just so it is well-built and provides a good, reliable connection. Getting rid of hash, RF noise and transients on power lines is the job of a power conditioner, not an expensive power cord. Spend $50 on a good power strip with an EMI filter to protect your equipment, and you'll have most of the benefit you need. It is ironic that fancy stuff like this is associated with high-end audio gear, when it can be argued that the cheaply engineered, mass-marketed stuff should need it the most. There appears only to be pseudo-science behind power cord marketing. The argument for boutique power cords is far weaker than the argument for boutique speaker cables, and even that is on thin ice.