In short - yes. Treat noise at the source. If a mega-cost cable reduced noise then it would make sense to use it on refrigerator, the boiler, the washing machine etc
Switched Mode Power Supply manufacturers are required to filter mains input but not for the reason you think. The filtering is to reduce the switching harmonics that it creates, otherwise those harmonics would prove damaging to the power distribution network. Once below a certain level they don't care - they've met regulations but mains input is still very noisy from all the sources in the house and even the mains from the street is really really bad quality - often with DC present and flat topped 50Hz wave with harmonics and noise added to that. Above a certain level of noise power companies actually charge money for noise introduced by industry that are deemed noisy.If you're going down that route you may as well buy a mains capable/rated spectrum analyser (shows frequency across the bottom and amplitude). Several thousand pounds - use it to tune your noise reduction. Only issue is most spectrum analyser frequencies start at 9KHz as the money for that market is in high frequency (ie RF/VHF/UHF of mobile phones etc).
Yes to your point about common noise on inputs, but with caveats.
Most amps are single ended - they have a single AC signal path with shielding around it to ground. Some use XLR and use differential signals where the signal in one conductor is sent 180 out of phase to the other conductor. If you combine (sum) these two signals they cancel out.
Common mode noise - this is when the same phase noise appears on the conductors from EMI or conducted. Amps can use the differential signal then, when one conductor phase is inverted - the signal becomes 2x the strength and the common mode noise (now with one noise signal 180 out of phase with the other signal) then cancel out. This is why XLR is used a lot in the audiophile community.
Differential mode noise - this is when you have noise on one conductor. Just like the RCA connector single ended connections - the amp does not have a second copy of the signal to remove the noise and thus you can't use the common mode trick.
Now noise on both RCA jacks isn't likely to make much of a difference to noise reduction - the source selection circuit only allows one signal to the amp and that's single ended. The inputs grounds are typically tied together so in fact that really does nothing either.
However if you had XLR inputs with noise on - just the one pair of differential signal inputs would have enough information for the amp to use the inverting signal trick to remove a large portion of noise (assuming the track lengths etc don't mess up the alignment which is unlikely for audio).
Most amps are built to a budget, removing noise before it hits the chassis is good. Keeping noise out is good. Mains power also has this common mode+differential mode noise present. So putting the IEC inlet filter on the power input targets common mode and differential noise.
Now going down the rabbit hole. Noise occurs at multiple frequencies and filters are typically targeting a frequency range (they attenuate the signals in that range). Any good mains filter would show the measured attenuation across frequency. My Schaffner IEC filter has multiple models, each with a different frequency-attenuation profile. You know that before you buy - this is mine: https://www.mouser.co.uk/datasheet/2/355/Schaffner_datasheet_FN9262-2898675.pdf on my amp. If you look at page 3 (!) you will see the common mode (CM) and differential mode (dm) attenuation graphs.
Mine is the 6A version.. I could have used a smaller current capable version but given the toroidal transformer inrush it means means enough input to cover that for longevity. The more current capacity the less attenuation.
The reason I went for this is that my mains has a high RF noise which came through the toroid transformer (the curse of the toroid), this adds good reduction at that range.
Why do we need noise reduction?
There's a couple of reasons:
* amplifier components respond to frequency noise outside of the human hearing and amplify those signals (consuming power - this is an important point I'll come to in a second). This can, in the case of bad designs or cost-cut designs, result in causing instability (where gain control and phase vary over frequency - this could result in a self reinforcing loop, and thus causing oscillation (creating a massive output signal) that could destroy the amp. The fact the amp component amplifies a signal means it draws power (ie if you have a 1watt signal in the audio range but a 50watt RF signal being amplified, the power consumed is still over 51watts) but the power system may or may not be able to cope with that. It may not be designed to cope.. that causes less power to be available to the audio signal and you get dipping power rails which cause compression and distort the amplified signal.
* filtering noise before it comes in - passives such as inductors etc can remove noise but need to target specific bands, active noise reduction can be done by both the design (some amp designs inject power rail noise into the input signal so the amplifier then cancels out the power rail noise for example) or by simply adding regulators to the power rail.
* power supplies attempt to reduce noise - between 1-1MHz your voltage regulators can help reduce noise but after about 100KHz their noise attenuation drops off. The amp builder then has to use local decoupling (both a reserve of power and to reduce the loop between the power pin and ground/opposing power rail) as close to the amp component as possible so that the power drawn by amplifying high frequency does not cause noise across the amp. After 100Khz you're starting to look towards using an inductor to block the power rail high frequency signal then local decoupling to provide the fast power response. The main power supply then reacts slower to return power to the drained local decoupled power reserves.
You can also use different regulators - but they're voltage and virtually all are "series pass" which means there's a semiconductor that has to act like a valve to vary the power in response to noise to cancel it out. That voltage regulation process is why they're slower and become useless at about 1MHz. An alternative here is to shunt - where the power is provided to the device.. and a shunt regulator then performs a constantly controlled short circuit. The benefit here is very very low impedance, thus very very fast response time - so there is nothing stopping the device from drawing more power and due to the regulation using current rather than voltage it's faster than voltage regulation. The downside for the shunt is that it can't control current during failure and it burns power.
Designed a 24MHz clock circuit and isolators for my ADC - to prevent noise, it uses local decoupling and uses shunt on the board (along with local power reserves) but with a voltage regulator in the power supply itself. The key design principle here is to both reduce noise incoming and travelling more than a couple of millimetres from the chip power pin itself, it also provides the smallest loop for high frequency return currents.
I have upgraded the caps in my A220, and added local decoupling on the pins of the pre-amp opamp. Adding just 0.1uF ceramics caps to the pins to earth improved the sound - why? because the original power supply is crap and the power supply is situated about 3-4 inches away.. I'm tempted to build a PCB with the same shunt as the ADC and close in power supply for the opamp then run all the signals on that board instead of the existing design.. it would improve the signal substantially.
Ok lots there.. but you get the idea.. TL;DR - quieter frequency spectrum the better. Cost-strapped design implementations leave a lot to be desired. Adding random **** to the equation without measuring and solving that issue is pure guesswork.
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