The problem is common to this type of audio system. I would bet if you looked at the noise spectrum you would see 60 Hz plus many of the harmonic frequencies (120 Hz, 180 Hz, 240 Hz, etc.). The fact that it is more than just 60 Hz, or 50 Hz in some countries, is an indicator that it is not just simple ground loops.
I would also bet that your laptop power supply has only a 2-prong AC plug-- lacking the third ground plug.
In this type of power supply, the output is electrically isolated from the AC input. But it is not perfectly isolated. There is a small amount of current that flows between the isolation barrier. This is called the "leakage current". It is not a lot of current, but it doesn't have to be.
Some laptop users report getting shocked or having a tingling sensation in the legs when using the laptop while wearing shorts! The reason for this is that leakage current is going through the screws in the bottom of the laptop and into their legs. It sounds dangerous, but the amount of current is well below the safety limit. It is more startling than anything else. If you are wearing pants then you're insulated.
Laptop chargers that have the 3rd prong on the AC plug do not have this problem because that third plug is connecting the laptop chassis shield to ground-- forcing that leakage current to go to ground instead of into your leg. Of course, there is no leakage if you are running off of batteries.
In your case, the leakage current is not just going into your leg, but into your radio receiver. The solution to this is to properly ground your laptop.
You will have to experiment with this a little bit to find the best solution. Getting a power supply with a 3-prong AC plug is the best, but not always possible. The next option is to find something on your laptop that you can ground. Make an adapter from that 3rd prong to "something". That something could be the signal-ground on the output cable of your power supply. It could be a screw on the laptop. Or a shield on an unused laptop connector. Or the ground/shield on your audio cable.
Make that 3rd prong adapter, but leave the other end bare for the moment. Then start poking it around to see if or where you can connect it and have the noise go away. Once you have found a place or two, then finish up the adapter so it is easy to use.
Two warnings when doing this: Make sure that whatever you are grounding is actually ground! On the power supply output, make sure you ground the negative or gnd conductor. And when poking around, understand that you might actually have to poke a little hard. Both the bare wire and whatever you are poking will likely have a thin layer of non-conductive stuff on it, and you need to apply enough force to poke through it. Rubbing sometimes helps too. The non-conductive layer is sometimes paint on screws, or an oxide (rust) on the metals.
Oops, here is a 3rd warning: Be super careful when making that 3rd prong adapter. You're messing with potentially lethal voltages and we don't want you to die. Build the adapter in a way that there is no possibility of it failing and shorting out against either one of the other two conductors in the AC plug.
Give it a try and report back what you found!
How do I wire it all up?
Towards the back of the data sheet it gives you a typical circuit to use and this shows where GND comes in: -
Note the incoming power arrives on the circuit at the top left (red rectangle).
The ampere rating of your power supply depends on how the speakers are configured and what supply voltage you decide to go for. This last part dictates how much power you deliver to the speakers. Once you have the power, you can assume the chip requires 20% more then calculate current from this i.e. Iin = Pin / V.
Best Answer
As long as it meets the voltage/power ratings, you can power it with whatever you like.
A transformer by itself is not a "power supply", an SMPS uses a transformer too, just at a higher frequency which makes it more efficient/smaller. What they are referring to on the DIY Audio forums is a "linear supply", which is more basic but easier to make less noisy than an SPMS so often used for audio. Ratings work the same for either type.
An SMPS can come with whatever voltage outputs you desire, there are plenty of dual rail (positive and negative) supplies out there.
If the SMPS is a good quality and quiet (check datasheet) then there is no reason you can't use it to power your amp.
The TDA7293 can supply up to 100W into 8 ohm. These boards specify 85W however so stick with that rating (or below). To find out the average current needed into 8 ohms for this wattage, the formula is sqrt(W/R) = sqrt(85/8) = 3.26A. The amplifier is not 100% efficient though so you need a higher input wattage to reach this level of output.
What supply depends on how hard you want to drive the boards, but something like they recommend is a good idea, e.g. +/- 30V 150W supply.