I dont quite understand what importance does having a 2nd or 3rd order RC Lowpass filter do to filtering power rail noises. If the first stage filter only allows frequencies below 15.9 Hz arent the other stages unnecessary? Adding more series resistance to the rail will always not benefit the load since it would be receiving slightly less voltage.
Does adding more stages equate to less noise than the previous one ?
simulate this circuit – Schematic created using CircuitLab
I would say the second and third stages are there to deal with self-resonance issues in the capacitors. (So this really isn't a "third-order filter", for any practical purposes.)
If the capacitors were ideal capacitors, then the second and third stages would have no appreciable effect. In an ideal capacitor, the impedance of the capacitor keeps getting lower as the frequency gets higher.
In the real world, all capacitors have some parasitic inductance. At low frequencies, this effect of this parasitic inductance is inconsequential, so the impedance-vs-frequency relationship resembles an ideal capacitor. But at higher frequencies the effect of the parasitic inductance becomes more and more significant (the capacitor actually looks like an inductor-capacitor "LC" circuit). At some point there will be a resonant frequency just like with any other LC circuit, and beyond that frequency the impedance of the capacitor will increase as frequency increases, just like an inductor. At this point the low-pass filter is no longer a low-pass filter!
https://resources.pcb.cadence.com/blog/2019-capacitor-self-resonant-frequency-and-signal-integrity
As you'd probably imagine, larger capacitors have a lower self-resonant frequency and smaller capacitors have a higher self-resonant frequency. So, it is a common practice to put multiple capacitors in parallel -- for example a 0.1µF capacitor in parallel with a 10µF capacitor -- to overcome this effect. Once the frequency gets high enough that the 10µF capacitor is no longer effective, the 0.1µF capacitor is still acting as an effective capacitor so the circuit overall still works.
The extra resistors in this circuit are new to me, but as this article suggests perhaps they are there to dampen out other resonant effects that could happen otherwise.
https://incompliancemag.com/article/using-capacitors-in-parallel-dangerous/
The additional RC sections are useful to attenuate at very high frequencies, where the ESR and ESL of the first capacitor acts to set an attenuation floor.
With 100 ohms in the first section, and 0.1 ohm ESR, you get at most 60dB (1,000:1) attenuation at any frequency, even ignoring the ESL.
If you truly want 100dB attenuation, which would be a mere 5 decades above the F3dB of the first RC section, all these irksome parasitics have to be including in the thinking.
