Notice the small value poly or ceramic (non-polar) C2 that is in parallel with the ubiquitous high-value electro cap(s) c1.
Many books and online articles omit the small value poly/ceramic low-value c2 cap. They just show c1 electro cap.
But in the high end audio PSU that I encounter, that c2 cap is v. often present. I've heard that one main advantage is to lower overall ESR.
Cost-no-object, offer arguments for/against the low-value c2 cap.

 

Have you considered that C2 & C3 might be for the benefit of the 7805 to maintain stability and prevent oscillation? At least that is what the datasheets suggest.

 

And filter out any remaining high-frequency noise that has managed to find its way through the transformer.
I would never use a 7805 without a 10uF electrolytic on the output (as well as the small ceramic capacitor) The larger ESR of the electrolytic acts as a snubber, further improving stability and dissipating high frequency noise.
Also, I'd choose a quieter regulator than a 7805 for audio. Texas have some specially quiet regulators for that purpose.

 

Notice the small value poly or ceramic (non-polar) C2 that is in parallel with the ubiquitous high-value electro cap(s) c1.
Many books and online articles omit the small value poly/ceramic low-value c2 cap. They just show c1 electro cap.
But in the high end audio PSU that I encounter, that c2 cap is v. often present. I've heard that one main advantage is to lower overall ESR.
Cost-no-object, offer arguments for/against the low-value c2 cap.
View attachment 313995

Electrolytics like that are known to not be able to handle high frequencies as well as ceramics so a small ceramic cap is often used in parallel.
A better value I think is 0.1uf though, and that was always a recommendation for IC chips like TTL.
The right place for it would be closer to the 7805 also.

Years ago the 7805 was one of my favorite regulators for lower power stuff until I found the LM317 and similar.
There are also other versions of the 7805 or similar that have lower dropout and lower quiescent power dissipation.

 

The Wiring between the Big-Cap, and the Regulator-Input,
will introduce a tiny amount of Inductance that can be detrimental to the
accurate performance and stated Specifications of the Regulator.

Always install a High-Quality Ceramic-Capacitor on the Input of a Linear-Regulator,
even if it doesn't actually appear to "need" it.
There may be some strange circumstance or situation that rarely occurs that
will make You scream with frustration when You are trying to diagnose a weird "occasional-glitch".
.
.
.

 

The Wiring between the Big-Cap, and the Regulator-Input,
will introduce a tiny amount of Inductance that can be detrimental to the
accurate performance and stated Specifications of the Regulator.

Always install a High-Quality Ceramic-Capacitor on the Input of a Linear-Regulator,
even if it doesn't actually appear to "need" it.
There may be some strange circumstance or situation that rarely occurs that
will make You scream with frustration when You are trying to diagnose a weird "occasional-glitch".
.
.
.

That’s very true. Even more important if it is a switched-mode regulator.

 

Folks, ignore the 7805 in that ckt. That was just a schematic I found online.
Just pretend there is:
-- no regulator after the filter caps
-- any regulator after the filter caps (fixed voltage [7805] or variable voltage [lm317])

Now argue for/against the small value cap (c2).

 

Folks, ignore the 7805 in that ckt. That was just a schematic I found online.
Just pretend there is:
-- no regulator after the filter caps
-- any regulator after the filter caps (fixed voltage [7805] or variable voltage [lm317])

Now argue for/against the small value cap (c2).

There is almost nothing to discuss because it really depends on what comes after that. An IC, a transistor, a light bulb, a computer, a microcontroller.
As mentioned, the main point is that the smaller ceramic cap handles high frequencies better than an electrolytic. If higher frequencies are an issue then you are better off with that extra little cap.

 

OK, in response to post #8: And this was for a TUBE TYPE audio amplifier! The small value capacitor was required to get rid of a nasty 2X mains buzz in a high gain amplifier that used silicon diodes in the high voltage (250volts) power supply. That was in addition to the good electrolytic filter capacitors. A scope investigation of the noise source showed a sharp spike of about 0.1 volts on top of the rectified and filtered DC, measured at the filter capacitor terminals. So that produced a very audible buzz at the speaker output.
This was a sort of high gain circuit, two cascaded stages with voltage gains over 100, plus an output stage with a gain of 5. The plans called the gains closer to 200, but I don't believe that. So the smaller value cap certainly can be the only simple solution, even in lower budget systems. (This was in 1964)
And for the IC voltage regulators, as has been mentioned, a mandatory addition to prevent serious oscillation.

 

I see that small cap in even very simple intended-for-audio diy projects.
E.g. this small "TREAD" reg.
Not sure what other electronic types -- military, computer, industrial - -are those small caps the rule (norm) rather than something esoteric.

 

The small value capacitor is present to shunt the much higher frequency voltages, some which are produced by the rectifier diodess.

 

Not sure what other electronic types -- military, computer, industrial - -are those small caps the rule (norm) rather than something esoteric.

Any circuit there can have high frequency noise on the power bus that can interfere with circuit operation, either analog or digital, will usually have 100nF ceramic caps from bus to ground distributed around the PCB, sometimes next to each IC.
They suppress high frequency digital noise and prevent oscillations in analog circuits.
It's cheap insurance against noise corruption in the circuit so don't scrimp in their use.