Amplifier Capacitance

This is why an amplifier can 'motorboat' (repeated thump) if a filter capacitor fails in the supply- the timing constant has become so high that the amplifier exhibits low frequency instability.

I recently bought an NAD 2600 with a disclosed possible flaw--a "thump" when it turns on and off. I got it for about $100, so it think it was a reasonable price. Amp plays great, but that on/off sound isn't so nice. So I had posted about this to confirm this was an issue and not just "the way this amp is" and someone confirmed this was a flaw. So my question is: is this the 'motorboat' thump to which you are referring Atmasphere, or is this a different problem?

the turn on/off thump in your NAD amplifier is a totally different issue compared to what Atmasphere is talking about.
The thump that you are hearing during on/off is the inrush current charging the capacitors. this (huge) inrush current will create a spike on the supply rails of the power amp which in turn will create a voltage spike on the power amp output terminals (speaker binding posts). This in turn will create a thump in your speakers. The issue with the NAD is that it never had any output protection circuitry to avoid 'thumping' the speakers (if the NAD had output protection circuitry that was malfunctioning, that amp would not play any music). This is indeed a design flaw. Back in the 1980s, I & some extended family members did own integrated amps that always thumped the speakers. I guess back then output protection circuits were not always put into cheaper amplifiers - just the way it was back then!
The thump that Atmasphere is talking about is when a power supply cap fails (bad part/age/heat, etc) & the power supply is now faulty. Then, the power amp can motorboat/thump which is a sign of low freq instability.
Two different issues but quite similar symptoms.
The thing to note about the motorboating is that the amp will thump every time it's playing low freq content.
The turn on/off thump occurs just once at turn on & once at turn off - no thumping while playing program material.

If the amplifier has a -3 db point that is a frequency lower than that of the timing constant of the power supply, then the amplifier can modulate the supply, which results in IM distortion amongst other things.

Ralph, let me see if understand what you wrote above. I'm getting confused because w.r.t. the amplifier you are using frequency & w.r.t. the power supply you are using timing constant. Freq & timing constant are reciprocals of each other.

So, what you are saying is that for motorboating to occur the time constant of the amplifier has to be higher ("If the amplifier has a -3 db point that is a frequency lower than...") than the time constant of the power supply. Correct?
So, basically, the bandwidth of the power supply should always be lower than the bandwidth of the power amp. Correct?

Class AB - there is not fixed "time constant" since discharge time depends on loudness/load. We could take discharge time at max volume and compare it to reciprocal of -3dB bottom frequency of the amplifier but it wouldn't make difference to me since I don't listen at full volume. We could argue that smaller modulation at lower volumes will be "proportional" to level of the signal but once we draw less than max current, power supply voltage modulation at low frequencies becomes compensated by amplifier (since it is regulated).

Class A - does not apply since amplifier draws the same current even at DC output.

I'm still working on some of this conversation, but could someone explain "time constant" to me? I'm assuming this is something like what it sounds, but I'm not sure. It sounds almost as if amplifier power supplies work like CPUs in the sense that they have clear cycles and clocks that designers must take into account to keep everything running. I don't know if the analogy holds, but it sounds similar to me.

I'm starting to realize just how much I DON'T know about power supplies. Wow. And I am the knowledgable one among my friends. Eeeeek!

Aewhistory, Time constant is amount of time it takes to bring voltage to 63.2% of desired value. For instance applying 10 volts to 1000uF capacitor thru 10ohm resistor will result in 6.32V on capacitor after time equal 10ohm x 1000uF = 10ms. Same would apply to discharging from 10V to 3.68V (10V-6.32V). This time is called time constant RC.

Instead of saying "Time necessary to charge capacitor" we say "time constant". It is shorter and more precise. In our case it just means amount of time to have significantly lower supply voltage (discharge supply capacitors) when playing very low frequencies very loud. We want this voltage steady since any variations might compromise amp's operation (output affected by supply voltage changes).
We are looking at small changes in supply voltage (not 63.2%) but using terms like "time constant" or "-3dB frequency" just to have some reference point. From that we can, if necessary, recalculate exact percentage changes at particular frequency.