Amplifier Capacitance

Aewhistory, Look at this chart: http://www.powerint.com/en/community/papers-circuit-ideas-puzzlers/circuit-ideas/careful-rectifier-diode-choice-simplifies-and-

Top graph shows amp's supply voltage. Capacitor is charged from transformer thru rectifier only in short moments of time when voltage goes up (bottom graph is charging current). Picture is greatly exaggerated - in reality line representing voltage is almost straight (very small ripple) and capacitor charging happens in very short high current "spikes". Amplifier current demand from capacitors might be constant (class A) or vary a lot with the music (class AB). Very large electrolytic capacitors are characterized by capacitance (opposition to change in voltage), inductance (opposition to change in current) and ESR (effective series resistance) that represents pure resistance. Obviously we want a lot of capacitance to store energy but we don't want inductance since it is opposing rapid current changes. Best solution to lower inductance would be to use less inductive capacitors (expensive) or to use more of small capacitors in parallel (capacitance increases, inductance decreases, ESR decreases).

Bombaywalla mentioned two problems with a lot of capacitance - rush current and over-stressing power supply. Initial current will be higher and last longer to charge larger capacitance resulting in blown fuse or damaged rectifier. Rush current could be limited by soft start circuit - basically a temporary current limiter but amplifier has to be designed for that.
Second part is a little more difficult to explain. Imagine perfect capacitor with a lot of capacitance, no inductance and no ESR. What will be the shape of the voltage on the upper graph? - almost straight line with very, very small ripple. Charging time of capacitors will now be very short (only when voltage goes up) while charging current spikes will have higher amplitude (to deliver same average power) limited only by transformer and power line. This large current spikes might damage rectifier or overheat transformer. Again, it is a little more complicated with transformer since average amp's power is technically the same. The problem is that core of transformer will be heated with high frequency component (iron losses) of narrow spikes, while copper windings will be heated (copper losses) more since, in spite of the same average value, RMS value of current (representing heat) will be much higher.
There is also possibility that ripple current (charging current) peaks might now be too high for caps you selected. Anything can be done (carefully), but linear power supply is not that simple to design properly.

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.

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.

Teaching? No, Almarg would be much better at this. He explains things with much more clarity. History was always difficult for me.

Bombaywalla - Amplifiers are line regulated. It means that amplifier supplied from 40V and set to produce 5V output voltage will still produce 5V output with supply lowered to 35V or increased to 45V. There will be small error because regulation is not perfect but it is in order of one percent or less. There is an easy way to test it - just set your amp at moderate listening level and then reduce line voltage from 110V to 90V. Your amp will play at the same level. You could measure it with test tone and voltmeter.

Bombaywalla, Yes, power supply should be clean but I was talking about modulation of power supply voltage by varying load that amplifier presents. Low frequency will definitely do it (biggest current) and high frequency will do it as well (inductance of the caps). It will be reduced by amplifier's PSRR (power supply rejection ratio) but will still affect the sound. Atmasphere was talking about very low frequency signals causing big sags of supply voltage that bounces back (motorboating). Limiting low frequency response of the amplifier, as he suggested, will help but I can imagine scenarios where it will still happen. Let's play "Kodo Drums" (Shefield) - enormous amplitude of low frequencies repated once a second. That will do it as well. It becomes obvious why good amps have so many caps in the power supply.

As for power supply being clean - the biggest offender there is 120Hz ripple proportional to load. At low sound level we cannot hear it because ripple is very low (light load) but at high sound levels when ripple is strong we cannot hear it either because sound is too loud. It is almost like jitter that is undetectable unless you play louder. There is also high frequency component related to charging current spikes and also limited "softenss" of rectifier diodes (late switch off, fast snap back).

That's why many designers started using switching power supplies instead. Modern SMPS switch at zero voltage/zero current, produce high frequency noise that is easier to clean than 120Hz, have line and load regulation plus protection against overcurrent or overtemperature. Jeff Rowland uses 1MHz SMPS in his newest creation model 625 (class AB) amplifier. There are some other benefits size being perhaps the least important. One of them I can appreciate in my Rowland 102 amp. It works from 85-265VAC or DC voltage to almost 400V making it less susceptible to overvoltage and completely immune to DC on the power line.

Also many Rowland amps have active power factor correction that makes amplifier "look" like resistive load loading power line evenly during sinewave instead current spikes near the peak: http://jeffrowlandgroup.com/kb/questions.php?questionid=144

why not increase the voltage rating, to improve the longevity, ESR, and inductance characteristics instead?

The price of higher voltage, low ESR, low inductance caps is perhaps too high. I checked once site that sells Hypex class D kits. Power supply module was by far the most expensive because of BHC slit foil low inductance electrolytic caps. People try to remedy inductance of large caps by placing small non-inductive caps in parallel. It lowers caps reactance at high frequencies but also creates parallel resonance circuit that will ring under rapid current draw. There is a reason design engineer avoided it.

Ralph, that's very interesting. I just looked at Jeff Rowland Capri preamp - the upper limit is 350kHz but bottom is only 10Hz. It could be direct coupled with servo (integrator) in the feedback set to 10Hz. In any case, he did it for a reason. My small Rowland 102, as well as big 625, have both 5Hz bottom -3dB but all his preamps have bottom at 10Hz. He also uses SMPS in preamps. I know he does in Capri, not sure about others. He might feel that limiting rumble or power supply effects should be done as early as possible. Additional 5Hz bandwidth in the amp improves slope, adding second pole, without affecting much overall 10Hz bottom limit.