This is the link I meant to use before, just for reference:https://www.audiocircle.com/index.php?topic=164248.msg1748275#msg1748275"So, for a Cherry MEGA putting 1000W into 4Ω, Ip = 22.4A"
Rail caps provide current for peaks, so the power supply provides the "average current" under most music listening circumstances, which can be calculated based on the signal, load, and efficiency.
With Cherry amps, the efficiency is quite high at max power (around 96%). Plus, with music (as opposed to sine waves used for testing), the peak-to-average power ratio is around 10:1 when playing loud. Of course, this depends on the type of music and volume setting. Some call this "crest factor", but crest factor is actually defined as "the ratio of peak value to rms value of a current waveform", which is for a signal (amplitude), not power. Power has a square for the signal (V^2/R, for example). Let's not get too deep into the math here. Just know that the proper terminology is "peak to average" followed by what you're comparing, which works for amplitude, power, or truckloads for that matter.
In pro audio, the rule of thumb is about 8:1 peak to average POWER -- with "heavy clipping". The goal in high performance audio is not to clip, but it happens even with systems that seem overpowered.
For super slow signals (super low frequency), the peaks can't be covered by the rail caps simply because they run out of steam, so the power supply itself needs to cover.
Here's an example involving test tones as opposed to music. Let's say a 1Hz signal is played at max power into 8Ω. We choose this frequency because 1Hz will most certainly discharge the rail caps, even if they are HUGE, so it's a bit unrealistic, but used for worst case analysis. For a 48V Maraschino, max power into 8Ω
at anything below 20kHz is about 120Wrms. 120Wrms is 240Wpk (instantaneous peak power of a sine wave is twice RMS, I'll spare you the math for that one). 240W peak output with 96% power efficiency requires 250W, and 48V @ 5.2A is 250W. Into 4Ω, it's double. This would facilitate operation with no (or almost no) rail capacitors down to almost DC. This example doesn't take into account the current to "run things" such as low voltage power supplies to power the modulation circuits.
Keep in mind we're playing music, and not test tones. So, if we apply the assumption that the rail caps can carry the load enough to prevent the supply from dipping below the minimum required for a given output, you can back off a lot on the required power supply max current. This is practical for 1kHz and up, and starts translating into impractical capacitance values as the frequency approaches zero. There is a happy medium where the power supply doesn't rely too much on energy storage. This is especially important for DC coupled amps. Maraschinos can actually function as a power supply since they are stable down to 0Hz.
Well designed amplifiers have a synergy between the amplifier circuits and power supplies. There are other factors involved, such as handling reactive loads, but that gets complicated. At idle and low volumes, Cherry Amps consume more power than other Class-D amps. This must also be taken into consideration when designing or selecting power supplies to drive Cherry Amps.
Bottom line is that the answer to your question depends on the many factors (load impedance, music type, volume setting, rail capacitance, load reactance), but if you're more specific, I can provide numbers as opposed to formulas.
Let's say you're playing loud enough to rarely, if at all, clip into 4Ω (nominal) speakers. For a 48V Maraschino, this is about 12W average into the load, and thus about 13W into the amp rail, plus the idle power, which is maybe 6W, very conservatively speaking, for about 19W total. That's less than 400mA average current, per channel.
Let's say you're playing LOUD enough to rarely, if at all, clip into 4Ω (nominal) speakers. With a 60V Maraschino and mid-90s dB sensitive speakers, this is very loud (not too difficult to calculate, but that's off topic)! For a 60V Maraschino, this is about 40W average into the load, and thus about 42W into the amp rail, plus the idle power, let's guess 6W, for about 48W total. That's about 800mA average current, per channel. Why, then, do we use a 1kW power supply with KING Maraschino mono amps? That way, we're not relying on the rail caps very much, and full power output is available down to DC.
So, what winds up being the determining factor is the current to drive low frequencies, which is much higher than for high frequencies. Things are somewhat different for amps like Cherry Classic and Cherry MEGA, which use "linear" (another misnomer) power supplies (toroidal transformer, rectifiers, rail caps, filtering, etc.). In those cases, the rail caps hold the rail voltage between charge cycles (120Hz in North America, for example).