As an electrical engineer I've never really thought too hard about what the caps do in our ESCs. I understand in theory a cap works by storing charge on the plates and that lets you do some useful stuff in electronic circuits but now I'm curious as to what exactly they're doing and whether or not the "common knowledge" I see passed around on-line regarding their operation is accurate.

The first question that strikes me as worth asking is "how much useable current can a capacitor provide in high load conditions?" That's a pretty straightforward question to answer. The amount of charge stored in a capacitor can be calculated using Q = C * V. Plug in typical numbers for our ESCs and you get Q = 8.4V * 900uF, which works out to roughly 0.0075 coulombs of electrical charge. An ampere is an electrical flow rate defined as a of 1 coulomb of charge over 1 second of time. If we assume an amp draw of maybe 30A when a car accelerates from a standstill, that 0.0075 coulombs of charge gets used up in 0.00025 seconds. Now, that assumes all of the 30A comes from the cap first, then the battery. That's not how it will really work - based on the impedances of the cap and the battery it will be a mixture of amps coming from the battery and the cap at the same time, possibly with the rate of charge coming out of each varying over time. But lets assume maybe it's a 50/50 split - battery provides 15A and the cap provides the other 15A? That's still 0.0005 seconds. Okay, so let's look at it from another angle - if we want 900uF of capacitance to provide current over a useful period of time to us, say maybe half a second, how much current would that be? 0.015A.

So the idea that caps are doing any kind of work to prevent the battery's voltage from sagging under heavy load or really helping our car to accelerate faster is looking pretty shaky.

The next interesting question to ask would be "how much capacitance is required to have some kind of meaningful impact to our car's acceleration?" So lets use the same assumptions here - we want the cap to provide 30A over half a second. We can use that to calculate how much capacitance we'd need using the same two formulas. 30A over half a second is 15 coulombs of charge. A cap that can store 15 coulumbs of charge at 8.4V would need to be 1.78 F, roughly 2000 times the capacitance of what you get with an ESC.

Interestingly, capacitors with that much charge do exist at not very exorbitant rates or sizes. A 4F cap rated for 8.4V is only $15 on mouser and roughly 1/4" x 1/4" x 1/2" in size. Unfortunately the ESR of the cap I'm looking at is rated at 45 ohms. A lipo cell is somewhere in the .02 to .04 ohm ranges so that means in practice the ESC will pull the overwhelming majority of current flow from the battery, but it's possible the cap could provide just enough current to help with voltage sag in some meaningful way.

Anyway, this was mostly a post to satisfy my own curiosity and nothing else really.