Hey Leaford, you got the timescale wrong, but that's close

(That's actually a 200ms sample while the battery in on and doing it's regulation magic)
Trying to explain in simple terms first, for those without electric/electronics training:
Unregulated batteries just pass along their "native" voltage to heat the cartomizer when vaping. In the case of lithium based batteries, like most e-cigs use, that actually means you start vaping at 4.2Volts (the voltage when the battery is fully charged) and end up vaping at about 3.5Volts (when the battery is near empty).
That actually translates to a substantial difference in the heat produced in the cartomizer, and so a very different vaping experience.
To avoid that, the BMF was actually the first 808 device i know to have introduced a form of voltage regulation - and a very effective one at that.
The regulation method used is called PWM (Pulse Width Modulation - in geek language)
The only other mass produced device I know from that time to have a similar (not exactly the same - just similar) voltage regulation scheme is the eGo.
In the mean time, other manufacturers seem to have introduced voltage regulation schemes in other 808 mini e-cigs, but I'm not in a position to evaluate that. At the time, the BMF was the only one.
So what does PWM do? Simple - It basically turns the battery on and off at a very fast rate - 53 times per second, in the case of the BMF - So fast that in practical terms you won't even notice it or are able to detect it.
The end result is that, since the battery is only "on" a part of the time (90.53% of the time in the case of the reading above for a charged battery), the final output will have an "equivalent" lower voltage.
As the "real" battery level starts getting lower (down from 4.2Volts all the way to 3,5Volts), the voltage regulation circuit simply adjusts by increasing how much of the time the battery is "on" in relation to the time it is "off". Near the end of the battery charge, the battery is "on" just about 100% of the time.
Explaning the graphic above then:
Horizontal Axis (The timescale): 20ms per division - 200ms for the whole graph
Vertical Axis: The battery output in Volts - 1 Volt per division
The (cyan) Line: The actual battery output as it varies in time.
The 2 dotted horizontal lines:
1 > Just indicating 0 Volts, to give a reference.
T > Ignore that - It's just a trigger level to help the oscilloscope get a stable reading
RMS: The actual "equivalent" voltage to a normal battery with no regulation - 3.76V (but remember I'm reading this with no cartomizer attached - Voltage in real usage will be a bit lower)
FRQ: The frequency at which the output is doing it's on-off dance - 53 per second in this case
DUT: Duty cycle - The percentage of time the battery is actually "on" - 90% in this case, which means it will be "off" 10% of the time (duh!)
MAX and
MIN: Maximum and minimum voltages, as the battery turns "on" and "off" - you can disregard the 0,4mV as an adjustment error -
Vpp actually gives a more accurate value.
Vpp: Voltage difference between "off" and "on" - Actually a more accurate reading for the maximum voltage:
battery "on": 4 Volts
battery "off": 0 Volts
As I said, this is a reading with the battery almost fully charged.
As the battery charge drops, along with its "real voltage" the PWM circuit should increase it's "Duty cycle" (
DUT) to compensate for that, and provide a constant vaping experience.
and... I'll end this here, or I won't shut up.