Step 5: Series Capacitor Banks
The Simple Math:
The maximum charge voltage (VT) of a series capacitor bank is found by simply adding the voltage ratings of the series capacitors together. The total capacitance (CT) of a series bank is found using a special formula. If you're familiar with paralleL resistor theory, you're going to have no problems here. The foruma for your capacitance total in series is:
CT = 1/[(1/C1)+(1/C2)+....(1/CN)] NOTE: CN is the last capacitor in the bank. Okay, that looks complicated.... Let's go through a few examples.
We have two capacitors in series. The first capacitor is a 100f 2.7v capacitor. The second is also a 100f 2.7v capacitor.
VT = 2.7v + 2.7v
VT = 5.4v
So we can charge our bank up to a MAXIMUM of 5.4v.
CT = 1/[(1/100f)+(1/100f)]
CT = 1/[(0.01)+(0.01)]
CT = 1/(0.02)
CT = 50f That's right! If you place two capacitors of the same calacitance value, you're total capacitance will be half!
So your capacitor bank will be rated for 5.4v at 50f!
To keep things simple, let's add a third capacitor of the same value into the equation. We now have tthree capacitors in series. All three capacitors are rated for 2.7v at 100f.
VT = 2.7v + 2.7v +2.7v
VT = 8.1v
So we can charge our bank up to a MAXIMUM of 8.1v.
CT = 1/[(1/100f)+(1/100f)+(1/100f)]
CT = 1/[(0.01)+(0.01)+(0.01)]
CT = 1/(0.03)
CT = 33.3f
So your capacitor bank will be rated for 8.1v at 33.3f!
Let's try something a little harder, shall we? We have four capacitors in series.
CAP#1 = 2.5v @ 10f
CAP#2 = 2.7v @1f
CAP#3 = 5.5v @ 0.47f
CAP#4 = 2.7v @ 3000f
VT = 2.5v + 2.7v + 5.5v + 2.7v
VT = 13.4v
So we can charge our bank up to a MAXIMUM of 13.4v.
CT = 1/[(1/10f)+(1/1f)+(1/0.47f)+(1/3000f)]
CT = 1/[(0.1)+(1)+(2.1276)+(0.000333]
CT = 1/(3.2279)
CT = 0.31f
WHAT THE HELL? Yes ladies and gents, your total capacitance will ALWAYS be lower than the capacitance of the LOWEST capacitor in the bank when working with series banks; in this case 0.47f. Try a few more examples for yourself! Here is a very simple super capacitor calculator:
Series / Parallel Capacitor Calculator: http://www.electronics2000.co.uk/calc/series-parallel-capacitor-calculator.php
PLACING SERIES BANKS IN PARALLEL:
You can place two series banks in parallel. To compensate for lost capacitance! I've done this on several occassions. If you have two series banks or more, look at each bank as a single capacitor. If you place two banks in parallel, think of them as two separate capacitors, and follow the rules of parallel capacitors. For example, if we have two series banks of 1000f 12v capacitors and we place them in parallel, we will have a 2000f 12v bank. Here is another example. You have three series banks:
Bank#1 = 1200f 14v
Bank#2 = 3000f 12v
Bank#3 = 4000f 10v
When you place these banks in series, you will have a 8200f 10v bank. Simple, eh?
PLEASE NOTE THAT THERE ARE PAGES THAT ARE DEDICATED TO CHARGING SUPER CAPACITORS, AS WELL AS BALANCING SERIES CAPACITORS! CHECK THEM OUT!