Practical Coilgun Design
Parallel and Serial Capacitors
How should youi connect multiple capacitors? What happens to total capacitance in serial and parallel circuits? How can you increase the total voltage rating? Will serial or parallel store more total energy?
Capacitors connected in parallel will add their capacitance together.
Ctotal = C1 + C2 + ... + Cn
A parallel circuit is the most convenient way to increase the total storage of electric charge.
The total voltage rating does not change. Every capacitor will 'see' the same voltage. They all must be rated for at least the voltage of your power supply. Conversely, you must not apply more voltage than the lowest voltage rating among the parallel capacitors.
Capacitors connected in series will have a lower total capacitance than any single one in the circuit.
If you have only two capacitors in series this equation can be simplified to:
If you have two identical capacitors in series this is further simplified to:
This series circuit offers a higher total voltage rating. The voltage drop across each capacitor adds up to the total applied voltage.
Caution: If the capacitors are different, the voltage will divide itself such that smaller capacitors hog more of the voltage! This is because they all get the same charging current, and voltage is inversely proportional to capacitance.
Worse yet, if one capacitor is slightly leaky, it will gradually transfer its voltage to the others, possibly exceeding their voltage rating in turn. And if one of them punches through its dielectric barrier, it can then damage others in a cascading fashion. This is why series capacitors are generally avoided in power circuits.
Resistor Network for Series Capacitors
But the series network is just too attractive when you have limited money and scavenged parts. How can you build in some safety?
When you connect capacitors in series, any variance in values causes each one to charge at a different rate and to a different voltage. The variance can be quite large for electrolytics. On top of that, once the bank is charged, each capacitor's leakage current also causes a *different* voltage across each capacitor.
If you charge a series bank up all the way, some caps are always undercharged and some overcharged (not good). To help them share voltage equally, you add balancing resistors. Basically the resistors act as a big voltage divider and counteract the effects of variance in capacitance and leakage current. And if there is no leakage current, the capacitors must eventually become charged according to the voltage divider values.
Use this equation from p.13 of this excellent guide provided by Cornell Dubilier, "Aluminum Electrolytic Capacitor Application Guide" to calculate balancing resistors:
Example: Suppose you have two identical 1000uf capacitors, and connect them in series to double the voltage rating and halve the total capacitance. Let's also assume they are rated for 100 wvdc (working voltage) and 125v maximum surge. Solve the equation, using Vm = 125, and Vb = 200.
Solution: R = (2x125 - 200) / (0.0015 x 1000 x 200) = 50/300 = 0.167 M = 167 K ohms
Some related consequences in this example are...
Total Energy of Series vs. Parallel
Let's see whether a series or parallel circuit can store more total energy.
Recall that energy in a single capacitor is proportional to the square of the voltage. It is tempting to use series capacitors to gain an energy boost by using 'voltage squared' to our advantage. But let's take a closer look...
Assume you have two identical capacitors, of capacitance C and voltage rating V. (The capacitors wouldn't have to be identical but the results are valid for the general case, and the math is much easier this way.) Let's calculate stored energy E for both circuits.
There is no difference! Both circuits store the same amount of energy. This should confirm a common-sense approach, that would say you can't increase total energy storage merely by reconnecting the same capacitors in different arrangements.
Parallel capacitors are safer and more reliable than series connections.
There is no advantage in total energy storage to choose one of these circuits over another. But! There may well be a time when you need lower capacitance (e.g. a faster timing pulse) and higher voltage than your parts on hand can provide.
Last Update 2013-09-04
©1998-2016 Barry Hansen