# Capacitor bank design considerations for coil gun?

I am designing a coil gun using a schematic that specifies a capacitor bank of 10 1500uF capacitors in a 2x5 arrangement to provide an effective 600uF at 1000V.

I am wondering why this configuration is desirable rather than, for example, using all 10 capacitors in parallel. An all-parallel design would reduce the maximum voltage requirement to 200V, avoid problems arising from variances in capacitance for capacitors in series, and would deliver the same energy through the coil.

Are there other advantages, disadvantages, or considerations to be taken into account when designing the capacitor bank?

• 5x the voltage, 1/5 the current, 1/25 the I^2*R losses. Or, the 200V one needs 25x the wire cross-sectional area. Got a copper mine? Go for it... – Brian Drummond Jan 27 '17 at 21:07
• I was under the impression that it has more to do with compensating for winding and cable inductance more than anything else. Applying a higher voltage will mean the current ramps up faster and usually reaches a higher peak current for the same system inductance (which is what you want for a coil gun). – Sam Jan 28 '17 at 9:48

You are right in that you get the same energy no matter how you arrange the capacitors. Putting capacitors in series is problematic, so all else being equal, I'd want to put all the capacitors in parallel too.

The tradeoff between voltage and current can be largely compensated for by adjusting the winding. Take a look at a datasheet for a family of relays or solenoids, for example. You will usually see what is otherwise the same product offered in different voltage and current combinations. The only difference is the coil.

Fortunately, the total size of the coil and the total copper used stays the same for a range of current/voltage tradeoffs that come out to the same power. For example, consider starting with a coil that draws 50 mA at 12 V. Now we want a 24 V version while keeping the overall device geometry the same. If we changed nothing, applying 24 V would cause twice the current, and therefore twice the magnetic field, and four times the power dissipation. Now imagine we make the wire cross-section half the area but double its length. That results in 4x the resistance, so half the current flows thru the coil at 24 V. Half the current around each turn in the winding is made up by twice as many turns, so the magnetic field stays the same. Half the area and twice the length is still the same amount of copper, just arranged differently. Twice the voltage and half the current is still the same power, so same heat to get rid of.

The same tradeoffs apply to your coil gun coil. To use a lower voltage, use thicker wire but less of it. To go from 1000 V to 200 V, use wire that is 5x shorter, but also has 5x area in cross-section. That means its diameter will be sqrt(5) larger.

Eventually the currents get so high that the feed lines start becoming significant. However, as long as you still have a reasonable number of turns, all should be OK. If the original used 50 turns, then 10 turns of the thicker wire should be fine. If the original only used 5 turns, then there isn't room left to scale down the coil to lower voltage and higher current. If so, this is probably why the original went to such awkward means to get a higher voltage.

Optimal force avoids oscillation with $\zeta$ = 1 (±0.3) near critically damped.

1. Maximize your coil size and also inductance/ resistance ratio by choice of coil design, then choose C for a Q of 1 with lowest ESR Caps you can afford.

• ESR of cap. array, coils, wire and switch are included in R as RLC are all in series on contact closure.

• $Q=\frac{1}{R}\sqrt{\frac{L}{C}} = \frac{1}{\zeta}~~$
2. For large low ESR e-caps my Rule of Thumb is T=ESR*C=100us so for 1500uF 250V rated , I estimate ESR=100us/1500uF=66 mΩ. The DCR of the coil ought to be about <=10x ESR of the cap so heat is wasted safely here and less stress on caps.

example

1. Let's say your coil is 1mH over laminated iron core with DCR of 0.5 Ω with heavy wire.

then for $\zeta=1~~~C=L/R^2~~$ = 1mH / (0.066+0.5)Ω^2 = 3.1 mF

But if Coil is only 100uH and 50 mΩ then C=100u/*(.05+0.066)^2=3.9 mF

Adjust ESR of cap array by s/p times each part. for s number in series and p in parallel.

But since energy stored is $Ec=\frac{1}{2}CV^2$ you will store more energy in series Caps using the max voltage rating (using MOV's to balance voltage or derating V by tolerance stackup) but then ESR is also squared.

Unfortunately power is lost from I^2R*t and this may only end up being 50% efficient with half the energy distributed in all the R losses.

So a better design increases t while reducing I by cascading coils with sequential switched power to reduce current discharge and stretch out acceleration over a longer arm with added complexity. You can work out the details from here.

Ultimately with 600uF @ 1kV = 300 J = watt-seconds you will end up with about 150 Joules in waste heat with dampening factor of 1 being near ideal.

This is my most important point using dampening ratio on impulse current of a linear motor to apply current in one direction only and not oscillate back and forth.

Not always as I expected here was my 1st cut.

• I wonder who the silent trolls are – Sunnyskyguy EE75 Apr 25 '18 at 6:41