How to measure a stun gun's performance

If you're thinking of buying a stun gun, you will notice that most stun guns don't make any claims in terms of electrical performance. Everyone claims to have a powerful stun feature and to be better than everyone else, so that's not really very helpful. Some stun guns will claim unrealistic voltage numbers, like tens of millions of volts, but that is nowhere near the maximum voltage you'll see on a stun gun (See my article about how stun guns work), plus voltage is only a good indicator of the stun gun's potential to penetrate clothing, not of the pain or incapacitation the stun gun can produce. 

Current (measured in Ampers) is a much more relevant measure of a stun gun's performance, but I'm yet to find a stun gun that specifies output current. 

The best specification of a stun gun's performance is really the amount of charge it delivers. Charge is measured in Coulombs and is the integral of current over time (basically how much current is supplied for how long). Some stun guns actually specify an output charge in Coulombs, but they are not common at all. 

So if you really want to compare stun guns in terms of performance you really have to do your own experiment. Touch the electrodes with the tip of your tongue and then... just kidding!!! Though, zapping yourself (on your leg or arm, definitely not your tongue) can be a good way to compare performance, it's definitely not the most pleasant way though. How much pain you feel can also be a bit subjective, specially if the stun guns are close in performance.

The more scientific method would be to actually measure the charge output of a stun gun. A fairly simple way to measure current, is to use a shunt resistor (just a low value resistor that can handle a large amount of current). Look for a resistor of just a few milliOhms that is meant for measuring current. Avoid resistors with an equivalent inductance of more than a few nH. If inductance is not specified, avoid wire-wound resistors, thin film resistors that have a spiraling or zig-zaging resistive element pattern, or very small packages, which usually translates into a higher inductance. The reason why you need a small inductance, is because the arcing signal we're trying to measure on a stun gun is a high frequency signal, and the inductance is going to translate into higher impedance and therefore higher error at higher frequencies. The impedance of an inductor is equal to 2*pi*Frequency*Inductance. Stun gun arcs will be in the MHz range, so you will see how nH of inductance can translate into several mOhms of impedance those frequencies.

To measure current with a shun resistor, you have to insert it into the current's path (in this case between the electrodes of the stun gun. This part is very easy. You don't even have to worry about touching both electrodes, because the stun gun's arc will much rather travel through the shunt's mOhms of impedance rather than through air (which is an insulator). If the shunt is somewhat in between the electrodes, the arc will jump from on stun gun lectrode onto the shunt, go through it and then jump to the other stun gun electrode. 

You some precision shunt resistors will have two bigger terminals that are used to pass the current through, and two smaller terminals that are used for measuring the voltage across the shunt. If your shunt doesn't have the smaller terminals, just solder some wires on each of the shunt terminals with a soldering iron. Then connect an oscilloscope to the wires (or the smaller shunt terminals if you have them). It doesn't really matter which wire goes to the oscilloscope probe tip and which wire goes to the oscilloscope ground, since the signal will be alternating current (both positive and negative values). Set the oscilloscope to trigger acquisition on an edge with the voltage scale set to the highest setting and a few milliseconds for the time scale. Push the stun gun trigger to cause an arc. If you don't get a trigger on the oscilloscope, adjust the trigger amplitude and the voltage range until you get a consistent trigger. You will probably see several spikes in the measurement, each spike corresponding to an arc, or one popping sound (the zapping sound the stun gun makes is made up of several pops close together, if that makes sense). You can then zoom in on one of those spikes until it looks like a damped oscillatory wave (a sine wave that decreases in amplitude). 

At this point you can compute what the current produced by the stun gun is. If you used a shunt resistor with a value of 1 mOhm, for example, the current would be the voltage measured by the oscilloscope divided by the resistor value, so if the amplitude of the voltage was 1V, the current would be 1/0.001 A, or 1000A. 

Now let's compute the amount of charge delivered by the stun gun. Let's say the stun gun arc waveform looked like this: 

  

The correct mathematical way to compute charge would be to compute the integral of the current over time, but that's not really fun, and probably not necessary. The amplitude of the voltage is about 80V and the duration of the pulse is about 700ns. Now imagine a triangle with the tips at the middle of the screen (0V,0ns position), the top center of the screen (80V,0ns) position and the right center of the screen (0V, 600ns position). If you mirrored all the negative current back up to the positive side of the graph, most of that triangle will be filled up by the current waveform. Therefore, we can use the area of the triangle as an approximation of the integral of the current, and therefore the charge delivered by the stun gun. The area of the triangle would be the amplitude (80V) times the duration (700ns) divided by 2. Convert the volts to Amps by dividing the voltage by the shunt resistance. Assuming a 1mOhm shunt, that would be 80,000V. The estimated charge would then be 80,000*0.0000007/2=0.028Coulombs, or 28mC. 

This method is not 100% accurate, because we're approximating the integral rather than actually calculating the integral and the shunt will have some parasitic inductance, plus it's own tolerance and temperature coefficient, which all add up as measurement errors. But, for the purposes of comparing two different stun guns, we would be making pretty much the same errors for each measurement, so the comparison will be pretty fair. 

I went through this whole process in this video using a simple stun gun. I also added a way to estimate output power as a bonus if you're interested: