How does a stun gun work?
In this post I want to talk about how a stun gun works, and I don't mean what button to push to do what, I mean in terms of the electronic circuits inside that produce the stun function. It might be worth noting what I mean by stun gun, since there are SO many words used to describe a stun gun and there are many parties out there trying to push their own naming convention. This article discusses the origins of the confusion if you're interested, but I'll just clarify that what I mean by stun gun is any device meant to produce pain or incapacitation of a person using electric energy. That definition applies to pretty much any word you might have heard being used for such a device, like stun gun, TASER, tazer, energy weapon, electroshock weapon etc.
I've seen several good posts talking about how to use a stun gun, so that's not going to be the topic today. In order to understand how to pick a good stun gun though, it's very helpful to understand how it actually works internally. I'm an electronics engineer, so I'll do my best to not geek out and make this too technical so most of you can follow along.
The circuit below is a simplified version of the stun circuit used in most stun guns on the market today.
- An energy source (V1 in this circuit): most stun guns use a battery
- A step up transformer (L1 and L2 in this circuit): the role of the transformer is to significantly increase the voltage from the battery into the tens of thousands of volts or more. Other circuits could be used, but this is by far the most popular, due to the relative low cost to achieve a high boost ratio
- An oscillator (V2 in this circuit): the role of the oscillator is to generate and alternating current (AC) from the direct current (DC) of the battery. This is important because a transformer can only pass an AC signal, so the battery voltage could not be amplified by the transformer without it. V2 is just a simplification of an actual circuit, which could be an oscillator IC or a simple RC oscillator (probably most common, in stun guns)
- A high current switch (M1 in this circuit): this is used to switch the battery voltage in and out of the transformer primary side according to the oscillator signal. The oscillator itself is not capable of providing enough energy to supply the transformer directly, so the role of the switch is to create an alternating waveform from the constant voltage of the battery by following the pattern of the oscillator. This is typically a pair of MOSFETs (here I only drew one for simplicity), but several designs are possible.
- A pair of electrodes (the right side of the circuit, where the electrical arc is drawn): Their role is to apply the high voltage produced by the tun gun to the target person.
The way the stun gun circuit works is pretty simple. The oscillator is supplied by the battery and will produce an AC waveform. It can be a square wave, triangle wave or even a sine wave. All that really matters is that it crosses the turn-on threshold of the MOSFETs in both directions. The frequency of the arc produced by the stun gun can be adjusted through the frequency of the oscillator. A frequency that doesn't interfere with the cardiac rhythm of a human is usually chosen, in order to prevent causing a heart attack.
Since the signal of the oscillator passes through the turn-on threshold of the MOSFETs in both directions, if the oscillator signal is applied to the gates of the MOSFETs, they will then get turned on and off periodically, with the frequency of the oscillator. The voltage of the battery can thus be applied and removed from the primary side of the transformer according to the oscillator signal. This is how the stun gun output frequency is set. If the battery voltage was applied directly to the transformer primary winding, without the use of the MOSFETs, the transformer will quickly saturate and just act as a short circuit across the battery and no signal will appear on the secondary side of the transformer or stun gun electrodes. Most MOSFETs have a threshold voltage in the range of 0.5V to 3V, so a 3V signal is usually sufficient to drive the MOSFETs. That means that a 3V or higher battery is good enough to drive the oscillator circuit, which in turn drives the MOSFETs. You will find 3.2V rechargeable batteries or a pair of 1.5V batteries in many stun guns.
Next, it's up to the transformer to step up the voltage. In "normal" conditions (in our case, when an arc has not yet formed on the stun gun electrodes) transformers will try to mirror the voltage applied to the primary side on the secondary side winding(s). If the number of turns (the number of times the wire is wound around the transformer core) in the primary and secondary windings are different, the voltage is multiplied by the ratio of secondary to primary turns. For example, if the primary winding had 1 turn and the secondary winding had 10.000 turns, then the ratio of secondary to primary windings would be 10.000. So the AC voltage on the secondary side of the transformer will look like the voltage on the primary side of the transformer, but will be 10.000 times larger. If we applied a 3.2V square wave on the input (primary side) of the transformer, we'd get a 32.000V square wave on the output (or secondary) side of the transformer. It's clear now why the transformer is an essential component of a stun gun too. The turn ratio is usually set so that a very large voltage is produced on the secondary side (stun gun output), in the tens of thousands of volts up to millions of volts.
Now that we have generated a high enough voltage, we have the electrical potential to create an arc. If we apply a high enough voltage across two metal pieces close to each other (the stun gun electrodes, in this case) we can create an electric arc. Air is normally an insulator (meaning it will not conduct current), so in normal conditions, there will be no current flow between the stun gun electrodes if they are separated by air. This is basically an open circuit condition for the secondary side of the transformer, which allows the voltage to ramp up to whatever the turns ratio times the input voltage is. However, if we reach what is called the breakdown voltage of air, air particles between the stun gun electrodes start to ionize and quickly form a conductive path through air. It's the exact same effect that produces lightning, just at a smaller scale in a stun gun. The breakdown voltage of air is roughly 3000V per millimeter at normal atmospheric pressure and humidity, but varies significantly with temperature, pressure, humidity and the shape of the electrodes. The actual formula used to calculate the breakdown voltage is called Paschen's law. Here's how the breakdown voltage varies with distance at different altitudes:
The breakdown voltage is actually lower if the electrodes are not flat, specially if they have sharp points (like most stun guns do), because the sharp points concentrate the electric fields around them (see image below for an example of how the field varies with the radius of the electrode when one electrode is a sphere and the other is a plane):
Lower pressure (which is normal for higher altitude) or higher humidity also decrease the breakdown voltage, so in most situations, the breakdown voltage across stun gun electrodes are is actually lower than Paschen's law.
Most stun guns have a gap of 3mm to 10mm and tend to have sharp or round electrodes, so you will get no more than 10mm x 30kV = 300.000V across the output electrodes, because an arc will form and the air becomes conductive, so you will get a short circuit across the electrodes, which will bring the voltage right back down to ~0V. Most stun guns will produce voltages just in the tens of thousands of volts. This is a very important point to note. You will see stun guns that claim an output voltage of more than a million volts, but you will never see that much voltage across the stun gun electrodes, it's just not physically possible. Those exaggerated ratings can come from the theoretical output voltage that the turns ratio of the transformer could produce if an arc would not form, but in practice, you will never get to experience that much voltage. Therefore, those stun gun voltage ratings are really meaningless.
With a short circuit across the stun gun electrodes, and therefore, the secondary winding, the transformer can no longer amplify the voltage according to the turns ratio, but it can supply current that is proportional to the current on the primary side according to the inverse of the turns ratio. So, for example, if the turns ratio of the stun gun transformer was 10.000, if the current on the primary winding was 10A, on the secondary side, we'd get 1mA. You can now see that there's a balance between output voltage and output current that has to be met. A higher turns ratio will produce a higher theoretical stun gun voltage but a lower stun current, while a lower turns ratio will produce a higher stun gun current, but a lower output voltage.
There isn't a big of benefit in designing a stun gun with a transformer that produces much more than the expected breakdown voltage. The only significant benefit is that you have some margin in case the stun gun battery voltage decreases, or if the atmospheric pressure is higher, or the air is particularly dry, to ensure that you can still produce an arc in the worst case conditions. Otherwise, it would be more beneficial to produce a stun gun with a higher output current, since the current is really the electrical parameter that corresponds to the amount of pain or incapacitation produced. Therefore, most stun gun designs will benefit from a lower transformer ratio rather than a higher one.
That said, there are design methods of increasing the output current beyond what the transformer can supply, like using a capacitor to store extra energy (this is commonly used in defibrillators, for example), but we will not discuss those methods now.
If current is the main factor in stun gun efficiency, you might be wondering if voltage plays any role at all. In fact the maximum possible voltage a stun gun can produce is still important, but for different reasons. As we've seen with Paschen's Law, a higher voltage can arc across a larger gap. When it comes to stun guns, that means a higher voltage can penetrate thicker clothes. The maximum voltage is just not set by the transformer design (those meaningless millions of volts specs you might have seen on some stun guns), but by the distance between the stun gun electrodes.
So, if you wanted to choose the best stun gun, it would ideally be one with a larger gap between electrodes and a higher current rating. Current ratings are not commonly specified, so you might have a hard time finding them though. The even more relevant electrical spec would actually be the amount of charge the stun gun outputs. Charge is just current integrated over time (if current was constant throughout a pulse, that would be current times the duration of the current pulse). Charge is measured in Coulombs (C). Charge is also not commonly published, so you might need to be a little resourceful when choosing a stun gun.
One trick you can use to choose a stun gun is to look at the size of the battery. A larger battery typically means that it can output more current, and is sometimes the next limiting factor in the output current after the transformer turns ratio. A larger battery has a smaller internal resistance and therefore a larger short-circuit current (which is critical during the arc stage). A larger battery can also hold more charge, but that doesn't always translate into a higher charge per pulse, as the pulse duration is actually dictaded by the stun gun oscillator parameters. At the very least though, a higher capacity battery will allow a stun gun to deliver more pulses for a longer total usable stun duration. So, when in doubt choose the stun gun that seems to have the larger battery. It becomes pretty obvious that compact stun guns, like key chain stun guns or pen stun guns will be limited in stun capacity, so a larger stun gun model that can hold a larger battery has better chances of being more effective. That's not a sure way to judge performance, so look for trusted brands and expert tested models whenever possible.
https://www.mdpi.com/1996-1073/16/17/6221
https://www.stungunshop.com/blogs/help/what-is-a-stun-gun
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