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I want to design a battery operated pest trap (electrocuter). So far I have found out that the electrocuter snaps the insect at about 2000 V when it completes the circuit by landing on 2 nearby wire-meshes.

Is it possible to design a 12 V to 2000 V step up circuit? What will be its circuit topology?

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    \$\begingroup\$ Yes, it is possible and it's topology will likely be "flyback" (not to be confused with "fly" as in insect). Try this as an alternative to flyback \$\endgroup\$ – Andy aka Dec 30 '18 at 11:28
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    \$\begingroup\$ One wonders if you should be handling 2000V if you have to ask. \$\endgroup\$ – Unimportant Dec 30 '18 at 11:29
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    \$\begingroup\$ On this site we expect you to come up with a suggested design. You need to do your research. Why do you need 2000 V? It sounds excessive. Is that AC or DC? I dislike "Is it possible?" questions because one person says "no" but the next person will say "yes". Both answers are pointless and so is the question. Can you do it? No because of the fact that you're asking what the circuit would look like. So go and do some research first and then come back. I'm not even going into the question if someone with little experience should do something with 2 kV. \$\endgroup\$ – Bimpelrekkie Dec 30 '18 at 11:29
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I provide this only because you have been given several other options and I think there's a chance this would be less lethal should you make a mistake. Please make every effort you can to learn about electrical safety before you attempt this project. It is very difficult to comprehend the basics of electrical safety without first understanding voltage, current, resistance, inductance and capacitance, so I would strongly recommend building a good understanding about these initial concepts at a bare minimum. Take every precaution to ensure life safety, both by making your circuit as safe as possible and taking mechanical precautions to ensure once the device is assembled nothing other than insects can be zapped.

Depending on how often you want it to be able to actuate, you may be able to use a lower AC voltage, as small a transformer as will work, and a voltage multiplier circuit to charge as small a capacitor as will work. You can use a capacitor to limit the discharge to exactly what will kill a bug, and because you would be charging it over multiple cycles of the transformer This will hopefully improve your survival probability should you go ahead with your project.

You would want to find the minimum sufficient voltage (probably by careful experimentation with a test rig), and then find the smallest capacitance that is effective at that voltage, then figure out the lowest current you can use to charge the capacitance quickly enough, and then wind your own transformer on the smallest toroid that will work, and fuse the input of the transformer very tightly to the smallest current that works. I believe following this advice will greatly decrease that chance that you hurt yourself, but this is a very dangerous project to do at entry level, so if you go ahead with this, take every precaution, with every action, every test, every design decision. There are many hazards that are not readily apparent until advanced levels of training. There are probably quite a few that I don't see at my skill level, but this should at least be safer than just using anything that can produce an arbitrary 2000V.

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A car ignition coil uses intermittent 12vdc to provide several kV of spark each time the primary voltage is removed. A 12vdc relay could be wired as a buzzer to provide the pulsing dc input voltage. The body of the coil is the ground that the spark seeks. A condenser across the points (relay contacts) is a good idea. Check out wiring diagrams for older vehicle ignition systems that use points and condenser.

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