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There are two transmitters to chose from. The first is a simple resonator. It has a series resonant line connected to multiply the output voltage level at the antenna.
The second transmitter is a multivibrator. It is an attempt to get beyond the theoretical efficiency limit of 25 %.
Both of these transmitters have several things in common. The most obvious feature is that they are build from junk. For example: the capacitors are made by gluing pieces of soda bottles and aluminum cans together. They took many hours to create. You can go to an electronics supply and purchase a much higher quality capacitor for a few dollars. They are built this way in an effort to rediscover how it would have been to live in the old days and be the first person to discover radio.
Exceptions are made to this line of thought in many ways. Anything that has to do with safety (such as the main power control relay and switches) uses modern commercial components. Other exceptions are made for convenience. Double sided Scotch tape and Goop adhesive are modern day products. You could wind your own power transformer in the old fashioned way. It would become a major project in itself to complete. A modern day transformer is accepted due cost and safety as well.
Another thing that they have in common is that they are quite crude and unstable. The outputs will be quite noisy and cause interruptions on several radio bands. For that reason they may only be operated under very carefully selected and controlled conditions. Do not ever operate one inside your house even for a brief pulse. This is particularly true if you live in a mobile home.
A metal skin of a mobile home is sufficient to cause a resonant tank effect. If a small fraction-of-a-watt transistor microwave oscillator is operated in a mobile home the effects are surprising. All electronic equipment becomes overpowered by it even though shielded cables are used. That same oscillator was to weak to even be received by the same equipment that it overpowered when it was taken outside of the mobile home and pointed at the antenna at close range.
Under similar conditions these transmitters will produce more severe effects. At these power levels even the briefest pulse will probably render your computer permanently useless. All occupants of a mobile home would basically be inside a giant microwave oven. Radiation injuries would result for longer exposures. That danger is especially true for the operator because he would be closest to the transmitter.
If you decide to duplicate these projects or even build anything similar to it here's another safety warning. Capacitors explode like bombs. The most dangerous ones are the ones that contain electrolytes. The electrolyte becomes the chemical propellant for the explosion. These capacitors use glass and plastic for the capacitive media. There is also the glue that holds them together to be considered.
Capacitors explode for either of two reasons. The first reason is that the voltage limit has been exceeded and a breakdown of capacitive media results. That will probably not occur for the glass or plastic capacitors. What will happen for them is the second reason, power dissipation.
A capacitor dissipates ½ of whatever energy it 'processes' as heat. The heat can make the glass crack and allow a direct arc to occur. The heat will probably cause the glue to release gas from residual solvent. The plastic will also 'outgas' and will melt eventually. For this reason the transmitter may be only be operated briefly to prevent heat build up.
This problem can occur in a surprising way. The power supply capacitor of a transmitter must be able to dissipate a amount of energy equal to the transmitters RF output. This means that while you're looking at the oscillator/transmitter to see if it is ok, the power supply goes boom for unknown reasons. It is possible to have this happen if you are using bulk audio capacitors for your power supply and are building FM oscillators using bulk 2n222 transistors. It is possible at as low a voltage as 12 volts to cause it with a capacitor rated at 35 volts. It will go off about like a firecracker of similar size.