Antenna design

[Elvis Oswald]

So, I guess the antenna is not the hard part.    How do you amplify the signal from the antenna with vacum tubes?  If the reports of Tesla's electric car are correct... he suppposedly used 12 tubes and some wire.  Any ideas?

[IcyBlue]

At first, I haven't seen teslas car. I personally only believe what I have seen and got my hands on to examine it 
So this all could be as well be nothing but tales - who knows ...

For the amplification; I think the main mistake about amplification everyone (here) does is, that there is no such thing like amplification at all. Imagine a pipe system with a valve. You can think of the valve as a amplifer. If you completely close it, nothing passes through it at all, if you completely open it, you have maximum throughput.  Every position inbetween attenuated the flow to some degree.  To change the flow in the system, you need very little work, while the flow in the system can be made to lift rocks (in a hydraulic system). So with just a fingertip you can lift a rock 
You can regard this as a mechanic amplifer. But without the pump providing the pressure to the system - and actually doing all the work for you - your fingertip at the valve will do nothing. The same is valid for all "amplifers". All they do is to apply the time characteristic of a very weak signal onto one with way more power. But the control and the load circuits are in principle always separated. The particles in the control circuit usually never enter the load circuit (well there are some exceptions to this; e.g. in current amplification where the electrons from the control circuit join the flow in the load circuit). Thus I say there is no amplification at all in any amplifer. No matter if it is a valve amp, a solid state amp, a magnetic amp or a optical amp - someone always needs to do the work for you.

In a "real amp", you would have a closed circuit, start out with a single electron while at the end of the loop at least two electrons come back which are not stolen from a secondary circuit/source. Tricky, and seems quite impossible - doesn't it ? 

Isn't it true though that a primary and secondary in a transformer should resonate for efficiency?

Erm, I'm not shure about this. Resonant transformers have a different transfer characteristics and are nothing but bandpass filters. RF amplifers usually use this aproach, thus they need to be tuned. The problem is, if your frequency slips away, the efficiency of the transformer changes damatically. If the load circuit is not in tune with the transformer, the whole power is burned in the driver circuit. This is well known among radio amateurs, since a badly mismatched load (antenna) can blow up the complete power amp. Tube based power amps get glowing red anodes in this case; solid state devices leave a plume of smoke.