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I know how shielded loop antenna work as a receiver antenna. (How behave electric and magnetic field).
But I can not understand how shielded loop antenna works as a transmitter.
There's no such thing as a "magnetic" and an "electric" wave. Only electromagnetic waves propagate – that's at the very basis of wave theory, so 1. is definitely wrong, and 2. would need rephrased to "will it produce an electromagnetic wave", and the answer to that is "yes!", otherwise it would not be an antenna.
So, you really might want to revisit your antenna theory when you say you know how your antenna works as a receiver.
- And it will produce the signal from the air gap?
Not quite sure which air gap you mean?
Generally, any antenna is always the same in receive as in transmit direction, when it comes on how it allows energy to flow between the free-space electromagnetic waves in free-space wave impedance and the conducted wave in a feed cable, waveguide, ladder line... with their respective impedance.
The only difference is when you look at how you deal with impedance mismatches that are inherent to the working principles of the antenna. But that's not about whether the antenna is magnetic or electric (or a mixture), but about whether it actually has transmission line and free space impedance, or just an approximation to these.
