That's a great project, together with an audio amplifier - very practical.
I helped a budding ham build a TRF trancseiver kit which needed a seperate audio amp.
We used a scavenged TDA-type audio chip to good effect.
A ferrite rod with inductor wound is usually used.
There are lots of ways to feed a receiver, but a good untuned starter antenna is a simple longwire, insulated at both ends.
Making the antenna resonant involves making the wire (or elements) physically longer or shorter.
Variable inductors and capacitors can "bend" this length only so much.
Now you are talking about an ATU (antenna tuning unit) to make the feedline together with the antenna resonant.
Some antennas like a magnetic loop have the ability to change their resonance right at the antenna.
You'd need to have a diode on the osciloscope lead with the antenna.
It would show all the strongest stations near the resonance of the antenna. (an audio amp connected would allow some extra "feedback" to what's going on.)
Build a simple crystal radio receiver first, then build an audio amplifier, then build your antennas and an ATU, everything you have asked should be easy for you to work out from there![]()
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