Hello,
RF design engineer here. Will try to comment on the points i know about.
Would I place the filter at the output of the SDR or at the output of the amplifier?
Both would be better. You dont want to amplfy the harmonics, waste the output power of your amplifier. Also if the harmonic levels of the SDR output is high, you can distort your signal too much during amplification.
But you dont want to broadcast the amplifier output harmonics either.
This is a quite deep topic involving power levels, amplifier specs and used modulation type.
My suggestion is to copy the existing work at first, and learn while doing it.
would/could the reflected amplified harmonic kill the amplifier?
It could in general terms. But i doubt it at the mentioned signal level.
Does a "tunable" Low/High-Pass filter even exist?
They do. They are big, expensive and unwieldly. In my opinion, it is best to use switched filter arrays as others mentioned.
A 1MHz bandwidth BPF at 470MHz is quite hard to design let alone building a tunable one.
As I understood from your comments, you dont own/have access to a network analyzer or equivalent equipment.
After 100MHz, it is unlikely that you would get a succesful result at designing an RF filter higher that 3rd degree without RF test equipment.
I even dare say 'dont bother trying'.
I suggest buying couple filters as your wallet allows, and staying in their passband.
How does amplification even work? Do I use a specific amplifier tuned for this frequency or do I use a broadband amplifier that amplifies 50MHz up to 3GHz by so many dB? Never thought of this before and so I really don't know how this normally is handled...
Both works. A tuned amplifier requires design, so designers mostly go with mimics(otherwise known as MMIC).
You can get a variable gain mimic, to be able to control the gain (duh). Below an example:
https://www.qorvo.com/products/p/TQM879006ALets assume SDR output level is 10dBm (10miliwatt). You want 10watt output (40dBm). So you need 30dB gain.
However, not all 30dB gain mimics can be used. The Qorvo part above can output 0.25W for example.
And so you need a high power amplifier. And its design is whole other business.
I dont like to say it but, designing every part in a VHF or upper band comm. equipment is a very big challenge, even for an experienced designer. Keep it small at first so you dont get frustrated.
Would be happy to help if you decide to go further.
Deniz