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Regarding the varible cap and the 2 coils - all 3 components are required.
You do not remove the enamel insulation - it is needed. The ENDS of each wire and the 'tap' location WILL need to be cleaned in order to make the solder joint. I usually hold the END of the wire over a match flame for a second or two. This will turn the enamel insulation black. Then, carefully scrape the black (chared enamel) away with a sharp knife. Practice on a scrap of wire a few times before you wind your coils. Look carefully at the photos and you will see the silver colored wire (in place of the gold color) on the ends of the wire.
During description of each of the items there is a description about the magnet wires with the price. In this the author says that I will require a 26 guage and 30 guage wire for the project. While during the description of the preparation of source coil it says I require a 30guage wire while the drain coil it says I require a 22 guage wire. What guage wire should I use for which coil? Also which is the L1 coil and L2 coil? The project says nothing about it???
Also, there is no mention about the capacity of the variable
tuning capacitor. Which capacity should I try? What is the technical term used for it(for calling the capacitor i.e. is it just called a tuning capacitor or something else as well?). I have asked around in many shops all they have is a variable capacitor(the one with 3 legs 2 to 22pF) and not a tuning capacitor with the 6 pins.
The word 'variable capacitor' and tuning capacitor' should be interchangeable for your application. The number of contacts are dependent on manufacturer's design and number of gangs/sections in the design. This little circuit is so specialized that I would try to get the variable (tuning) capacitor the author recommended.