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That's incorrect, you need a DC blocking capacitor between the varicap and the other capacitor.
Its possible that the inductor could be of suffciently high dc resistance not to affect the tuning voltage
Can you really imagine a coil high enough inductance and thin enough wire to do that
Particularly bearing in mind the small capacitance change of a varicap, which means you're usually talking VHF or above.
I've a frequency standard that tunes to radio4, it uses a 1n4007 as a varicap, that particular diode works well as a varicap, the capacitance of the diode is adjusted using dc to 'pull' the frequency of a crystal osc to sync up with the radio 4 signal using a very simple pll.
Rectifier diodes make pretty decent varicaps, their large chip size gives them decent capacitance.
about 25p min to 50p max 0-12V