Question about calculating LC resonator for VCO

when calculating the values of an LC resonator for vco,the resonant frequency will change from the center frequency after adding the reflection amplifier,so should i change the values after that to have the center frequency that i want? on what bases?

Yes, the active device has reactance of its own that has to be cancelled out by the resonator circuit. If you plot the active device port impedance on a smith chart with radius greater than 1, you will see that that port has a negative resistance and a reactance.

Basically, oscillating energy bounces back and forth between the active device and the resonator. Right at start up, this is mostly broadband noise. After 100 or so bounces, the "noise" looks a lot like it is peaked in frequency right at the point where the reactances all cancel. After a little while longer the oscillations reach steady state, and good oscillator phase noise results.

It is the reactance slope that is the restorative force that keeps the oscillating energy centered at the correct frequency.