Actually, VCO has a frequency-gain given by varactor accuracy. This is measured in Hz/V. This means that oscillator frequency depends on voltage signal from synthesizer.
\[\omega_{out}=\omega_0+K_{VCO}V_{control}\]
Amplitude signal in VCO is given by resonator transconductance and flow current:
\[V_{tank}=\frac{I}{g_{tank}}\]
for a current-limited regime.
See:
"Concepts and Methods in Optimization of Integrated LC VCOs", by Donhee Ham and Ali Hajimiri.