Hi,
raja.cedt by spiky you mean that the MOS switch between on/off?, then it's one of the operating point for colpitts oscillator(always in saturation, saturation and cut-off or linear and saturation). Derivation comes from a large signal analysis of that oscillator and ends with something like this:
Vout≈I_biasR_p(5+x)/12;
where:
Ibias-->bias current
Rp--->equivalent resistance at the drain
x--> a parameter that determines the operating region of the transistor, it varies from -1 to 1(-1 always in saturation, 1 always in cut-off).
From the expression it can be seen that the duty cycle that maximizes output amplitude it's an always off transistor(although in reality it will not oscillate).
Hope it helps,
PD: some references about this issue
“Exact calculation of oscillation amplitude and predicting power consumption for CMOS Colpitts oscillators”, Qiuting
Huang; Circuits and Systems, 1997. ISCAS '97., Proceedings of 1997 IEEE International Symposium on , Volume: 2 , 9-
12 June 1997, Page(s): 1401 -1404 vol.2
“Output voltage analysis for the MOS Colpitts oscillator”, Mayaram, K.; Circuits and Systems I: Fundamental Theory and
Applications, IEEE Transactions on , Volume: 47 Issue: 2 , Feb. 2000, Page(s): 260 -263