Thank you for the explanation!! Can you please mention any papers that talk about this. May I know why/how phase noise improvement happens only for a small range of capacitor values; above and below this cap range the phase noise degrades.
Thank you!!
As you increase the capacitor value, the amplitude peak increases (for the same tail current). This could push the cross coupled transistor in to triode. In fact if the rds of these transistors reduce below certain value that reduces the effective Q of the tank(before they get in to triode), you will start to see the degradation in phase noise. Even if this rds reduction is only for a small fraction of the oscillation period the phase noise could get worse compared to not having any capacitor at all.
This phenomenon could be understood from different perspectives
1. Reduction in oscillation amplitude - As the transistor enters triode, tail node starts to move towards the peak and vice versa
2. Tank Q reduction
3. Wasting current when it is not needed results in less current spent on amplitude - for a fixed tail current
4. The Vgs for the off transistor (when the other transistor is in triode) becomes too negative than what it would be when they dont enter triode, with the same current and tank capacitance to recover and reach the peak - the amplitude gets limited
The easiest way to observe this is to look at the tail voltage. Class-C provides best results(FoM) when there are only two peaks in the tail voltage - i.e when the two transistors only move between cutoff and saturation. When the degradation starts, 4 peaks start to appear at the tail voltage.
In the paper vivekroy mentioned, read section III-C for the popular explanation