I am thinking about what we trade off between 3 stages and 4 stages of RCO. I am talking about simplest ring oscillator with P-mos triode resistor tuned by bias current.

1. max frequency:  3-stage can achieve higher frequency.
2. noise: 3-stage should be less noisy due to less device.
3. Gain: 3 stage need more DC gain.

I do see several papers and designs used 4 stage RCO, any reason we use that?