Phase noise analysis question
时间：04-11
整理：3721RD
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I have a question on phase noise analysis process presented in Razavi's paper. It might requrie some math skill.
Question:
Assume VCO output
V(t)=Vo*cos[ωot+Φ(t)];
excess phase:
Φ(t)=∫ω(u)du + Φ(0); ω(u) is the offset frequency.
auto-correlation of ω(t):
R(ω(t+τ)ω(t))=2Dδ(τ);
Author concluded that variance of Φ(t) equal to 2Dt. I did not know how to derive it, any suggestion?
Question:
Assume VCO output
V(t)=Vo*cos[ωot+Φ(t)];
excess phase:
Φ(t)=∫ω(u)du + Φ(0); ω(u) is the offset frequency.
auto-correlation of ω(t):
R(ω(t+τ)ω(t))=2Dδ(τ);
Author concluded that variance of Φ(t) equal to 2Dt. I did not know how to derive it, any suggestion?