Question 19.18: The P-cycle jitter of a VCO operating at 1.5 GHz is observed......
The P-cycle jitter of a VCO operating at 1.5 GHz is observed for different P to obtain a plot like Fig. 19.32 with P_{c} = 30 . The P-cycle jitter over 10 cycles (P = 10) is 2.0 ps rms. Estimate the phase noise of the VCO using the model in (19.86)
S_{\phi ,~osc}(f) = h_{0} + \frac{h_{2}}{f^{2}}+ \frac{h_{3}}{f^{3}} (19.86)
but neglecting the white-phase noise term h_{0} , which is only important at very high frequencies.
Substituting P = 10, \sigma _{J(10)}= 2~ ps , and T_{0} = (1/1.5 · 10^{9}) s into (19.89)
\sigma _{J(P)} = \sqrt{h_{2}T_{0}^{3}} · \sqrt{P} (19.89)
yields an estimate of the phase noise model parameter h_{2}\cong 1350~ rad^{2} · Hz. Using (19.90) with P_{c} = 30 yields f_{c} \cong 2~ MHz .
P_{c} \cong \frac{1}{25T_{0}f_{c}} . (19.90)
Finally, substitution into (19.88) yields h_{3} \cong 2.7 · 10^{9}~ rad^{2} · Hz^{2} .
f_{c} = \frac{h_{3}}{h_{2}} (19.88)
Hence, the phase noise of the VCO may be modeled as follows:
S_{\phi ,~ osc}(f) = \frac{1350~ rad^{2} · Hz}{f^{2}} + \frac{2.7 · 10^{9}~ rad^{2} · Hz^{2}}{f^{3}} (19.91)