(vii) (viii)
Fig.3. S-Band PLL performance results
Phase noise performance degrades by factor 20log times ratio of translated frequency and the reference source frequency. It is defined in (1) and (2)
Degradation factor= 20 x log (M) dB (1) M =\(\frac{\text{Multiplier\ Output\ Frequency}}{\text{Reference\ source\ frequency\ of\ TCXO}}\)(2)
Here, M is the multiplication factor with respect to reference source frequency.
Effect Of Random Vibration On Reference Source Of PLL System
Vibration causes mechanical deformations in frequency-determining piezoelectric components that cause phase fluctuations. In general, these effects are more prominent in higher-frequency oscillators, due to increased signal phase sensitivity to mechanical deformation and decreased resonator quality factor. If these phase fluctuations are inside the oscillator feedback loop, they convert to frequency fluctuations via Leeson effect within the resonator half-bandwidth (HBW).
Reference source (oscillator) sensitivity to vibration is traditionally characterized by acceleration sensitivity, which is the normalized frequency change per unit g (9.8m/\(s^{2}\)). When an oscillator is subjected to acceleration, its resonant frequency shifts. The frequency shift (Δf) over the time is proportional to the magnitude of the time-dependent acceleration and depends on the direction of acceleration. In random vibration amplitude of vibration level is defined in terms of power spectral density (PSD). Its effect in change in level of phase noise change (\(L(f_{v}))\)at particular offset from fundamental carrier frequency is measured in (3).
\(L(f_{v})\)= 20\(\times\)log (\(\frac{\overline{\Gamma}A_{\text{peak}}f_{0}}{2f_{v}}\)) dB (3)
Here, Peak g-sensitivity is \(A_{\text{peak}}\)=\(\sqrt{2\ \times PSD}\)
Where \(\overline{\Gamma}\) is acceleration sensitivity, \(f_{o}\) is the fundamental frequency of reference source (i.e. TCXO) and \(f_{v}\)is the offset frequency from fundamental frequency [4].
\(\overline{\Gamma}\) of any reference source used in PLL is dependent on PSD and vibration spectrum. It is defined in (4).
\(\overline{\Gamma}\)=\(\frac{2.f_{v}}{A_{\text{peak}}.f_{0}}10^{\frac{L(f_{v})}{20}}\)Hz/g (4)
Reference source selection depends on many factors that need to be taken care like g-sensitivity reduction profile and its phase noise degradation in random vibration environment. Spectrum of random vibration is known as PSD [\(\frac{g^{2}}{\text{Hz}}\)] which is critical while selecting the reference source as shown in Fig. 4. Fig.5 shows typical phase noise performance of reference source which must be taken into consideration while making reference source selection for PLL design and maintaining during random vibration. Acceleration sensitivity of reference source of PLL system is also dependent of axial behavior and it is measured in [ppb/g] as shown in Fig. 6.