(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.