Performance analysis of PLL

Reference crystal (i.e. TCXO or OCXO) is a piezoelectric material which is prone to physical disturbance. Reference crystal acts as clock for phase frequency detector (PFD) of PLL. Phase noise degradation of reference crystal has direct impact on PLL output. Hence, stabilization of reference crystal under intense vibration environment is essential for maintaining phase noise performance. Loop filter design also play a critical role in determining the final output phase noise. Selection of type (i.e. passive or active) and order of loop filter is based on requirement and limitation.

Fundamental of PLL active loop filter

When charge pump generated by passive PLL is not sufficient enough to drive VCO, then we prefer active PLL approach. It is having disadvantage of added in-band phase noise which is added by the op-amp used. It is generally recommended to have at least third-order loop filter in which added extra pole reduces additional flicker noise of the active device. One such scheme of implementation of active loop filter is shown in Fig. 2 [Reference Banerjee3–Reference Kosinski and Ballato5].

Fig. 2.

Active loop filter PLL system.

Use of higher order loop filter has advantage in case PFD frequency of PLL is larger than loop filter BW. Fig. 3 shows phase noise performance, locking time, and gain of active S-band PLL output. Making use of multiplier IC's for transforming lower frequency PLL signal to high frequency helps in lowering phase noise degradation factor as compared to direct generation. In present S-band PLL design, VCO phase noise is dominant outside the loop BW as seen in Figs 3(a) and 3(f). The voltage requirement (V _tune) of VCO for frequency generation is shown in Fig. 3(b). Estimation of close loop BW of PLL along with the gain of the active loop filter is shown in Fig. 3(e). Reference phase noise which is dominant within the loop BW of the PLL is shown in Fig. 3(c). The VCO sensitivity which can be seen as constant for the V _tune voltage range is shown in Fig. 3(d). The combined effect of the phase noise for the PLL is shown in Fig. 3(f). The second-order response of the system which shows system stability at the lock frequency 2.66 GHz is shown in Fig. 3(g). Close look can be taken for the frequency lock in Fig. 3(h) which takes 50 μs lock time.

Fig. 3.

S-band PLL performance results.

Phase noise performance degrades 20log times the ratio of translated frequency to reference crystal as shown in equations (1) and (2).

(1)$$D\acute{e}gradation factor = 20 \times {\rm log\ }\lpar M \rpar\, {\rm dB}$$

(2)$$M = \displaystyle{{Multiplier\,Output\,Frequency} \over {Reference\,source\,frequency\,of\,TCXO}}$$

Here, M is the multiplication factor with respect to reference crystal frequency.

Effects of RV

Vibration causes lattice disturbance in piezoelectric material components that causes phase fluctuations. In general, this effect is 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 get converted as frequency fluctuations via Leeson effect within the resonator's half-BW. Reference crystal sensitivity to vibration is traditionally characterized by acceleration/vibration sensitivity, which is normalized frequency change per unit g, due to which 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 RV test, amplitude of vibration level is defined in terms of power spectral density (PSD). Level shift of phase noise (L(f _v)) at particular offset from fundamental carrier frequency is shown in equation (3).

(3)$$L\lpar f_v\rpar = 20 \times \log \left({\displaystyle{{\bar{\Gamma }A_{\,peak}f_0} \over {2f_v}}} \right)\;{\rm dB}$$

Here, peak g-sensitivity is A _peak = $\sqrt {2 \times PSD}$ where $\bar{\Gamma }$ is acceleration sensitivity, f _o is the fundamental frequency of reference crystal, and f _v is the offset from fundamental frequency [4–Reference Tustin8].

$\bar{\Gamma }$ of any reference crystal used in PLL is dependent on PSD and vibration spectrum. It is defined in equation (4).

(4)$$\bar{\Gamma } = \displaystyle{{2.f_v} \over {A_{\,peak}.f_0}}10^{{{L\lpar f_v\rpar } \over {20}}}{\rm Hz/g}$$

Selection of reference crystal depends on stability and its g-sensitivity which governs the phase noise characteristic under vibration. Spectrum of RV is known as PSD [${{g^2} \over {Hz}}$] which is critical while selecting the reference crystal as shown in Fig. 4. PSD curve governs intensity of vibrations induced during RV testing. PSD in vibrational testing has direct effect on phase noise amplification as it has impact on the piezo electric property of reference oscillator. Phase noise performance of typical reference crystal is shown in Fig. 5. Acceleration sensitivity of reference crystal of PLL system is also dependent of material axial behavior and is measured in [ppb/g] as shown in Fig. 6. Hence, mounting position of frequency determining components is axial dependent for effective stabilization mechanism.

Fig. 4.

Random vibration spectrum.

Fig. 5.

Phase noise of typical reference source.

Fig. 6.

Axial acceleration-sensitivity of reference source.

Hence phase noise performance in different axis gets affected in different ways which needs to be taken care while selecting reference crystal.

Stabilization techniques under RV

Phase noise of PLL-based frequency synthesizer system is direct dependent on reference crystal phase noise. Reduction in g-sensitivity of reference crystal performance is important for system. g-sensitivity reduction is achieved in two ways in present article, i.e. reference oscillator spatial location and stabilization techniques. Finest spatial location (center of gravity) for mounting reference crystal is determined through structural analysis method. Mechanical and electrical [Reference Tustin8, Reference Lakshminarayanan9] stabilization techniques are used in this design to achieve improved phase noise performance under vibration.

Structural analysis

Structural analysis needs to be carried out for mounting of reference crystal at center of gravity and filtering out unit under test (UUT) resonance from PSD spectrum. This helps avoiding magnification of UUT resonance pickups during test as shown in Fig. 7. In present analysis as shown in Fig. 7, mechanical enclosure of UUT has self-resonance at 1.4 kHz. Hence, it needs modifications (i.e. positional weight analysis, physical profile alteration) in present design to filter out self-resonance from RV spectrum.

Fig. 7.

UUT resonance pickup.

Stabilization of reference source

Mechanical stabilization

Vibration isolators or dampers are a special class of silicone rubber made of high mechanical properties rubbers with high damping in order to reach Q factor at resonance lower than 3. Vibration isolators are in use to isolate reference crystal module to avoid direct contact with UUT. It provides free floating, stress less assembly for reference crystal module which experiences lesser level of vibration than direct fixing arrangement. Such reference crystal assembly arrangement is shown in Fig. 8. Vibration isolator selection is critical as these are profile-dependent special class of rubber also making sure it qualifies environmental test requirements, i.e. temperature, shock, acceleration, humidity, and so on. To measure the effective performance improvement using vibration isolators, specialized sensors are used. Specialized sensors are class of high precision accelerometers which can even sense minor changes in magnitude of applied force. Significant improvement in reduction in intensity level (PSD) or damping effect by mechanically stabilizing to access of RV on reference crystal is shown in Fig. 9 [Reference Li and Das10–Reference Walls13].

Fig. 8.

Reference source assembly with vibration isolators.

Fig. 9.

PSD damping effect of mechanical stabilization.

Electrical stabilization

Electrical stabilization can be achieved by taking below mentioned point into consideration during design. These are combination of best practices followed while PBC design and lesson learnt (from electrical issues) during environmental testing of developed system.

• • Decoupling capacitors on power supply voltage to each IC's and charge pump supply lines as these are most vulnerable to noise. Use of tantalum capacitors of different values (10 μF, 1 μF, 0.1 μF, 100 pF, and 1 kpF) at supply to reference crystal is must.

• • Electrolytic capacitor in UUT main power supply for filtering external noise.

• • Use of DC–DC converters with proper decoupling capacitors and make sure that their switching frequencies are not falling within PSD spectrum.

• • Use of low noise voltage regulators for improved phase noise performance. Check their ripples are not within PSD spectrum.

• • Protect charge pump line and VCO tuning voltage line of PLL from noisy signals by making trace length shorter (max 6 mm) and routing close to PLL chip.

• • Isolated routing of reference signal to PLL using shielded co-axial cable to avoid conducted and radiated pickups.

• • Avoid effect of acoustic noise and external vibration in the test chamber.

• • Avoid any strain in RF and power supply cables during test.

• • Use of shielded power connectors for UUT for avoiding external electromagnetic interference.

• • Minimize the ground loops are of utmost importance for accurate measurements. Ground loops may interact with magnetic and electric field generated by the vibrating actuator and degrades the performance [Reference Hati, Nelson and Howe2].

All design aspects listed here are implemented while doing electrical design of PCB's and interconnections between them within the system. Assembly quality and workmanship also play important role in reducing vibration sensitivity of any system. Implementing all techniques and methods as per present disclosure reduces overall system vibrational sensitivity.

Precautions

Sensor mounting

Use good quality sensor to monitor any misalignment between applied input vibration profile and that appears on surface of fixture. Such misalignment between input and feedback (monitor sensor) is shown in Fig. 10. There are many reasons for such type of errors, i.e. after implementing appropriate changes (i.e. improper fixture mounting, incorrect profile, loose sensor mounting, etc.) output profile follows input profile as shown in Fig. 11.

• • There should not be any physical contact of reference crystal module with UUT during test.

• • Potting is recommended for leaded electronic components to provide rigidity for assembly during test [Reference Howe, Lanfranchi, Cutsinger, Hati and Nelson12–Reference Kumar, Jayasheela, Shivakumar and Manjunath14].

Fig. 10.

Halt condition of random vibration profile.

Fig. 11.

Typical random vibration profile.

Performance results

This section discusses practically achieved phase noise performance stabilization results in X, Y and Z axis during RV test. RV test is subset of forced vibration in which in spite of single frequency, a spectrum of frequency random in nature applied to system under RV test with pre-defined PSD magnitude. For accessing phase noise performance of PLL frequency synthesizer under harsh vibrational environment, RV test is conducted at magnitude of 7.5 g in three axes inside vibration chamber. During conduction of RV test, applied vibrations of defined PSD get translate on system under testing. To ensure proper conduction of RV test, proper mounting and fastening is must for matching applied PSD profile on system under test. Generated RVs disturb the performance of vibration prone components used in any system, hence need of special compensation mechanisms to reduce its effect is must. Inside view of mounting of reference crystal module which is isolated from rest of the system for reduction in direct translation of vibration effect is shown in Fig. 8. As discussed in earlier section, X-band signal is generated using S-band PLL signal along with frequency multiplier IC. PLL uses 100 MHz reference crystal for synchronization.

PSD spectrum ranging from 20 to 2000 Hz defines amplitude of vibration test as shown in Fig. 11. Realized system has gone for RV test in all three axes of 5 min duration for 7.5 g value. From equations (1) and (2), it is calculated theoretically that ~38–42 dB phase noise degradation factor implies on translation of 100 MHz signal into X-band 10.6 GHz. Phase noise of reference crystal and X-band signal in ambient condition is shown in Figs 12(a) and 12(b), respectively, at three offset frequencies viz. 100 Hz, 1 kHz, and 10 kHz. One hundred megahertz reference signal has phase noise of −109, −131, and −138 dBc/Hz while in X-band as −70, −96, and −95 dBc/Hz at three offset, respectively. High g-value RV affects the phase purity of a piezoelectric material reference crystal. Any phase fluctuation occurrence in reference signal gets directly translated into X-band signal. Phase noise performance of reference signal and X-band signal during 7.5 g RV test without any vibration isolation implemented is shown in Figs 13(a) and 13(b). Significant degradation in phase noise of around ~ 50, ~45, and ~15 dB is observed at offsets of 100 Hz, 1 kHz, and 10 kHz, respectively, in Fig. 13.

Fig. 12.

(a) Ambient phase noise performance of reference signal. (b) Ambient phase noise performance of X-band signal.

Fig. 13.

(a) Phase noise degradation of reference signal. (b) Phase noise degradation of X-band signal.

Hence to improve the phase noise performance, the implementation of structural analysis, spatial analysis, and stabilization methods (i.e. mechanical and electrical) as per present disclosure are implemented. Significant impact in phase noise stabilization during all axes is achieved. Results of phase noise performance of reference crystal of 100 MHz and X-band signal are shown in Figs 14–16 [Reference Kumar, Jayasheela, Shivakumar and Manjunath14–Reference Kumar and Sarkar16].

1. i) X-axis RV

2. ii) Y-axis RV

3. iii) Z-axis RV

Fig. 14.

(a) Inset X-axis phase noise performance of reference signal. (b) Inset X-axis phase noise performance of X-band signal.

Fig. 15.

(a) Inset Y-axis phase noise performance of reference signal. (b) Inset Y-axis phase noise performance of X-band signal.

Fig. 16.

(a) Inset Z-axis phase noise performance of reference signal. (b) Inset Z-axis phase noise performance of X-band signal.

Tables 1 and 2 summarize comparison of phase noise results of reference signal and X-band signal measured before and during (with or without stabilization mechanism) RV.

Table 1.

Reference source random vibration results

PV – pre vibration, DVS – during vibration without stabilization, DVWS – during vibration with stabilization.

Table 2.

X-band random vibration results