Vibration-Induced Phase Noise
Quartz crystal oscillators change frequency slightly when accelerated. Crystals exhibit an acceleration sensitivity and, if the designer is careless, so will the circuitry. This sensitivity may be observed in stable oven oscillators by employing the “two-g tip-over” test. When an oscillator is turned upside-down, the force on the crystal changes by two g (plus-one g to minus-one g). A typical SC-cut 10 MHz crystal will change about 0.02 Hz which gives a sensitivity of about 0.01 Hz per g. Generally, higher frequency crystals will have less g sensitivity but the sensitivity can vary significantly from one to the next crystal and from one crystal holder type to the next. Changing stress on critical components or even slight movement can also shift the frequency, adding to the oscillator’s overall sensitivity.
The sensitivity to acceleration means that the random and periodic mechanical vibrations found in many equipment bays and instruments can induce significant phase noise in high-performance crystal oscillators. Portable units are exposed to significant vibration in trucks, tanks, ships, helicopters, jets, and even back-packs. Stationary units may be near vibrating machinery or simply shaken by a nearby cooling fan. Crystal holders, circuit boards, and cases can exhibit mechanical resonance giving the oscillator substantially increased sensitivity at particular frequencies of vibration but careful design and crystal mount selection can move these resonance to high frequencies where mechanical damping is more effective.
Acceleration sensitivity is a vector quantity which may be expressed by a magnitude and direction or as the summation of three orthogonal vectors usually aligned with the sides of the oscillator’s case. The induced phase noise may be calculated from the following equation:
L(f) = 20 log ((acceleration sensitivity x acceleration x oscillator frequency) / (2 x vibration frequency)),
where the acceleration is the g level for sine wave vibrations or the square-root of twice the power spectral density in a one hertz bandwidth for random vibration.
The spreadsheets supplied below perform this calculation for random vibration. (They may be used to calculate the vibration for a sine wave by entering one-half the actual vibration level.) The first section of the spreadsheet calculates the effect of a single degree-of-freedom vibration isolation system given the natural frequency and the damping factor. The second graph shows the phase noise of an oscillator with a specified acceleration sensitivity mounted on the vibration damping system. The vibration isolation system may be removed from the calculation by entering a very high natural resonance frequency (1E6) so that no vibration damping occurs over the frequency span shown. Vibration profiles may be entered by changing a scaling factor, either increasing or decreasing the level from some nominal point. The frequency points may be changed or additional columns may be added.
It is worth noting that the vector nature of the acceleration sensitivity means that the oscillator will be most sensitive to vibration in one particular direction and that there is a plane where the sensitivity approaches zero (any direction orthogonal to the sensitivity vector). In critical systems, the oscillator may be positioned so that the sensitivity vector points in the direction of least vibration or in the direction of best isolation when a vibration isolator is used. There have been efforts to compensate crystal oscillators by pointing an accelerometer in the direction of the sensitivity vector to develop a correction voltage to apply to the electrical tuning. An enhanced version of this approach could use a digital signal processor (DSP) to convert the rather linear accelerometer output into the rather non-linear profile needed to correct the phase of the oscillator, possibly even compensating for mechanical resonance. Another scheme uses two crystals with matched acceleration vectors pointing in opposite directions. The author has proposed a bootstrapping scheme employing two crystals with the acceleration vectors pointing in the same direction but with different magnitudes.
The most common approach to reducing vibration-induced phase noise is to select low sensitivity crystals and isolate the oscillators with a low natural frequency vibration isolators. Small, omni-directional urethane shock mounts may be contained within the oscillator package when size is critical. When space permits, an external vibration mount can provide a lower natural frequency, taking advantage of the entire oscillator’s weight along with the weight of the mounting plate and additional ballast if necessary. Vibration mounts must be chosen carefully since many materials exhibit substantial stiffness changes over temperature and most mounts exhibit direction-dependent isolation. The designer must allow sufficient room around the isolated assembly to prevent impact with other objects with normal vibration levels.
The reduction of crystal oscillators’ vibration sensitivity is currently receiving the attention of many in the frequency control industry including both crystal and oscillator manufacturers. Oscillators have reached the level of performance where a person walking across the room can degrade the close-in phase noise and a relatively quiet fans can generate sidebands well above the noise floor of the better oscillators. SC-cut crystals have not yielded the performance improvements that were hoped but occasional units exhibit superb performance for reasons not fully understood hinting that a solution is just around the corner.
Zipped spreadsheet files:
Excel spreadsheet (best choice)
A related Excel spreadsheet converts phase noise to Allan variance.
Vibration isolation systems are only effective in reducing the level of vibration above the system’s resonant frequency. And, at the resonant frequency, an amplified response will occur which depends upon the damping characteristics of the isolator. Below the resonant frequency, the isolation system has little effect on the vibration. When single-tone vibration or high levels of low-frequency vibration are present, the designer must pay careful attention to the vibration amplification near resonance and to the “rattle room” and the behavior of the mounts near the end of their travel. In some situations, a poorly chosen vibration system can make matters worse and even cause damage that would not otherwise have occurred! However, in most situations a vibration isolation system will significantly reduce the total vibration level reaching the protected device and its relatively low resonance frequency will protect components with high natural frequencies. For example, a modest effort will yield a crystal oscillator isolation system with a natural frequency below 200 Hz and the resonance frequencies of the PCB and crystal mount are often above 1000 Hz so potentially troublesome vibration energy will be significantly attenuated before reaching these resonance frequencies.
Attaining a low resonance frequency below about 100 Hz can prove difficult when mounting small components like crystal oscillators and usually additional mass must be added. A brass mounting plate is a convenient mass, providing a place to attach the oscillator, shock mounts, and cable tie-down points. Interconnecting cables should be flexible and secured so that flexure occurs along the length of the cable and not at the ends. A short, stiff cable can devastate the isolation characteristics of good mounts! Lower frequency mounting systems will need more room to move and highly non-linear stops can generate high frequency vibrations. Several components may be mounted in a machined housing for additional mass but careful attention must be paid to the design of the enclosure to avoid resonance in the sides and top. Soft elastomer mounts change stiffness over temperature and a reasonable system at room temperature might become too stiff at cold temperatures or allow the assembly to move too far when hot. Many shock mounts are non-linear, becoming significantly more stiff at the deflection extremes but to take full advantage of this non-linearity the designer must allow the mount sufficient room to stretch. The stiffness of the mount will be direction-dependent so it is often necessary to determine the resonance frequency in the worse-case axis. Often the device can be oriented on the mounting plate to take advantage of the best axis of isolation. For example, a crystal oscillator has an acceleration sensitivity vector which could be pointed along the axis of best isolation. Resonance frequencies as low as 10 Hz are attainable with a few pounds of mass and suitably “springy” mounts.
The choices of available shock mounts and vibration isolation materials will fill a bookshelf and can bewilder the newcomer with choices. The designer must consider the cost of the various approaches, the lifetime of the materials, the effects of temperature, the space available, and dozens of other application-specific considerations. In some instances the assembly may be wrapped in one of a variety of foam blankets and slipped into a can, much the way a product is packed in a cardboard box for shipping. This method usually results in a high resonance frequency and the damping can be rather low for many foams, particularly the long-life silicone rubbers. Specialty foams are available with good damping characteristics but the designer must beware of operating temperature and aging effects. Another common approach is to mount the device on neoprene or other elastomer mounts. Very small mounts rated for light weights are available and will provide good isolation and low resonance frequency but many of the materials used change stiffness significantly over temperature.
One of the better types of isolator is manufactured by Aeroflex International, Inc. The all-metal design provides consistent performance over temperature and time and the stranded wire rope design offers excellent damping and omni-directional isolation. The “Circular Arch Series” is particularly convenient for smaller assemblies:
Courtesy Aeroflex International, Inc.
These isolators feature stainless steel rope and aluminum attachment housings and come in a variety of sizes and styles. The damping factor is considerably higher than similar size elastomer mounts. The actual numbers are a bit elusive but a good starting value is 0.2 or more and a typical elastomer mount might have a damping factor below 0.1. The actual damping will depend on the installation and amount of deflection. These mounts exhibit a helpful non-linearity, becoming softer with increased vibration level, which tends to prevent large resonance-induced deflections.
In addition to shock mounting the assembly, additional steps may be taken to improve vibration isolation. Insulation may be added to block acoustical noise and vibration deadening materials may be added to flat surfaces exhibiting resonance. Electrostatic and magnetic shields may be necessary in some installations since the isolated device will have motion relative to the chassis and other components. And last, but not least, the intrinsic sensitivity of the device itself might be reduced.
Aeroflex International, Inc.
35 South Service Road, Plainview, N.Y. 11803
Phone: 516-694-6700, Fax: 516-694-4823