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)

Works spreadsheet (still
beats a slide-rule!)

A related Excel spreadsheet
converts phase noise to Allan variance.

Vibration Isolation Systems

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.

REFERENCES:

Aeroflex International, Inc.

35 South Service Road, Plainview, N.Y. 11803

Phone: 516-694-6700, Fax: 516-694-4823