Basic Technology of Quartz Crystal Oscillators

1. Categories of Quartz Crystal Oscillators

Quartz crystal oscillator is a timing device consisting of quartz crystal resonator and an oscillation circuit to generate an output waveform at specified frequency.  It can be classified into four main categories based on its typical applications.

XO - Crystal Oscillator

The device does not have temperature control or temperature compensation.  Frequency - temperature characteristics depend on the crystal units.  It is also called SPXO – Simple Packaged Crystal Oscillator or Clock.

TCXO - Temperature Compensated Crystal Oscillator

The device has temperature compensation circuit to suppress output frequency deviation caused by surrounding temperature.  That is, e.g. the output signal from a temperature sensor (e.g., a thermistor) is used to generate a correction voltage that is applied to a variable reactance (e.g., a varactor) in the crystal network.  The reactance variations compensate for the crystal's F vs. T characteristic. Analog TCXO can provide about a 20X improvement over the crystal's F vs. T variation.

OCXO - Oven Controlled Crystal Oscillator

The device usually contains an oven block where the temperature sensor, heating element, oven circuitry, and insulation function to maintain a stable temperature. By keeping the temperature of the crystal and other temperature sensitive components, great improvements in oscillator performance are realized such that the crystal's F vs. T has zero slope.  OCXOs can use either AT-, SC-, or IT- cut crystals depending on temperature range and aging performance.  Typical OCXO can provide a >1000X improvement over the crystal's f vs. T variation. The following table summarizes the best stability each type of oscillator can hold based on today’s typical manufacturing process.

VCXO - Voltage Controlled Crystal Oscillator

Crystal oscillator that has tunable output frequency or modulated output frequency by external control voltage.  The connection of a variable capacitance diode (varactor) with crystal unit in series can lead the diode capacitance to be changed according to the voltage applied for frequency tuning, thus pulling frequency away from its normal value based on the load capacitance characteristics of the crystal unit.

2. Terminology Discussion on Quartz Crystal Oscillators

Frequency Stability

Deviation from the nominal output frequency (F_measured – F_norminal )/ F_norminal, including the frequency deviation from the following factors:

Manufacturing process – Initial Accuracy and Aging: Initial Accuracy is where the frequency is set close to the nominal frequency at room temperature (25 C) ranging from ± 100 ppm to ± 0.25 ppm; Aging is the frequency shift of the crystal over a certain time period.  The following table shows typical first year aging for 10 MHz Clock, TCXOs, and OCXOs.

Temperature - How the unit changes frequency over the temperature range.  In a well-designed oscillator the frequency stability vs. temperature is determined primarily by the temperature characteristic of the crystal, and the oscillator manufacturer must select the crystal characteristics that conform to the oscillator circuit to insure that the intrinsic stability of the crystal is not degraded.

Power source variation – Oscillator frequency will change slightly as the supply voltage changes.  The typical fractional change ranges from ±1 ppb to ±10 ppb for a ±10% change in supply voltage. Voltage sensitivity tends to be largest in TCXOs having a low supply voltage.

Load variation – Oscillator frequency will also change slightly as the load applied to the output port varies.  The typical fractional frequency change ranges from ±0.1 to ±10 ppb for a load change of ±10% for sine wave outputs, or ±1 gate for logic outputs.  Since the load can be made nearly constant in most applications, load sensitivity is usually not significant.

Operating Temperature Range

Temperature range satisfies the output frequency stability and output signal characteristics specifications.  Military: -55 °C to +125 °C; Industrial: -40 °C to +85 °C; Commercial: 0 °C to +70 °C.

Oscillator Output

The output of a hybrid quartz crystal oscillator is a highly stable reference signal, and it can be characterized in the following parameters:

Frequency – It is how fast the output signal is changing, measured in Hertz (Hz). One Hertz corresponds to one complete cycle of a waveform occurring in one second.

Waveform – The waveform is periodic, which means it repeats the same pattern indefinitely.  The most popular waveform is squarewave as shown in the following schematic drawing:

                                Squarewave Waveform

Logic - The vast majority of systems require a crystal oscillator output that is TTL compatible, CMOS compatible, ECL compatible or some combinations of logic families such as TTL/HCMOS compatible.  Details on those output logic are summarized in the following tables:

TTL (Transistor – Transistor Logic)

CMOS (Complementary Metal-Oxide Semiconductor)

ECL (Emitter Coupled Logic)

LVDS (Low Voltage Differential Signaling) - It is a new industry technology, which provide a low cost, multi-gigabit data transfer (100 Mbps and higher) on copper cables or printed circuit boards traces.  LVDS technology has many advantages including fast bit rates, low power consumption (16 times less than PECL), and good noise performance.  LVDS uses differential data transmission of 300 mV.  This differential signal is immune to common-mode noise, which is the primary source of system noise.  The low voltage swing of 300 mV decreases emissions and cross talk problems.

Fan-out (Loads) – the number of logic chips the IC can drive.

Drive Capability - Indicating the maximum load the oscillator can drive specified at pF in CMOS logic and the number of gates in TTL logic.  If this value exceeds the maximum rated load of the oscillator, signal degradation can occur.

Startup Time - The startup time is specified as the time that an oscillator take to reach its specified RF output amplitude.  The startup time is determined by the closed loop time constant and the loading condition of its circuit.

Rise & Fall Time (t_r & t_f) - The rise time of an oscillator is defined as the transition time of the output waveform from low stage (logic “0”) to high stage (logic “1”).  The fall time of an oscillator is defined as the transition time of the output waveform from high stage (logic “1”) to low stage (logic “0”).  Fast rise & fall time requirements can steer a user to using ECL, even for frequencies typically satisfied by HCMOS/TTL.  Increasing the load will increase the rise and fall times of the device.

Symmetry or Duty Cycle - The measure of output waveform uniformity or the shape of the waveform, which is made up of logic “1” and logic “0” cycle times.  It is defined as the ratio of the time periods of the logic 1 level (T_H) to the time periods of one complete cycle (T), measured at 1.4 volts for TTL logic and 50% of the peak-to-peak voltage for CMOS and ECL logic.  Sym = T_H/T x 100%.

Tri-state Enable – By applying a command input signal to the oscillators, the output of the clock oscillators is turned off or disabled.  When this feature is activated, the oscillators assume a high impedance state.

Input Current and Supply Voltage

Input current is the amount of current drain by an oscillator in its operating condition.  Different logic oscillators require different input current.  Supply voltage is the voltage necessary to operate the oscillator.  It is typically 5 V or 3.3 V.

Phase Noise & Jitter

Phase noise is the term used to quantify signal noise in the frequency domain and such phase noise measurements and specifications are common to most RF engineers in their work.  In the time domain, signal purity is described in terms of jitter so measurements and specifications on jitter are common to digital signal engineers.  The root causes of phase noise and jitter are essentially the same, so the design and production techniques used to optimize both are the same.

Phase noise is a small fraction of undesirable frequency near the output frequency, and is usually expressed as the SSB spectral density in dBc/Hz.  Phase noise is dependent mostly on the crystal with the circuitry making up the unit playing a small role.  The measurement is commonly in the 1 Hz bandwidth.  The description of phase noise is "at x Hz offset it is y dBc/Hz".  Low levels of phase noise are achieved through careful circuit design and use of carefully processed high-Q resonators.

Harmonic Distortion

The non-linear distortion due to un-wanted harmonic spectrum component related with target signal frequency.  Each harmonic component is the ratio of electric power against desired signal output electric power and expressed in terms of dBc.  Harmonic distortion specification is important especially in Sine output when a clean and less distorted signal is required.

Activity Dip

Activity dips result from mechanical coupling of the principal mode to one or another of a number of interfering modes, which exist but are not electrically excited by the resonator electrodes.  At some temperature, the frequency of the interfering modes coincide with the frequency of the desired mode, energy is lost from the main mode, thereby causing an increase in the resonator equivalent resistance at that temperature.  Accompanying the activity dip is a deviation of the F vs. T characteristic from a smooth curve, but this is often much less pronounced than the resistance increase. In extreme cases, when the oscillator gain is insufficient, the resistance increase stops the oscillation over a range of temperature.  In addition, even when the resistance increase is not large enough to stop the oscillation, the frequency change can cause intermittent failures, e.g., it can cause a loss of lock in phase locked systems.

G-Sensitivity

It is a measure of the sensitivity to acceleration, also known as Acceleration Sensitivity, which is the frequency shift caused by subjecting the crystal to a constant acceleration.  The most notable test is the Two G Tip-over test.  Here the G-sensitivity is measured by allowing the oscillator to stabilize, and the frequency is measured.  The oscillator is then turned upside down, 180º, and the frequency is measured again.  This test is repeated for each major axis of the oscillator.  The difference in frequency is divided by 2, yielding the static G-sensitivity.  The following table shows the typical g-sensitivity numbers

Vibration Sensitivity

It is the measure of the oscillator sensitivity to vibration.  It can be viewed in two ways: dynamic and static.  Dynamic sensitivity refers to degradation of phase noise due to vibration while the unit is powered in the target system.  This can be different from the static G-sensitivity number in that the oscillator may posses an internal structural resonance, which will have a higher sensitivity as certain frequencies.  In most case, the dynamic sensitivity is not an issue, since typical oscillators are rack mounted and not subjected to significant vibration levels.  The static sensitivity, also known as sensitivity to transportation, is a more important factor, as it happens in transit from manufacturer to customer and is normally outside of the control of the manufacturer.  The shock and vibration can result in shifts in the calibration frequency, resulting in an offset as the customer.  Packaging and design of the oscillator can help to reduce this effect, so that the part is still within specification on arrival at the customer site.

Stand by Function

A function built in the IC that temporary turns off the oscillator to save power.

3. Voltage Controlled Crystal Oscillators

A VCXO is a quartz crystal oscillator that includes a varactor diode and associated circuitry allowing the frequency to be changed by application of a voltage across that diode.  This can be accomplished in a simple logic clock or sine wave crystal oscillator, or a TCXO (resulting in a TC/VCXO-temperature compensated voltage controlled crystal oscillator), or an oven controlled type (resulting in an OC/VCXO-oven controlled voltage crystal oscillator).  In addition to those characteristics that define the fixed frequency crystal oscillators (XOs), there are several characteristics peculiar to VCXOs.  Primary among the specifications that are peculiar to VCXOs are the following:

Control Voltage

This is the varying voltage, which is applied to the VCXO input terminal causing a change in frequency.  It is sometimes referred to as Modulation Voltage, especially if the input is an AC signal.

Deviation/Pulling Range

This is the amount of frequency change that results from changes in control voltage.  For example, a change of control voltage from 0.5 to 4.5 volt might result in a deviation of 100 ppm.  This parameter can also define so-called average slope which is the total frequency deviation divided by the total control voltage swing.

Slope Polarity/Transfer Function - This denotes the direction of frequency changes with respect to the control voltage.  A positive transfer function denotes an increase in frequency for an increasing positive control voltage.  Conversely, if the frequency decreases with a more positive (or less negative) control voltage, the transfer function is negative.

Linearity

The generally accepted definition of linearity is that specified in MIL-0-55310.  It is the ratio between frequency error and total deviation, expressed in percent, where frequency error is the maximum frequency excursion from the so-called “Best Straight Line” drawn through a plot of output frequency vs control voltage.  If the specification for an oscillator requires a linearity of ±10% and the actual deviation is 10 kHz total as an example, the curve of output frequency vs control voltage input could vary as much as ±1 kHz (10 kHz ±10%) from the Best Straight Line.  On the other hand, if the maximum deviation from the Best Straight Line is 20 ppm and the total deviation is 200 ppm, the linearity is ± 20 ppm/200 ppm = ± 10%, which is the linearity value for a typical VCXO.  Good VCXO design dictates that the voltage vs frequency curve be smooth (no discontinuities) and monotonic.

Modulation rate/Frequency Response

This is the rate at which the control voltage can change resulting in a corresponding frequency change.  It is measured by applying a sinewave signal with a peak value equal to the specified control voltage, demodulating the VCXO's output signal, and comparing the output level of the demodulated signal at different modulation rates.  While non-crystal controlled VCOs can be modulated at very high rates (greater than 1 MHz for output frequencies greater than 10 MHz), the modulation rate of VCXOs is restricted by the physical characteristics of the crystal.

Stability vs. Pullability

A quartz crystal is a high Q device, which is the stability-determining element for the crystal oscillator.  It inherently resists being "pulled" (deviated) from its designed frequency.  In order to produce a VCXO with significant pullability, the oscillator circuit must be "de-Q'd".  This results in degrading the inherent stability of the crystal in terms of its frequency vs temperature characteristic, its aging characteristic, and its short-term stability (and associated phase noise) characteristic.  One particular scenario with VCXOs is that increased deviation results in degraded stability which can result in the need for still wider deviation, further degrading stability, resulting in a spiraling increase in the required deviation.  Therefore, it is in the user's best interest not to specify a wider deviation than that absolutely required.

Phase Locking Application

When a VCXO is being used in phase lock loop application, the deviation should always be at least as great as the combined instability of the VCXO itself and the reference or signal onto which it is being locked.  However, if the open loop stability requirements of a system are more stringent than what a standard VCXO can provide, a TC-VCXO may be required. For the highest stability open loop requirements, the appropriate oscillators may be those TCXOs or OCXOs that incorporate a narrow deviation VCXO option.

Oscillator Output Frequencies

Fundamental mode crystals (generally 10 - 35 MHz) permit the widest deviation, while 3rd overtone crystals (generally 30 - 125 MHz) allow deviation approximately 1/9^th of that which applies to fundamentals.  Therefore, all wide deviation VCXOs (greater than ±100 to ±200 ppm deviation) uses fundamental crystals.  On the other hand, narrower deviation VCXOs can use either fundamental mode or 3rd overtone crystals, and the selection of which often depends upon such specifications as linearity and stability.  It is rare that higher overtone, and therefore higher frequency crystals find applications in VCXOs.  Thus, VCXOs with output frequencies higher or lower than available frequencies from the appropriate crystals include frequency multipliers or dividers.

4. Temperature Compensated Crystal Oscillators

The temperature characteristics of crystal oscillators are largely depending on those of crystal units used which are generally expressed by cubic curves of AT cut quartz blank.  The temperature compensating circuit, which must be custom-built for each unit, is used to tune the oscillator just enough to offset the uncompensated frequency change with temperature.  TCXO features excellent temperature characteristics, fast warm-up time (typically 50 to 1000 ms), low power consumption (10 to 150 mW), lightweight, compactness, and with a fraction of the cost of an OCXO’s.  It is ideally suited for various communications equipment such as cellular phones, two-way radios, cordless telephones, microwave communications equipment and satellite communications system, measurement instrument and many more other applications.

                                    Example of TCXO Compensation

Temperature Stability

With standard compensation techniques, fractional stabilities of around ±1 ppm for a temperature range of –40 C to +85 C can be achieved.  Better stabilities can be achieved over narrower temperature ranges.  The actual technique employed in all except the most simple TCXOs is based upon use of a varactor diode in series with the crystal as follows:

A change in voltage causes a change in the capacitance of the varactor diode resulting in a change in frequency of oscillation. The thermistor network is tailored to the crystal to cause voltage to vary with temperature in such a manner that will compensate for the crystal's frequency versus temperature characteristic.  As each individual TCXO requires that its compensation network be matched to its individual crystal, the cost of a TCXO is closely related to the difficulty of the frequency versus temperature specification.

Frequency-temperature hysteresis limits the ultimate attainable stability of a TCXO.  The crystal resonator is a primary source of this hysteresis, which can be minimized but not eliminated.  To allow for aging, most TCXO are made tunable over a small frequency range, using a voltage control function (VCTCXO).  A typical functional tuning range is ±5 ppm.

Further, it should be noted that the frequency versus temperature characteristic of a TCXO is not linear; thus a 2xl0^-7 total error over O°C to +50°C will not produce a gradient of 2x10^-7 ÷ 50 = 4x 10^-9 per ºC.  Perturbations in the crystal characteristics (activity dips) make it virtually impossible to guarantee exceptional stability on a per degree basis in TCXOs.

Thermal Hysteresis

It is a measure of a TCXO to repeat the frequency versus temperature data over multiple temperature cycles.  Here the frequency of a TCXO is measured at one temperature.  The temperature is changed and then returned to the original temperature and the frequency is measured again.  The two frequencies are not the same.  The difference between the two frequencies is called “thermally induced hysteresis”.  This phenomenon is present even if the unit is allowed to stabilize at the same temperature for a long time.  The value of this thermal induced hysteresis is normally of the order of ±0.1 ppm for a good TCXO.

Thermal Transient

Thermal transient occurs when the rate of temperature change is high enough for the frequency to no longer tack the well-behaved curve that is generated when measured with slow temperature changes.  An acceptable rate of the temperature change would be of the order of 0.5 C per minute.  This effect is in a large part due to the transient response of the crystal resonator, and the separation between resonator and temperature sensing devices within the oscillator.  In an OCXO, it can also depend on the stability and gain of the error amplifier used in the temperature controller.  Typical values are less than ±0.2 ppm.

The testing and compensation accuracies of TCXOs can be adversely affected by the thermal-transient effect.  As the temperature is changed, the thermal-transient effect distorts the static F vs. T characteristic, which leads to so-called apparent hysteresis.  The faster the temperature is changed, the larger is the contribution of the thermal-transient effect to the F vs. T performance.

Aging

In clock oscillators with moderate temperature stability, aging is usually of little consequence. However, in highly temperature stable TCXOs, crystal aging becomes a significant factor in the oscillator's overall frequency error.  Therefore, it is very common for TCXOs to employ specially processed crystals in evacuated glass or cold weld holders.

Shock

Shock is defined as a sudden powerful blow.  A typical shock number for TCXOs is 100g.

Mechanical Trim and EFC (electrical frequency control)

Mechanical trim allows the frequency to be adjusted via an internal potentiometer (pot).  The pot is accessed through a sealed or unsealed hole.

EFC (electrical frequency control) requires an external circuit to adjust the frequency.  The external circuit usually consists of a pot or DAC.  The power for this circuit can be applied via an external voltage source supplied by the customer or an internal reference voltage supplied by the manufacturer.

5. Oven Controlled Crystal Oscillators

In an OCXO the crystal and other temperature sensitive circuitry is placed in a temperature controlled structure.  The idea is to keep the crystal at a stable temperature higher than the highest ambient temperature to which the OCXO will be exposed.  For best results, the oven is set to the resonators turnover temperature.  Either AT-cut or SC- cut crystal resonators may be used.  The SC-cut crystal resonator offers the best overall performance, while the AT-cuts offers lower cost.

The primary reason behind controlling the temperature is to remove the effect of temperature induced anomalies.  All quartz crystal resonators are associated with those thermal anomalies that only allow compensation (or predictability) to within ±0.1 ppm.  The other reason is to allow the use of higher overtone crystals which are not very pullable but very stable, to be set at particular frequency by controlling the temperature.  The use of higher overtone crystals also results in improved short-term stability resulting from higher Q of the resonators, and improved long-term performance resulting from the increased quartz mass of the resonators.

The greatest advantage of an OCXO is its stability, which is unequalled by other crystal oscillator types.  The frequency versus temperature stability of an OCXO depends on the static and dynamic F vs. T characteristics of the resonator, the design temperature range of the OCXO, the stability of the oven and of the components in the sustaining circuitry, and the accuracy with which the oven is set to the turnover temperature of the resonator.  Typical fractional stability can range from ± 20 ppb (±20E-9) to ±100 ppb.  This stability can be valid for a temperature range of –40 C to + 85 C.  Improved stability can be obtained over narrow temperature ranges.

The main disadvantage of an OCXO is power consumption, unit size, warm-up time and cost.  The amount of oven power required is determined mainly by the quality of insulation used and the temperature differential between the oven and the external environment.  Increasing amount of insulation to reduce heat loss requires an increase in size, resulting in a tradeoff between power and size.  Warm-up time is the time required for the oven to reach operating temperature and for the frequency to stabilize.  It is largely dependent on available power, the thermal mass of the oven, the quality of insulation, and ambient temperature.  Typical warm-up times are from 15 seconds to 5 minutes.

Setting Oven Temperature

The oven operating temperature (crystal turnover temperature) must be several degrees higher than the highest ambient temperature in which the oscillator is to operate in order that the oven may maintain good control (considering the internal heat rise generated by the oscillator itself).

However, there are disadvantages associated with high oven temperature operation. First, the crystal's frequency vs. temperature characteristic is sharper with higher turnover crystals resulting in more sensitivity to minute changes in oven temperature.  Second, and more important, crystal aging degrade with an increasing temperature.  Therefore, in designing an oven controlled crystal oscillator, one is faced with a compromise in determining the desired oven operating temperature; it should be low as practicable, but it must be high enough to provide good control at the maximum ambient operating temperature.

Warm-up on Crystal Resonator

Changing the temperature surrounding a crystal unit produces thermal gradients when, for example, heat flows to or from the active area of the resonator plate through the mounting clips.  The static F vs. T characteristic is modified by the thermal-transient effect resulting from the thermal-gradient-induced stresses.  When an OCXO is turned on, there can be a significant thermal-transient effect. 

For an OCXO utilizing the AT-cut resonator, the crystal resonator frequency rapidly decreases as the oven warms up.  This is simply due to the fact that the frequency of an AT cut crystal is considerably higher at room temperature than at its upper turnover temperature.  In a standard OCXO, the oven balances in 10 to 15 minutes, but the thermal gradients in the AT-cut crystal produce a large frequency undershoots (rubber band effect) that anneals out to its final frequency several minutes after the oven reaches equilibrium.  Typically, relatively high degree of stability is achieved within 30 minutes after turn-on and this time can be reduced to less than 5 minutes in special fast warm-up designs.  On the other hand, the SC-cut crystal, being "stress-compensated" and thereby insensitive to such thermal-transient-induced stresses, reaches the equilibrium frequency as soon as the oven stabilizes.

Oven Stability

The oven stability depends on the temperature range outside the OCXO and the thermal gain of the oven.  The thermal gain is defined as the external to internal temperature excursion ratio.  For example, if during an external temperature excursion from -40^oC to +60^oC, the temperature inside the oven changes by 0.1^oC, the thermal gain is 10³.  In addition, the thermal transient effect makes small oven offsets more difficult and time consuming to achieve with AT-cut resonators than with SC-cut designs.

When the required temperature stability is beyond that which can be achieved with a standard proportionally controlled oven, a double oven system can be employed in which the standard oven is housed within a second oven. The outer oven then buffers the ambient temperature changes to the inner oven, which contain the oscillator circuit.

Stabilization Time and Steady State

This defines as the time taken to reach a certain level of stability after a long period of being turned off.  Oven power reaches the specified maximum, after which it cuts back to reach steady state when the oven has reached its operating temperature.  Power consumption for OCXOs is typically around 5W at warm-up and 1.5W at steady state, depending on size.

Retrace

Retrace is the frequency error after power is applied, comparing to the previous value and aging rate before power was removed.  When measuring the retrace, the normal period that the OCXO is powered off is 24 hours, and the normal period powered up is to have sufficient time to allow complete thermal equilibrium.  Good retrace is obtained by proper design of the oscillator, oven mechanics, and crystal resonator.  This is of the order of ± 20 to ±50 ppb. There is significant variation in these characteristics from crystal to crystal.  In addition to the crystal related effected described above, thermal stresses from heating and cooling the oven structure can also contribute to the retrace, and changes in aging rate.  In most applications, OCXOs are continuously powered up.  This being the case, aging is the critical characteristic with turn-off/turn-on characteristic being of little or no significance.  However, when applications require frequent turn-off, an additional series of characteristics (such as Retrace) should be considered.

Double Rotated (SC-cut) Crystals

While most high stability crystal oscillators use AT-cut crystals, SC-cut crystals are often used in the highest stability OCXO models.  An SC-cut crystal is one of a family of double rotated crystals (quartz crystals cut on an angle relative to two of the three crystallographic axes).  Others in the family include the IT-cut and FC-cut.  The SC-cut represents the optimum double rotated design as its particular angle provides maximum stress compensation.   Following is a comparison between double rotated and AT-cut crystals.

            Advantages of the SC-cut crystals:

Improved aging – For a given frequency and overtone (e.g. 10 MHz, 3^rd overtone), the SC-cut crystal provides 2 to 3 times aging improvement relative to AT-cut.

Thermal transient compensated - Allowing faster warm-up in OCXOs

Phase noise – For a given oscillator design for a particular crystal frequency and overtone, the SC-cut crystal provides higher Q and associated improved phase noise characteristics.

Planar stress compensated - Smaller changes in frequency due to edge forces and bending

Static and dynamic F vs. T - Allowing higher stability OCXO and MCXO

Better F vs. T repeatability - Allowing higher stability OCXO and MCXO

Far fewer activity dips

Lower drive level sensitivity

Lower sensitivity to radiation

            Disadvantages of the SC-cut crystals:

Cost - Because of difficulties associated with tightly-controlled angle rotations around two axes in the manufacture of SC crystals vs one axis for the AT, the SC crystal is significantly higher in cost than that of an AT of the same frequency and overtone.

Pullability - The motional capacitance of an SC crystal is several times less than that of an AT of the same frequency and overtone, thus reducing the ability to "pull" the crystal frequency.  This restricts the SC crystal from being used in conventional TCXOs and VCXOs, or even in oven controlled oscillators requiring the ability to deviate the frequency of oscillation by any significant degree.

In summary, the suitability of double rotated crystals for use in crystal oscillators is essentially restricted to those oven controlled applications where the improved aging, warm-up, and close-in phase noise characteristics justify a significant cost increase.

Allan Variance

Allan Variance, also known as short-term stability, is the measure of oscillator stability in the time-domain.  It measures the RMS change in successive frequency measurements for short gate times (milliseconds to seconds) and is important in timing applications.  It typically improves as the gate time increases until it becomes a measure of the medium to long term drift of the oscillator.  This drift is either the result of the temperature coefficient of the oscillator, and/or the aging.  Typical numbers for a 10 MHz OCXOs are shown in the following Table.

6. Spread Spectrum Crystal Oscillators

A spread spectrum crystal oscillator is an oscillator that has the output frequency intentionally modulated in order to reduce the EMI on the output signal.  By modulating the output signal, the EMI on the output signal is 'spread' over a larger frequency 'spectrum'.  The total amount of energy is still present, but the spreading of the output power over the frequency band results in a reduction of EMI at any one frequency.  The regulatory bodies like the US FCC have maximum limits for the peak EMI emissions (emissions at any one frequency within the spectrum).  Therefore, a quartz crystal clock oscillator can be used to pass FCC regulatory EMI test requirements by reducing EMI peak emissions.