Introduction to Quartz Frequency Standards - Oscillator Comparison and Selection

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The discussion that follows applies to wide-temperature-range frequency standards (i.e., to those which are designed to operate over a temperature range that spans at least 90°C). Laboratory devices that operate over a much narrower temperature range can have better stabilities than those in the comparison below.

Commercially available frequency sources cover an accuracy range of several orders of magnitude--from the simple XO to the cesium-beam frequency standard. As the accuracy increases, so does the power requirement, size, and cost. Figure 34, for example, shows the relationship between accuracy and power requirement. Accuracy versus cost would be a similar relationship, ranging from about $1 for a simple XO to about $40,000 for a cesium standard (1991 prices). Table 1 shows a comparison of salient characteristics of frequency standards. Figure 35 shows the comparison of short term frequency stability ranges as a function of averaging time [43]. Figure 36 shows a comparison of phase-noise characteristics, and Table 2 shows a comparison of weaknesses and wear-out mechanisms.

Figure 34
Figure 34. Relationship between accuracy and power requirements (XO=simple crystal oscillator; TCXO=temperature-compensated crystal oscillator; OCXO=oven-controlled crystal oscillator; Rb=rubidium frequency standard; Cs=cesium beam frequency standard).

Figure 35
Figure 35. Stability as a function of averaging time comparison of frequency standards.

Figure 36
Figure 36. Phase instability comparison of frequency standards.

 Quartz OscillatorsAtomic Oscillators
(per year)
2 x 10-66 x 10-81 x 10-85 x 10-107 x 10-102 x 10-11
Aging/year5 x 10-72 x 10-85 x 10-92 x 10-102 x 10-100
Temp. Stab.
(range, °C)
5 x 10-7
(-55 to +85)
3 x 10-8
(-55 to +85)
1 x 10-9
(-55 to +85)
3 x 10-10
(-55 to +68)
5 x 10-10
(-55 to +85)
2 x 10-11
(-28 to +65)
Stability, sy(t)
1 x 10-93 x 10-101 x 10-123 x 10-125 x 10-125 x 10-11
Warmup time
(to 1 x 10-6)
(to 2 x 10-8)
(to 1 x 10-8)
(to 5 x 10-10)
(to 5 x 10-10)
(to 2 x 10-11)
Power (W)
(at lowest temp.)
Price (~$)1001,0002,0008,00010,00040,000
*Including environmental effects (note that the temperature ranges for Rb and Cs are narrower than for quartz).
Table 1. Comparison of frequency standards' salient characteristics.

 WeaknessWearout Mechanisms
Radiation hardness
Rubidium depletion
Buffer gas depletion
Glass contaminants
Temperature range
Cesium supply depletion
Spent cesium gettering
Ion pump capacity
Electron multiplier
Table 2. Comparison of frequency standards' weaknesses and wearout mechanisms.

Characteristics are provided in Table 1 for atomic oscillators: rubidium and cesium frequency standards and the rubidium-crystal oscillator (RbXO). n atomic frequency standards, the output signal frequency is determined by the energy difference between two atomic states, rather than by some property of a bulk material (as it is in quartz oscillators). An introductory review of atomic frequency standards can be found in reference 44, and reference 45 is a review of the literature up to 1983. (Reference 44 reviews both atomic and quartz frequency standards; the report you are reading is based on the quartz portion of that document.) The RbXO is a device intended for applications where power availability is limited, but where atomic frequency standard accuracy is needed [46,47]. It consists of a rubidium frequency standard, a low-power and high-stability crystal oscillator, and control circuitry that adjusts the crystal oscillator's frequency to that of the rubidium standard. The rubidium standard is turned on periodically (e.g., once a week) for the few minutes it takes for it to warm up and correct the frequency of the crystal oscillator. With the RbXO, one can approach the long-term stability of the rubidium standard with the low (average) power requirement of the crystal oscillator.

The major questions to be answered in choosing an oscillator include:

  1. What frequency accuracy or reproducibility is needed for the system to operate properly?
  2. How long must this accuracy be maintained, i.e., will the oscillator be calibrated or replaced periodically, or must the oscillator maintain the required accuracy for the life of the system?
  3. Is ample power available, or must the oscillator operate from batteries?
  4. What warmup time if any, is permissible?
  5. What are the environmental extremes in which the oscillator must operate?
  6. What is the short-term stability (phase-noise) requirement?
  7. What is the size constraint?

In relation to the second question, what cost is to be minimized: the initial acquisition cost or the life-cycle cost? Often, the cost of recalibration is far higher than the added cost of an oscillator that can provide calibration-free life. A better oscillator may also allow simplification of the system's design.

The frequency of the oscillator is another important consideration, because the choice can have a significant impact on both the cost and the performance. Everything else being equal, an oscillator of standard frequency, such as 5 MHz or 10 MHz, for which manufacturers have well established designs, will cost less than one of an unusual frequency, such as 8.34289 MHz. Moreover, for thickness-shear crystals, such as the AT-cut and SC-cut, the lower the frequency, the lower the aging [17]. Since at frequencies much below 5 MHz, thickness-shear crystals- become too large for economical manufacturing, and since all the highest stability oscillators use thickness shear crystals, the highest stability commercially available oscillator's frequency is 5 MHz. Such oscillators will also have the lowest phase-noise capability close to the carrier. There are also some excellent 10 MHz oscillators on the market; however, oscillators of much higher frequency than 10 MHz have significantly higher aging rates and phase noise levels close to the carrier than do 5 MHz oscillators. For lowest phase-noise far from the carrier, where the signal-to-noise ratio determines the noise level, higher frequency crystals (e.g., 100 MHz) can provide lower noise because such crystals can tolerate higher drive levels, thereby allowing higher signal levels.

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