Introduction to Quartz Frequency Standards - Static Frequency versus Temperature Stability

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As an illustration of the effects that temperature can have on frequency stability, Figure 19 shows the effects of temperature on the accuracy of a typical quartz wristwatch. Near the wrist temperature, the watch can be very accurate because the frequency of the crystal (i.e., the clock rate) changes very little with temperature. However, when the watch is cooled to -55°C or heated to +100°C, it loses about 20 seconds per day, because the typical temperature coefficient of frequency of the tuning fork crystals used in quartz watches is -0.035 ppm/°C².

Figure 19. Wristwatch accuracy as it is affected by temperature.

The static f vs. T characteristics of crystal units are determined primarily by the angles of cut of the crystal plates with respect to the crystallographic axes of quartz [3-5]. "Static" means that the rate of change of temperature is slow enough for the effects of temperature gradients (explained later) to be negligible. As Figure 11 illustrates for the AT-cut, a small change in the angle of cut (seven minutes in the illustration) can significantly change the f vs. T characteristics. The points of zero temperature coefficient, the "turnover points," can be varied over a wide range by varying the angles of cut. The f vs. T characteristics of SC-cut crystals are similar to the curves shown in Figure 11, with the inflection temperature (T_i) shifted to about 95°C. (The exact value of T_i depends on the resonator's design.)

Other factors that can affect the f vs. T characteristics of crystal units include the overtone [21]; the geometry of the crystal plate; the size, shape, thickness, density and stresses of the electrodes; the drive level; impurities and strains in the quartz material; stresses in the mounting structure; interfering modes; ionizing radiation; the rate of change of temperature (i.e., thermal gradients) [22]; and thermal history. The last two factors are important for understanding the behaviors of OCXOs and TCXOs, and are, therefore, discussed separately.

The effect of harmonics, i.e. "overtones," on f vs. T is illustrated for AT-cut crystals in Figure 20 [21]. This effect is important for understanding the operation of the MCXO. The MCXO contains an SC-cut resonator and a dual mode oscillator that excites both the fundamental mode and the third overtone of the resonator. The difference between the fundamental mode f vs. T and the third overtone f vs. T is due almost exclusively to the difference between the first order temperature coefficients. Therefore, when the third overtone frequency is subtracted from three times the fundamental mode frequency, the resulting "beat frequency" is a monotonic and nearly linear function of temperature. This beat frequency enables the resonator to sense its own temperature.

Figure 20. Effects of harmonics on f vs. T.

Interfering modes can cause "activity dips" (see Figure 21), which can cause oscillator failure [23]. Near the activity dip temperature, anomalies appear in both the f vs. T and resistance (R) vs. T characteristics. When the resistance increases at the activity dip, and the oscillator's gain margin is insufficient, the oscillation stops. Activity dips can be strongly influenced by the crystal's drive level and load reactance. The activity-dip temperature is a function of C_L because the interfering mode usually has a large temperature coefficient and a C₁ that is different from that of the desired mode. Activity dips are troublesome in TCXOs, and also in OCXOs when the dip occurs at the oven temperature. The incidence of activity dips in SC-cut crystals is far lower than in AT-cut crystals.

Figure 21. Activity dips in the frequency versus temperature and resistance versus temperature characteristics, with and without C_L.

An important factor that affects the f vs. T characteristics of crystal oscillators is the load capacitor. When a capacitor is connected in series with the crystal, the f vs. T characteristic of the combination is rotated slightly from that of the crystal alone. The temperature coefficient of the load capacitor can greatly magnify the rotation [24].

The f vs. T of crystals can be described by a polynomial function. A cubic function is usually sufficient to describe the f vs. T of AT-cut and SC-cut crystals to an accuracy of ±1 ppm. In the MCXO, in order to fit the f vs. T data to ±1 x 10^-8, a polynomial of at least seventh order is usually necessary [25].

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