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Generally, AT-cut quartz crystals have a limited scope of use when it comes to high-precision measurement of very small impedance changes due to their nonlinear frequency-temperature characteristics in the range between 0 °C and 50 °C. The new method improving quartz oscillator frequency-temperature characteristic compensation is switching between two impedance loads. By modifying the oscillator circuit with two logic switches and two impedance loads, the oscillator can switch oscillation between two resonance frequencies. The difference in resonance frequencies compensates the frequency-temperature characteristics influence as well as the influence of offset and quartz crystal ageing. The experimental results show that the new approach using the switching method highly improves second-to-second frequency stability from ±0.125 Hz to ±0.00001 Hz and minute-to-minute frequency stability from 0.1 Hz to 0.0001 Hz, which makes the high-precision measurement of aF and fH changes possible.

Quartz crystal temperature characteristics are of primary importance in high-precision measurement of small impedances. Generally, sensor techniques involve capacitance and inductance changes, particularly for the measurement of pico extensions, hollow pico-sphere magnetic properties, novel magnetic pico-adsorbents, displacement field forces, humidity sensors, Van der Waals force measurement,

The application of quartz crystals for the measurement purposes using external electrical elements (_{0} capacitance compensation and high improvement of pulling sensitivity. The latter requires very stable frequency-temperature characteristics, determining the accuracy within a given measurement range. And even if an AT-cut quartz crystal with the angle of cut = 0 is selected, the temperature dependence of some ppm can still be registered [

Capacitive and inductive changes with the resolution up to 0.01 pF or 0.01 nH can also be measured with LCR instruments (Hewlett-Packard 4284A-Precision LCR meter, 20 Hz–1 MHz, 0.05%), however, once again the second-to-second and minute-to minute frequency stability plays an important role [

This research focuses on the temperature and ageing characteristics compensation of AT fundamental quartz crystals (5 MHz) operating over the measurement temperature range of 0 °C to 50 °C. Crystals fabricated in this manner exhibit excellent frequency

The new measurement method is based on a quartz oscillator [_{1} and _{2} in the oscillator circle with the signal of ones and zeros

The output _{out} represents the output oscillator frequency which is synchronously measured with regard to the switch _{1} and _{2} are equal, then _{out}(_{out}_{com} is in series with the quartz crystal and together with the compensation method (_{0}) increases and linearilizes the frequency pulling range. The quartz crystal’s parasitic capacitance _{o}_{out} remains the same at _{0}, AT-cut quartz crystal temperature characteristics Δ_{out} depends on the quartz crystal resonant frequency _{0}, the Δ_{2} or Δ_{2} change (frequency pulling) and AT-cut quartz crystal temperature characteristics Δ

The ouput frequencies for both switching conditions are:

When joining _{0} and Δ_{2}) (_{0} and at the same time linearizes the quartz characteristics due to the Δ_{2} change (

pulling sensitivity value [

mechanical behavior of the crystal element [

_{com}

compensation inductance,

_{o}

parasitic capacitance of the crystal element and holder,

_{0}

quartz crystal series resonant frequency.

The pulling sensitivity in _{2)} [_{2} change. This means that it is dependent neither on the AT-cut quartz crystal temperature characteristics Δ

If _{2} (_{2} [

While the specified counter accuracy (HM 8122) ±5 × 10^{−7} does not allow high precision measurements of small frequency changes at 5 MHz, the use of an additional reference frequency _{r}

The switching from _{r}

Due to their physical properties, AT-cut crystals are predominantly used in oscillator circuits. Their main advantage is the lower temperature sensitivity in the temperature range between 10 °C and 40 °C (

environment temperature

_{ref}

reference temperature

_{1}and

_{3}

coefficients determined with regard to the angle of the cut

For higher accuracy, five measuring points (to measure the frequencies) or more may be necessary. By means of these, the best adapted cubical parabola is applied and the appropriate coefficients _{1} and _{3} determined. Nevertheless, this mathematical approximation is not precise enough for the high-precison measurements of small impedance changes [

Frequency variation is normally considered in short term stability (second-to-second and minute-to-minute temperature characteristics) and long term stability over days, months or years, called ageing. The short term stability of a quartz crystal depends on the actual oscillator design and is totally controlled by the quartz crystal at low drive levels (30 μW). The ageing rate is substantially influenced by the cleanliness of the resonator, the stability of the inert gas filling and the security of the final sealing process. Ageing is naturally greater during the first part of the life of the crystal unit. The frequency ageing can often be described by function of the form of time

It is necessary to distinguish between active and passive ageing. Active ageing is the frequency shift, when the crystal works under operating conditions—permanently oscillating in the circuit. Typically the ageing rates of the best cold weld crystals are less than ±1 ppm/year (10 °C to 40 °C). Passive ageing is the frequency shift during storage.

Counter error Δ_{out} (^{−7} (through entire working temperature range +10 °C up to 40 °C), in 5 × 10^{−9}/day after 48 hours continuous operation with crystal oven controlled (OCXO). Frequency repetition accuracy after 24 hours of “power off”: ±5 × 10^{−8}. Resolution is determined as ±1 or 2 LSD, while frequency measurement accuracy is defined with the following term [

The novel switching method highly reduces the influence of the short- and long-term accuracy of the above described counter due to the compensation of previously mentioned influences of a single quartz crystal and the circuit as well as the influence of the difference method using additional reference frequency _{r}_{r}^{−11} (max) in the temperature range between 0 °C and 50 °C following the warm-up time of 30 min [

The experimental data values in the 5 MHz quartz crystal equivalent circuit were measured by a HP 4194A impedance/gain-phase analyzer. The quartz crystal (HC-49/U) was selected due to its high Q value (

In _{0} represents the AT fundamental mode quartz crystal resonant frequency. _{q} is quality factor [

For this research a quartz switching oscillator circuit (_{1} and _{2} with the frequency 1 Hz. The impedances in this research are defined as

Two impedances _{1} and _{2} in the form of an open capacitor were used experimentally. The impedances were produced on a temperature stable material _{2}_{3}_{1} = _{2} = 4pF (

For three _{0} compensation in the range of change _{2} from 2.5 to 40 pF can be seen in

Experimental results show that the use of the switching method excellently compensates AT-cut frequency-temperature characteristics and highly improves second-to-second and minute-to-minute accuracy by ×100 for _{0} compensation. This high frequency difference accuracy represents a novelty and a major advantage of the switching method discussed in the measurement of ato and femto ranges. With fine tuning of a series load compensation inductance _{com} connected in series with the crystal, the frequency of the oscillator is set to an appropriate output circuit frequency. It should also be emphasized that the exact pulling limits depend on the crystal’s Q value as well as the associated stray capacitances and the factor _{com} is determined from known stray capacitances and the known factor

The factors affecting frequency stability such as wide operating temperature range, ageing and drive level as well as all other crystal characteristics influencing the stability should also be considered because a stable oscillator circuit plays an important role in the frequency pulling sensitivity increase. Frequency stability also depends on the temperature coefficient of the compensation inductance _{com}

Quartz crystal switching oscillator.

AT-cut quartz crystal temperature characteristics [

The quartz crystal frequency ageing [

Oscillator circuit and capacitances _{1} and _{2} produced on _{2}_{3}

Quartz crystal sensitivity and linearity for _{z} = 2.5 – 40 pF.

Quartz data for resonant frequency 5 MHz [

_{0} |
_{o} |
_{com} |
_{q} | |||
---|---|---|---|---|---|---|

5 | 10 | 25 | 40.7 | 4 | 78.2 | 230153 |