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Generally, quartz crystal inductance frequency pulling in oscillators is very low and therefore is not often used in practice. The new method of improving frequency pullability uses inductance to compensate for quartz stray capacitances. To this end, a special AT fundamental quartz crystal working near the antiresonance frequency is selected. By modifying its equivalent circuit with load inductance and series tuning capacitance, the magnetic sensing of the circuit can be highly improved. The experimental results show that the new approach using the quartz crystal stray capacitance compensation method increases the frequency pulling range (from ≅ 2 kHz/μH to ≅ 600 kHz/μH) by × 300 depending on the type of oscillator, making possible the measurement of nano-magnetic changes.

The high precision measurement of small inductance changes has become increasingly important in sensor techniques, particularly for the measurement of nano extensions, hollow nano-sphere magnetic properties, novel magnetic nano-adsorbents, displacement field forces,

Impedance measurement methods for inductors are divided into three basic groups: current and voltage methods based on impedance determination, bridge and differential methods based on comparison of the voltage and currents of the measured and reference impedances until a state of balance is reached, and resonance methods based on physical connection of the measured inductor and a capacitor to create a resonant system [

The advantage of the current and voltage method lies in limiting the influence of stray capacitances as a result of attaching one of the terminals of the measured impedance to a point of “virtual ground”. However, to obtain small measurement errors, especially at high frequencies, amplifiers with very good dynamic properties must be used. Combined inductance measurement errors obtained by current and voltage methods depend on the following factors: voltmeter errors, errors in calculating resistance, system factors (residual and leakage inductances, resistances and capacitances), and the quality of approximation of the measured impedances by the equivalent circuit [

For correct measurements when using ac bridges, it is essential to minimize the influence of harmful coupling among the bridge elements and connection wires, between each other and the environment. These couplings are produced by the capacitances, inductances, and parasitic resistances of bridge elements to the environment and among themselves. The joint error of the inductance measurement results depends then on: the accuracy of the standards used as the bridge elements, mainly standard resistors and capacitors; errors in determining the frequency of the bridge supplying voltage; errors of the resolution of the zero detection systems; errors caused by the influence of residual and stray inductances; resistances and capacitances of the bridge elements and wiring; and the quality of approximation of the measured impedances in the equivalent circuit [

Resonance methods are a third type of inductance measurement method. They are based on the application of a series or parallel resonance LC circuit as elements of either a bridge circuit or a two-port (four-terminal) “T”-type network. The joint error of the inductance measurement results are similar as when using ac bridge method (depending on the quality of the elements) [

Instruments commonly used for inductance measurements are built as universal and multifunctional devices. The results of inductance measurements depend on how the measurements are preformed, including how the measured inductor is connected to the meter. Care should be taken to limit such influences as inductive and capacitive coupling of the inductive element to the environment, sources of distortion, and the choice of operating frequency (Hewlett-Packard 4284A—Precision LCR meter, 0.01 nH–99.9999 kH, 20 Hz–1 MHz, 0.05%) [

The quartz crystal method is another possible method. A prior study of the quartz crystal pulling increase has shown that it is also possible to increase the inductive frequency pulling [

In the equivalent circuit of an electrical representation of the quartz crystal’s parasitic capacitance _{o}_{o}_{o}_{m}_{o}_{o}_{m}_{m}

The special value of the chosen compensated _{m}_{m}_{m}_{f}

Using the compensation criterion (_{m}_{0}_{o}_{m}

_{m}_{0}

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

The frequency _{r}_{m}_{0}_{f}

In the case of fn3 (_{m}_{m}_{m}_{0}

The capacitance _{f}_{f}

Experimental results show the quartz crystal frequency sensitivity in relation to the applied use of circuits and increased inductance frequency pulling. Taking into account the long-term quartz crystal frequency stability (0.1 Hz) (described in reference [

The most common factors affecting frequency stability such as operating temperature range, aging, hysteresis 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 increase of pulling and linear frequency dependence. As a consequence of hysteresis, the frequency _{m}

Experimental results show that the use of series inductance compensated crystals with a special determined value of _{m}_{m}

Compensation inductance _{m}_{f}

Frequency pulling for fn1 (_{m}_{m}_{m}_{m}

Frequency pulling fn3 (_{m}

Fine-tuning of the working frequency using _{f}_{m}

Quartz data for resonant frequency 3.5 MHz [

_{r} |
_{o} |
_{m} |
||||
---|---|---|---|---|---|---|

3.5 | 10 | 25 | 82.83 | 4 | 520.0 | 181980 |