How to determine the resonant frequency of a quartz resonator using radio measuring instruments. Scheme, description

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How to determine the resonant frequency of a quartz resonator using radio measuring instruments in amateur conditions. Encyclopedia of radio electronics and electrical engineering

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Encyclopedia of radio electronics and electrical engineering / Measuring technology

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A quartz resonator (Fig. 1a) can be represented by an equivalent circuit in the form of a series circuit RkLkSk, shunted by capacitances of metallized surfaces and a quartz holder Co, as well as by a mounting capacitance Cm (Fig. 1b).

How to determine the resonant frequency of a quartz resonator using radio measuring instruments in amateur conditions
Ris.1

Dynamic resistance Rk, inductance Lk and capacitance Sk are determined by the mechanical resonance frequency of the quartz plate and the amount of losses occurring in the resonator. The value of the capacitance Co is determined by the geometric dimensions and physical properties of the plate and the design of the quartz holder, for each resonator it is a constant value. Capacitance Cm depends on the design of the socket, the location of the wires, the capacitance between the points of connection of the resonator to the device, etc.

The resonator according to the equivalent circuit can be considered either as a series circuit RkLkKk, or as a parallel circuit RkLkKk(Сo+См'). In accordance with this, the behavior of the resonator at different frequencies is determined.

Figure 2 shows the dependence of the reactance of the resonator on the frequency of the alternating voltage applied to it. At low frequencies, capacitance Ck is decisive, the resonator behaves like a capacitance.

How to determine the resonant frequency of a quartz resonator using radio measuring instruments in amateur conditions
Ris.2

As the frequency increases, the capacitance decreases, and at some frequency f_last, called the serial resonance frequency or resonant frequency of the resonator, it becomes equal to zero. The resonator exhibits the properties of a series circuit, its impedance is minimal and equal to the active resistance Rk. The serial resonance frequency is

How to determine the resonant frequency of a quartz resonator using radio measuring instruments in amateur conditions

With a further increase in frequency, the inductive resistance of the resonator increases, and at the frequency f_steam the resonator acquires the properties of a parallel circuit, which at resonance has infinitely large and equal in absolute value inductive and capacitive resistances.

With an even greater increase in frequency, the shunting effect of the capacitances Co and Cm begins to affect, and the resonator acts as a capacitor of small capacitance.

The parallel resonance frequency is expressed by the formula

How to determine the resonant frequency of a quartz resonator using radio measuring instruments in amateur conditions

As can be seen from the formula, the frequency f_steam depends on the capacitance cm, so it can vary within certain limits.

The ratio of the frequencies of parallel and series resonance is determined by the expression:

How to determine the resonant frequency of a quartz resonator using radio measuring instruments in amateur conditions

The difference between these frequencies is small, the maximum difference is close to 0,4% of the series resonance frequency.

Consequently, the measurement of the resonant frequency of a quartz resonator using instruments can be carried out by the same methods that are used to determine the resonant frequency of the circuits.

To determine the frequency of the series resonance of the resonator, it is connected between the output of the signal generator and the input of a high-frequency tube voltmeter (Fig. 3). The output voltage of the generator should be about 100 mV, the voltmeter is set to a measurement limit of 1-8 V. With a generator frequency equal to f_last the voltmeter needle deviates sharply to the right. Due to the high quality factor of the quartz resonator, the band of frequencies transmitted by it is very narrow, therefore, the generator frequency should be changed slowly, otherwise the voltmeter, due to its inertia, does not have time to respond to the received short voltage pulse.

How to determine the resonant frequency of a quartz resonator using radio measuring instruments in amateur conditions
Ris.3

The frequency measurement error with this method is determined by the calibration error of the generator. The disadvantage of this method is the significant time spent on passing the ranges of the generator.

It should be borne in mind that some resonators have side resonant frequencies, but at these frequencies the voltmeter readings are much lower than the readings obtained at the main resonant frequency.

Literature

Radio No. 9 1966, c.62

Publication: N. Bolshakov, rf.atnn.ru

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