GB2190753A - Measuring quartz crystal resonance frequency - Google Patents

Abstract

For determining the resonant frequency of a quartz crystal blank (36) the crystal is driven by two beat frequencies derived by mixing (34) a low and a high frequency (f, F), one beat frequency being in resonance. The beat frequencies are then mixed (35) with the original high frequency (F) to recover the low frequency. At resonance the input and output low frequencies are in phase, e.g. as sensed by an amplifier or phase comparator (37). The technique obviates the need for tuning out of the shunt reactance of the crystal. <IMAGE>

Description

SPECIFICATION Measuring quartz crystal frequency This invention relates to a method and apparatus for determining a resonant frequency of a piezoelectric resonator device, e.g. a quartz crystal.

Piezoelectric resonators such as quartz crystals are manufactured from blanks which are etched or lapped to provide a desired resonant frequency. This frequency is determined primarily by the thickness of the resonator material. In practice this thickness cannot easily be measured to a sufficient degree of accuracy to provide high resonant frequencies, e.g. 10 to 200 MHz, and it is thus necessary to test each blank electrically during the manufacturing process. Conventionally the blank is placed between a pair of electrodes to which a source of alternating current of variable frequency is connected. The frequency is adjusted until resonance is detected. The technique suffers from the disadvantage that the resonance of an ummounted blank is very weak.

As is well known, a resonator can be described electrically in terms of an equivalent circuit of an inductor, a capacitor and a resistor in series. At resonance the quadrature components of the impedance balance and the device thus functions as a resistor. The resonant frequency can thus in theory be determined as the frequency at which zero phase shift is observed. However, the resonator also has a shunt reactance which swamps a weak resonance so that a zero phase shift is not obtained. At present this difficulty is overcome by tuning out the shunt reactance with an equal and opposite reaction. This technique is both skilled and time consuming and cannot readily be automated.

The object of the present invention is to minimise or to overcome this disadvantage.

According to one aspect of the invention there is provided a method of measuring a resonant frequency of a piezoelectric resonator, the method including providing a first high frequency signal whose frequency approximates to the resonant frequency, providing a second, variable frequency, low frequency signal, mixing the signals to provide first and second beat frequencies, applying said beat frequencies to the resonator, remixing the beat frequencies with the high frequency signal thereby recovering the low frequency signal, and adjusting the frequency of the low frequency signal such that the phase difference between the low frequency signal and the recovered signal is zero, thereby indicating resonance at one of said beat frequencies.

According to another aspect of the invention there is provided an apparatus for measuring a resonant frequency of a piezolelectric resonator, the apparatus including a first high frequency signal source, a second low frequency signal source, means for mixing said signals and for applying the two beat frequencies thus derived to a resonator, means for remixing signals received from the resonator with the high frequency signal thereby recovering the low frequency signal, and means for adjusting the frequency of the low frequency signal so as, in use, to obtain a zero phase difference between the low frequency signal and the recovered signal thereby indicating resonance at one of the beat frequencies.

An embodiment of the invention will now be described with reference to the accompanying drawings in which: Figures 1 and 2 show the equivalent circuit of a piezoelectric resonator under conditions of resonance and off-resonance respectively, Figure 3 is a schematic circuit diagram of a resonance detection apparatus.

Referring to Figs. 1 and 2, a piezoelectric resonator behaves electrically as a Pi-network of a shunt reactance CO and two resistors R1 and R2, these resistors being physical components forming part of the test network and being small in comparison with CO and R,. At resonance (Fig. 1) the resonator appears as a resistance R0 shunted by the reactance CO. Under offresonance conditions (Fig. 2) the resonator appears as a rectance CO to the applied signal.

In use the network input I/P receives a pair of signals comprising the two beat frequencies obtained by mixing a low frequency signal f and a high frequency signal F, the latter having a frequency near the expected resonant frequency.

If we have f=A cos (co1t) and F=B cos (a)2t) then on mixing we obtain the product frequency AB F'=-cos (w2+co1)t + cos (a)2-(c)1)t 2 where cos (o,+o,)t and cos (w2-w1)t correspond to the upper and lower sidebands respectively.

The beat signals thus have frequencies given by (F+f) and (F-f), the low frequency signal being adjusted such that one frequency, e.g. the sum frequency matches the resonant frequency of the resonator.

Generally for a network we have VouT=G VTN where G is a dimensionless complex valued function of frequency characteristic of the network, and can be written in the form G=GR+j GI =IGI eiU where

For a sinusoidal input to the network we then have VOUT = VINI GRe (el ) Thus, if the signal F' is applied to the network the corresponding output F" is given by

where IG+l and 6+. IG-l and 6- are the amplitudes and phases of the upper and lower sidebands respectively.

On remixing this network output signal with the original low frequency signal f we obtain a recovered low frequency signal having the form

As can be seen the condition for zero phase difference between this signal and the original low frequency f is that G,=G, or V,m(oo1 + Ct)2) Vlm((91 02/ It can be shown that close approximation to this condition can be achieved provided that R1 and R2 are small compared with R,.

Thus, assuming identical electrical path lengths, when the signal from the resonator is mixed with the original high frequency signal F the imaginary component of the voltage cancels out leaving only the real voltage corresponding to the current through R0 under resonant conditions.

In other words the recovered low frequency signal is in phase with the original low frequency signal. Further, at resonance, the amplitude of the recovered low frequency signal has a maximum value.

The effect of the reactance CO is thus eliminated, and by remixing the resultant signal with the original high frequency signal F the low frequency f is recovered.

Referring now to Fig. 3, there is shown an apparatus for measurement of a resonant frequency of a piezoelectric resonator. The apparatus includes first and second oscillators 31 and 32 for generating the low frequency f and high frequency F respectively. Oscillator 31 is a tunable oscillator. Signals from the high frequency oscillator 32 are fed via a power splitter 33 to first and second mixers 34 and 35. The first mixer 34 mixes the high frequency signal F with the low frequency signal f and applies the resulting beat frequencies (F+f) and (F+f) to a network 36 incorporating the piezoelectric blank whose resonant frequency is to be measured.

This network corresponds to the network of Figs. 1 and 2. The beat frequency signals passing through the network are fed to the second mixer 35 where they are remixed with the high frequency signal F received via the power splitter 33 to recover the low frequency signal. As the two electrical path lengths from the splitter 33 to the mixer 35 directly and via the network 36 are substantially identical, the currents from the two beat frequencies through the shunt reactance in network 36 cancel one another out. Thus the resonance is translated back to the low frequency f but with the shunt reactance effectively eliminated so that at the resonance there is zero phase difference between the recovered signal and the original low frequency signal. The low frequency amplifier 37 can therefore be used to complete the loop providing positive feedback and forming an oscillator under the resonance conditions. The sum of the frequency and the high frequency will thus give the frequency of the resonance. All that is required for operation at a different frequency is to alter the high frequency. Since the phase shifts at the second mixer track with frequency the system works over a wide frequency range (typically 10-200 MHz). The measurement of the two frequencies along with the adjustment of the high frequency source can be under computer control. This latter source does not need to be of high stability since the low frequency is moved automatically to compensate for any shifts.

In an alternative embodiment the amplifier 37 may be replaced by a spectrum analyzer. In this arrangement the high frequency oscillator remains at a constant frequency whilst the low frequency oscillator is swept through a range of frequencies including the frequency at which resonance is obtained. Resonance in this case is indicated as a maximum amplitude in the swept frequency range.

In a further tecnique the recovered low frequency signal and the original low frequency signal may be fed to a phase comparator, the resonant condition being indicated by a zero phase difference between these two signals.

An alternative use for the above technique is for investigating a resonance and any spurious resonances where measurement apparatus at the required frequency is not available.

Claims (8)

1. A method of measuring a resonant frequency of a piezoelectric resonator, the method including providing a first high frequency signal whose frequency approximates to the resonant frequency, providing a second, variable frequency, low frequency signal, mixing the signals to provide first and second beat frequencies, applying said beat frequencies to the resonator, remixing the beat frequencies with the high frequency signal thereby recovering the low frequency signal, and adjusting the frequency of the low frequency signal such that the phase difference between the low frequency signal and the recovered signal is zero, thereby indicating resonance at one of said beat frequencies.

2. A method as claimed in claim 1, wherein resonance is indicated as a maximum in the amplitude of the recovered low frequency signal.

3. A method as claimed in claim 1 or 2, wherein the resonator is a quartz crystal blank.

4. A method of resonant frequency measurement substantially as described herein with reference to the accompanying drawings.

5. An apparatus for measuring a resonant frequency of a piezoelectric resonator, the apparatus including a first high frequency signal source, a second low frequency signal source, means for mixing said signals and for applying the two beat frequencies thus derived to a resonator, means for remixing signals received from the resonator with the high frequency signal thereby recovering the low frequency signal, and means for adjusting the frequency of the low frequency signal so as, in use, to obtain a zero phase difference between the low frequency signal and the recovered signal thereby indicating resonance at one of the beat frequencies.

6. An apparatus as claimed in claim 5, wherein an amplifier is coupled between the mixing and remixing means such that, under resonance conditions, positive feedback is provided at the low frequency.

7. An apparatus for resonant frequency measurement substantially as described herein with reference to and as shown in Fig. 3 of the accompanying drawings.

8. A piezoelectric resonator tested by a method as claimed in any one of claims 1 to 4.