CN106134453B - A kind of measuring system of quartz resonator impedance operator parameter - Google Patents

Abstract

The present invention relates to a kind of method for fast measuring of quartz resonator impedance operator parameter, the method adopts automated closed-loop to follow the tracks of quartz resonator resonant frequency and the method that accurately frequency sweep combines, and can test fast quartz resonator equivalent impedance property. Utilize DSP technology to carry out signal detection and processing, realize by the CO parameter of compensation quartz resonator the closed loop driving and follow the tracks of to detect its resonant frequency, near resonant frequency, carry out accurate frequency sweep, gated sweep precision is to reach the optimization of precision and speed, thereby obtain the impedance curve of quartz resonator, and calculate its equivalent parameters. The method combines DSP technology and quartz resonator equivalent model, and reasonable design method is feasible, can realize faster the measurement of quartz resonator equivalent impedance property.

Description

System for measuring impedance characteristic parameters of quartz resonator

Technical Field

The invention relates to a system for measuring impedance characteristic parameters of a quartz resonator, which can quickly test the equivalent impedance characteristic of the quartz resonator by adopting a method of combining automatic closed-loop tracking of the resonance frequency of the quartz resonator and accurate frequency sweep.

Background

The gyroscope is also called as an angular rate sensor, can be combined with an accelerometer to form an inertial measurement or guidance system, is combined with other navigation systems such as a GPS (global positioning system) and the like to form a high-reliability navigation and positioning system, and is widely applied to the fields of spacecrafts, aircrafts, platform attitude control, missiles and the like. In recent years, micro-mechanical gyroscopes have attracted attention because of their advantages, such as small size, low power consumption, low cost, and suitability for mass production, and quartz tuning fork gyroscopes are one of them, and have advantages of high dynamic response and high sensitivity.

The quartz structure has the characteristics of relatively simple processing technology, higher quality factor Q value, good product performance reliability and the like. In actual production, in order to obtain a high Q value and better performance, a quartz sensitive element is often sealed in a tube shell structure, so that whether the quartz sensitive element has defects such as short circuit, open circuit and gas leakage can be judged by testing equivalent parameters of the sensitive element in later screening.

The quartz tuning fork gyroscope mostly adopts an H-shaped double-end tuning fork structure, and comprises a driving tuning fork and a pickup tuning fork, wherein each end tuning fork is a quartz resonator. The equivalent models of the quartz drive tuning fork and the pickup tuning fork are both a circuit model of an RLC series circuit and a capacitor C0 in parallel, as shown in FIG. 2. The natural resonant frequency of the tuning fork structure is determined by L1 and C1, the Q value of a quality factor is determined by R1, L1 and C1 together, when the sensitive element works at a resonant point, R1, L1 and C1 are equivalent to R1, the phase shift of arctan (R omega C0) is generated due to the existence of C0, the method of a national defense patent 201010048498.0 is referred to for the estimation and compensation technology of C0, and a Rockwell patent US005893054A is referred to for the way of digital gyro closed loop driving. At present, in the aspect of testing the impedance characteristics of the quartz resonator in China, an Agilent impedance analyzer is mainly used for testing, and the method is relatively complicated and extremely low in efficiency.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the invention can be used for testing the quartz tuning fork gyroscope, can also be used for other electrical models, can be equivalent to a quartz resonator with an RLC series branch and a C0 branch which are connected in parallel, and has high testing precision.

The technical solution of the invention is as follows: a measuring system for impedance characteristic parameters of a quartz resonator is used for establishing an equivalent circuit of the quartz resonator and comprises a C0 measuring and calculating and closed-loop driving circuit and a frequency scanning circuit, wherein the C0 measuring and calculating and closed-loop driving circuit detects the size of a distributed capacitor C0 in the equivalent circuit and performs digital compensation on the distributed capacitor C0, when the driving amplitude value output by the C0 measuring and calculating and closed-loop driving circuit is smaller than a driving amplitude threshold value, a frequency scanning circuit is started, the frequency scanning circuit performs frequency scanning on the equivalent circuit of the quartz resonator, and finally the equivalent parameters of the equivalent circuit of the quartz resonator are obtained through calculation;

the C0 measuring and closed-loop driving circuit consists of an analog conditioning circuit, an A/D converter, a C0 measuring and compensating circuit, a tracking filter, a phase discriminator, an automatic gain controller, a phase shifter, a reference signal generator, a first multiplier, a second multiplier and a D/A converter, wherein the analog conditioning circuit detects an output signal V of an equivalent circuit₁And to the output signal V₁Filtering and amplifying to obtain signal V₂The A/D converter converts the signal V₂Is converted into a digital signal V₃The output is sent to a C0 measuring and compensating circuit, and a C0 measuring and compensating circuit is used for measuring and compensating the digital signal V₃After compensation, a signal V is obtained₄Output to a tracking filter, which tracks the signal V₄Filtering to obtain a signal V₅Phase detector for reference signal Q₂Sum signal V₅Performing phase comparison, transmitting the comparison result V6 to a reference signal generator, adjusting the frequency of an output signal I, Q according to the value of the comparison result V6 by the reference signal generator, controlling the center frequency of a tracking filter by the reference signal generator output signal β, controlling the working frequencies of an automatic gain controller and a phase discriminator by the reference signal generator output signal β 1, and shifting the output signal Q by a certain phase by a phase shifter to become a reference signal Q₂The magnitude of the shift phase is equal to the output signal I and the signal V₅By detecting the phase difference, by an automatic gain controllerSignal V₅The amplitude value of the driving amplitude signal aa is adjusted, and the driving amplitude signal aa and the output signal I are multiplied by a first multiplier to obtain a signal I₁C0 evaluation and compensation circuit based on signal I₁Output drive signal V₇The driving amplitude signal aa and the output signal Q are multiplied by a second multiplier to obtain a signal Q₁Driving signal V₇After being converted into analog signals by a D/A converter, the analog signals are applied to the electrodes of the quartz resonator;

the frequency scanning circuit consists of an analog conditioning circuit, an A/D converter, a C0 measuring and compensating circuit, a tracking filter, a reference signal generator, a D/A converter, a multiplier, a frequency doubling wave trap and a frequency control module, wherein the analog conditioning circuit detects an output signal V of the equivalent circuit₁And to the output signal V₁Filtering and amplifying to obtain signal V₂The A/D converter converts the signal V₂Is converted into a digital signal V₃The output is sent to a C0 measuring and compensating circuit, and a C0 measuring and compensating circuit is used for measuring and compensating the digital signal V₃After compensation, a signal V is obtained₄Output to a tracking filter, which tracks the signal V₄Filtering to obtain a signal V₅The frequency control module is used for controlling the frequency of an output signal of the reference signal generator, the reference signal generator generates two signals I, Q with constant amplitude and orthogonal phase, the two signals are input to the C0 for measurement and compensation, and the C0 measurement and compensation circuit outputs a driving signal V according to the signal I₇Driving signal V₇Converting into analog signal by D/A converter, applying to the electrode of quartz resonator, controlling the center frequency of tracking filter by reference signal generator β, controlling frequency doubling wave trap by reference signal generator β 1, and tracking filter by output signal V₅Multiplying the sum signal I in a multiplier to obtain a signal V₂₆Signal V₂₆And obtaining a signal V through a frequency doubling wave trap, and finally obtaining the corresponding relation between the signal V and the frequency f in the frequency control module.

The C0 measuring, calculating and compensating circuit comprises a band-pass filter, an evaluation signal generator and a frequency doubling wave trapA C0 calculation module, a first multiplier, a second multiplier, a third multiplier, an I channel compensation parameter, a Q channel compensation parameter, a first adder and a second adder, wherein the evaluation signal generator generates an evaluation signal V deviating from the working frequency of the quartz resonator₁₀Evaluating the signal V₁₀And signal I₁After superposition, a driving signal V is obtained₇Digital signal V applied to drive circuit of quartz resonator₃Outputting and evaluating signal V after filtering by band-pass filter₁₀Signals V of the same frequency₉Multiplier pair signal V₉And an evaluation signal V₁₀Performs demodulation to output signal V₁₁The output signal V of the multiplier is converted by the frequency-doubling wave trap₁₁The double frequency signal in the intermediate frequency is suppressed to obtain a direct current signal V which is proportional to the distributed capacitor C0₁₂The C0 resolving module converts the signal V₁₂Dividing by the circuit gain to obtain a signal V₁₃Signal V₁₃Channel I compensation parameter and signal I₁Multiplying by a multiplier to obtain a signal V₁₄Signal V₁₃Q channel compensation parameter and signal Q₁Multiplying by a multiplier to obtain a signal V₁₅Signal V₁₄Sum signal V₁₅Adding the signals by an adder to obtain a signal V₁₆Will signal V₁₆From signal V₃Is subtracted to obtain a compensated signal V₄。

The working principle of the invention is as follows: an electric equivalent model of a quartz resonator is composed of a parallel connection structure of an R1, L1, C1 series circuit and C0. Wherein R1 represents the impedance characteristic of the quartz resonator when the quartz resonator works at the resonance point, L1 and C1 constitute the frequency characteristic of the quartz resonator, and C0 is the distributed capacitance of the quartz resonator. Therefore, the impedance characteristic parameters are 4, and four equations are needed to obtain a fixed solution. When a voltage signal deviating from the resonant frequency of the quartz tuning fork is input to pass through the quartz resonator, the impedance of the R1, L1 and C1 channels is very large and can be equivalent to open circuit, and therefore the electrical model of the quartz tuning fork can be equivalent to C0.

The signal passing through the quartz resonator is amplified and filtered by an analog conditioning circuit, and when the equivalent model is represented as C0, the gain of the analog conditioning circuit is as follows:

$H_1\left(s\right)=\frac{{\mathrm{sR}}_2{C}_0}{1+{\mathrm{sR}}_2{C}_2}\·\frac{R_4}{R_3}\frac{1}{1+{\mathrm{sR}}_4{C}_3}---\left(1\right)$

transfer function H₁The amplitude and phase of(s) are as follows:

${\mathrm{\φ}}_1\left(\mathrm{\ω}\right)=atan\left(\frac{1}{{\mathrm{\ωR}}_2{C}_2}\right)-a\tan \left({\mathrm{\ωR}}_4{C}_3\right)---\left(2\right)$

$\left|H_1\left(\mathrm{\ω}\right)\right|=\frac{{\mathrm{\ωR}}_2{C}_0}{\sqrt{{\mathrm{\ω}}^2{R_2}^2{C_2}^2+1}}\·\frac{R_4}{R_3\·\sqrt{{\mathrm{\ω}}^2{R_4}^2{C_3}^2+1}}=A_1\left(\mathrm{\ω}\right)C_0---\left(3\right)$

whereinω is the angular frequency of the input signal.

It can be seen from the formulas (2) and (3) that the phase of the transfer function of the analog conditioning circuit is independent of C0, the amplitude is proportional to C0, and the value of C0 can be obtained by performing demodulation filtering and other calculations on the output signal of the quartz resonator. The compensation of the signal according to the value of C0 can make the whole loop easily work in the resonance state, and the resonance frequency of the quartz resonator is obtained.

Then, a voltage signal with fixed amplitude and gradual frequency change is input near the resonant frequency to carry out frequency scanning on the quartz resonator, and the amplitude of the output waveform of the quartz resonator can be obtained. The quartz resonator is similar to a narrow band-pass filter, and its output is maximum V at resonance frequency_maxWhen the corresponding frequency is f_ResonanceAt V_maxIs/are as followsAt a corresponding frequency ofThe quality factor Q of the quartz resonator can be obtained:

whereinFor the output curve at V_maxIs/are as followsThe difference in frequency of (d).

At f_ResonanceAt the point where the quartz resonator is in the working resonance state, its electrical model may be equivalent to R1 after compensating for C0. The voltage signal of resonance work is applied on the quartz resonator, and is amplified and filtered by the analog conditioning circuit, and the transfer function of the analog conditioning circuit is as follows:

$H_2\left(s\right)=\frac{R_2}{R_1}\frac{1}{1+{\mathrm{sR}}_2{C}_2}\·\frac{R_4}{R_3}\frac{1}{1+{\mathrm{sR}}_4{C}_3}---\left(5\right)$

transfer function H₂The phase and amplitude of(s) are as follows:

φ₂(ω)＝-atan(ωR₂C₂)-atan(ωR₄C₃) (6)

$\left|H_2\left(\mathrm{\ω}\right)\right|=\frac{R_2}{R_1}\frac{1}{\sqrt{{\mathrm{\ω}}^2{R_2}^2{C_2}^2+1}}\·\frac{R_4}{R_3}\frac{1}{\sqrt{{\mathrm{\ω}}^2{R_4}^2{C_3}^2+1}}=A_2\left(\mathrm{\ω}\right)\frac{1}{R_1}---\left(7\right)$

wherein,ω₀is the resonance angular frequency of the quartz resonator.

It can be seen from the formulas (6) and (7) that the phase of the transfer function of the analog conditioning circuit is independent of R1, and the amplitude is inversely proportional to R1, and the value of R1 can be calculated by detecting the output of the corresponding signal of the quartz resonator.

The quality factor Q is related to R1, C1, ω as follows:

Q＝1/(R1×C1×ω) (8)

the value of C1 can be obtained by equation (8).

The relationship between the angular frequency ω of the input signal and L1 and C1 is as follows:

$\mathrm{\ω}=1/\sqrt{L1\×C1}---\left(9\right)$

the value of L1 can be obtained from equation (9).

Compared with the prior art, the invention has the beneficial effects that: at present, an impedance analyzer is mostly adopted for testing impedance characteristic parameters of the quartz resonator, the impedance analyzer is heavy and has complicated procedures, the method is easy to realize in a digital circuit based on a DSP or FPGA chip and the like, the circuit is small in size, light in weight, easy to carry, simple in testing process and high in testing precision.

Drawings

FIG. 1 is a schematic structural view of an "H" shaped quartz tuning fork;

FIG. 2 is an electrical equivalent circuit diagram of a quartz resonator;

FIG. 3 is a flow chart of the testing of the impedance characteristic parameters of the quartz resonator;

FIG. 4 is a schematic diagram of the C0 evaluation and closed loop driving circuit;

FIG. 5 is a block diagram of the components of the analog conditioning circuit;

FIG. 6 is a structural diagram of the component of the C0 estimation and compensation circuit;

FIG. 7 is a block diagram showing the components of an evaluation signal generator;

FIG. 8 is a block diagram showing the components of the band-pass filter;

FIG. 9 is a block diagram of a dual frequency trap;

fig. 10 is a constitutional view of a tracking filter;

fig. 11 is a structural view of the composition of the phase detector;

FIG. 12 is a block diagram of a double frequency tracking trap;

FIG. 13 is a block diagram of the phase corrector;

FIG. 14 is a block diagram of a reference signal generator;

FIG. 15 is a view showing a constitution of a phase shifter;

fig. 16 is a constitutional view of an automatic gain controller;

FIG. 17 is a structural view of a frequency scanning circuit;

FIG. 18 is a graph of resonator output amplitude versus scan frequency.

Detailed Description

The following detailed description of embodiments of the invention refers to the accompanying drawings.

Fig. 1 shows an H-shaped double-ended tuning fork structure adopted by a quartz tuning fork gyroscope, which comprises a driving tuning fork 1 and a pickup tuning fork 2, and the structure and surface electrodes 3 and 4 are obtained by a series of processes such as film coating, photoetching and corrosion on a Z-cut quartz wafer. Although the electrodes and structures for driving and picking up the tuning forks are different, they are one type of quartz resonator, and only the direction of vibration is different. The alternating voltage signal is loaded on the driving electrode and vibrates in the XY plane in a reciprocating manner under the action of the inverse piezoelectric effect, and similarly, the alternating voltage signal is loaded on the pickup electrode and vibrates in the YZ plane in a reciprocating manner under the action of the inverse piezoelectric effect.

FIG. 2 is an electrical equivalent model of a quartz tuning fork, wherein R1, L1, C1 and C0 collectively reflect the state of the quartz tuning fork, and the purpose of the invention is to rapidly measure the parameters of R1, L1, C1 and C0 by using a digital signal processing method.

As shown in fig. 3, the present invention includes a C0 evaluation and drive closed loop circuit 7 and a frequency scanning circuit 9. The C0 measuring, calculating and closed-loop driving circuit 7 detects the size of a distributed capacitor C0 in the equivalent circuit and performs digital compensation on the distributed capacitor C0, when the driving amplitude value output by the C0 measuring, calculating and closed-loop driving circuit 7 is smaller than a driving amplitude threshold value, the frequency scanning circuit 9 is started, the frequency scanning circuit 9 performs frequency scanning on the equivalent circuit of the quartz resonator, frequency scanning precision and speed are reasonably controlled, a corresponding output curve is obtained, and finally equivalent parameters Q, R1, L1 and C1 of the equivalent circuit are obtained through calculation; the threshold is determined by hardware circuitry, which may be different.

FIG. 4 is a schematic diagram of a C0 estimation and resonator driving closed loop circuit of the present invention, which mainly includes an analog conditioning circuit 10, a C0 estimation and compensation 12, a tracking filter 13, a phase detector 14, a phase detector,automatic gain controller 15, phase shifter 16, reference signal generator 17, etc. The analog conditioning circuit 10 detects the output signal V of the quartz resonator 5₁And is filtered and amplified, and converted into a digital signal V by an A/D converter 11₃Then the compensated signal V is provided to C0 for calculation and compensation 12₄Input to a tracking filter 13. The tracking filter 13, which has a center frequency of the resonance frequency of the quartz resonator under a stable operation condition, filters a signal of the operation frequency of the quartz resonator to obtain a signal V₅. The C0 calculation and compensation 12 has the functions of calculating the size of C0 and compensating the working frequency signal to eliminate the influence of C0 on the working frequency signal. The phase detector 14 is arranged to compare the reference signal with the output signal V of the tracking filter 13₅Whether the phase between the phase information V and the phase information V satisfies the oscillation phase relation of the driving loop₆To a reference signal generator 17, the reference signal generator 17 being dependent on V₆Adjusts the frequency of the output signal I, Q such that it generates the reference signal I, Q at a frequency that stabilizes the overall drive loop to satisfy the oscillation phase relationship.

The output signal β of the reference signal generator 17 is used to control the center frequency of the tracking filter 14 and ensure that the center frequency of the tracking filter 14 can be adapted to the frequency variation of the standard signal I, the output signal β 1 of the reference signal generator 17 is used to control the operating frequencies of the automatic gain controller 15 and the phase detector 14 and ensure that the operating frequencies of the automatic gain controller 15 and the phase detector 14 can be adapted to the frequency variation of the standard signal I, the phase shifter 16 shifts the signal Q by a certain phase to become the signal Q₂The magnitude of the shift phase is equal to the phase difference between the driving voltage signal I and the signal V5, which can be calculated theoretically. The automatic gain controller 15 functions by detecting the signal V₅The magnitude of signal aa is adjusted to obtain the value of output signal aa, and signal aa and signal I, Q are multiplied to obtain signal I₁、Q₁The multiplication function is implemented by multipliers 18, 19. Drive signal V₇Operating frequency signal I comprising a quartz resonator₁And a signal, V, deviating from the operating frequency, input for the calculation of C0₇Through D/A conversionThe signal is converted into an analog signal by the converter 20 and applied to the electrode 3 or 4 of the quartz resonator. Signal V₆Determining the frequency f, V of the operating signal in the circuit₆The relationship with the frequency f is shown in the formula (10).

V₆＝-cos(ωT) (10)

Where ω is the angular frequency, ω is 2 π f, and T is the sampling time of the A/D converter. When the circuit works stably, i.e. the signal aa is smaller than the set threshold and has stable magnitude, and the signal V₆The magnitude is also stable, at which time the signal V₆The corresponding frequency f is the resonant frequency f_Resonance。

Fig. 5 is a schematic diagram of the analog conditioning circuit 10, which is composed of two operational amplifiers 21, 22 and resistor-capacitor devices R2, R3, R4, C2, and C3. When the quartz resonator is in operation, its output V₁The operational amplifier 21, R2 and C2 form a current amplifier pair V for current signals₁Detection and amplification are performed, and the operational amplifier 22, R3, R4, C4 constitute an anti-aliasing filter.

Fig. 6 is a schematic diagram of the C0 estimation and compensation 12 module, which includes a band pass filter 32, an estimated signal generator 23, a frequency doubler trap 26, a C0 solution 27, multipliers 25, 30, 31, an I channel compensation parameter 28, a Q channel compensation parameter 29, and two adders 33, 34. The evaluation signal generator 23 generates a reference signal V deviating from the operating frequency of the quartz resonator (Δ f > 1kHz)₁₀And then added to the signal I by an adder 24₁To obtain a signal V₇Will V₇Applied to the drive electrode of the quartz resonator. Signal V₁₀And also to multiplier 25 for demodulation. The center frequency of the band-pass filter 32 is the evaluation signal V₁₀With a bandwidth of 5Hz, and an output signal V₉Frequency of and evaluation signal V₁₀The same is true. The frequency doubling trap 26 is used to suppress the frequency doubled signal in the output signal of the demodulator 25 to obtain a dc signal proportional to C0. Signal V is evaluated in C0 calculation 27₁₂Dividing by the circuit gain to obtain a signal V₁₃I.e., the size of C0, the circuit gain mainly includes two partsDividing into: firstly, the gain generated when the evaluation signal V10 passes through a hardware circuit can be obtained through theoretical calculation, and the calculation method is shown in formula (3); the second is the gain of the frequency doubling trap 26. Similarly, the I channel compensation parameter 28 and the Q channel compensation parameter 29 can be calculated according to the equations (1), (2) and (3). The I channel compensation parameter is A₁(ω)cos(φ₁(ω)), the compensation parameter of the Q channel is A₁(ω)sin(φ₁(ω)), where ω is the signal I₁Of the angular frequency of (d), its value and the signal V₆The relationship of (a) is arccos (-V)₆)f_sWherein f is_sThe sampling frequency of the digital circuit. Signal V₁₃Channel I compensation parameter and signal I₁Multiplied by a multiplier 30 to obtain a signal V₁₄Signal V₁₃Q channel compensation parameter and signal Q₁Multiplied by a multiplier 31 to obtain a signal V₁₅Signal V₁₄Sum signal V₁₅Added by an adder 33 to obtain a signal V₁₆Will signal V₁₆From signal V₃The C0 compensation process is completed by the subtraction, and the compensated signal is V₄.

Fig. 7 is a schematic diagram of the evaluation signal generator 23, which comprises two delay units 35, 37, an adder 36 and a booster 38. The output of the delay unit 37 is also the output of the generator, whose initial value is sin (ω)_eT)，ω_eTo estimate the angular frequency of the signal, T is the sampling period of the digital circuit. The delay unit 35 is initialized to 0 and delays the output of the signal generator by one sampling period. The amplification factor of the booster 38 is 2cos (ω)_eT) which amplifies the output of the signal generator. The output signal of adder 36 is the output signal of multiplier 38 minus the output signal of delay unit 35, whose output is the input of delay unit 37, and evaluation signal generator 23 outputs:

V₁₀＝cos(ω_et) (11)

fig. 8 is a schematic diagram of a bandpass filter 32 comprising six summing nodes 39, 41, 42, 44, 46, 48, three multipliers 40, 43, 49 and two delay units 45 and 47, the two delay units 45, 47 delaying the respective input signals by one sample period. The amplification factor a of the gain 40 of the band pass filter determines the bandwidth of the filter, the amplification factor B of the gain 43 determines the center frequency of the filter, and the gain 49 reduces the amplitude of the output signal by a factor of 1, so that the gain of the entire filter is 1. Wherein

$A=\frac{1-\tan \left(0.5f_{h}T\right)}{1+\tan \left(0.5f_{h}T\right)}---\left(12\right)$

B＝cos(ω_eT) (13)

Wherein f is_hIs the bandwidth, T is the sampling period, ω_eThe central angular frequency. The transfer function of the band pass filter is:

$H\left(Z\right)=\frac{A-1}{2}\·\frac{z^{-2}-1}{{\mathrm{Az}}^{-2}+B(1+A)z^{-1}+1}---\left(14\right)$

fig. 9 is a schematic diagram of the frequency doubler limiter 26, which comprises a summing node 52, a booster 53 and two delay units 50, 51, which delay the respective output signals by one sample period. The booster is a booster that amplifies the output of the delay unit 50 by 2cos (2 ω)_eT) times. The addition node adds the signal V₁₁Adding the signal of the delay unit 51 and subtracting the output signal of the booster to obtain a signal V₁₂Signal V₁₂Proportional to the size of C0. It can be seen from the figure that the gain of the frequency-doubling filter is 2-2cos (2 ω)_eT)。

Fig. 10 is a schematic diagram of a tracking filter 13, which differs from the bandpass filter of fig. 8 in that the multipliers 55 and 59 are replaced by multipliers 40 and 43, which are multiplied by signals α and β, respectively, and its tracking function is performed by a signal β, which determines the center frequency of the tracking filter.

$\mathrm{\α}=\frac{1-\tan \left(0.5f_{h}T\right)}{1+\tan \left(0.5f_{h}T\right)}---\left(15\right)$

$H\left(z\right)=\frac{0.5(1-\mathrm{\α})(1-z^{-2})}{1+\mathrm{\β}(1+\mathrm{\α})z^{-1}+{\mathrm{\αz}}^{-2}}---\left(16\right)$

When the output signal aa of the agc in fig. 4 is 1.75, f_h20Hz, when aa < 1.75, f_h＝5Hz。

Fig. 11 is a schematic diagram of the phase detector 14, comparing the signal V₅Sum signal Q₂Multiplying to obtain a signal V₁₇Signal V₁₇The signal V is obtained by a frequency doubling trap 67₁₈，V₁₈V is obtained through the phase corrector 68₁₉，V₁₉The signal of (2) is amplified by C times, and the value of C is generally about 0.002. The amplified signal passes through an integrator to obtain a signal V₆. The integrator is composed of an adder 71, a limiter 72 and a register 73, and the limiter is used for converting the signal V₆The limit is between-0.707 and 0.707.

Fig. 12 is a schematic diagram of a double frequency tracking trap, and compared with fig. 9, a gain unit 53 is changed to a multiplier 77, and the center frequency of the trap is determined by a signal β 1, so as to realize the tracking function.

Fig. 13 shows a phase corrector, which mainly functions to damp and damp the output signal V18 of the double frequency tracking wave trap to prevent the signal from sudden change. The phase corrector consists of five adders 79, 80, 84, 85, 87, two registers 78, 83 and 3 multipliers 82, 81, 86, of which

D＝exp(-Lω_hT) (17)

$E=\frac{1}{2L}---\left(18\right)$

F＝2L (19)

L is the coefficient of resistance, omega_hIs the turning frequency of the damper, and the value of the turning frequency is determined by the specific condition of an input signal in the debugging process of the system.

Fig. 14 is a detailed schematic diagram of the reference signal generator 17, which includes 5 multiplying units 89, 96, 98, 99, 101, three adding units 91, 94, 95, two delay units 97, 100, and two compensators 102, 103. Signal V₆Multiplied by itself to obtain a signal V₂₀，V₂₀Is input to an arithmetic unit 92, and the transmission characteristic of the arithmetic unit 92 isSignal V₂₀The signals β 1, β 1 obtained by the gain device 90 and the adder 91 determine the center frequency of the frequency doubling tracking trap, and the signal V₆The signal β obtained by the gain 88 determines the center frequency of the tracking filter the output of the reference signal generator comprises signals I, Q, β, β 1, signal I, Q is a sine wave with amplitude 1, phase difference is 90 °, and its frequency is given by signal V₆The value of (c) is determined. The whole reference signal generator has the following relation

β＝-V₆＝cos(ωT) (20)

$\mathrm{\&beta;}1=4V_6^2-2=4{\cos }^2\left(\mathrm{\&omega;}T\right)-2=2\cos \left(2\mathrm{\&omega;}T\right)---\left(21\right)$

The delay units 97 and 100 delay the respective inputs by one sampling period to obtain V₂₁、V₂₂The initial values are 1 and 0, respectively, and the transfer characteristics of the compensators 102 and 103 are as follows:

signal(i)＝1，V₂₁＞0 (22)

signal(i)＝-1，V₂₁＜0 (23)

signal(i)＝0，V₂₁＝0 (24)

signal(q)＝1，V₂₂＞0 (25)

signal(q)＝-1，V₂₂＜0 (26)

signal(q)＝0，V₂₂＝0 (27)

$I=signal\left(i\right)\&times;(1+b_1{V}_{21}^2+b_2{V}_{21}^4),V_{21}<0.1---\left(28\right)$

I＝V₂₁，V₂₁＜0.1 (29)

$Q=signal\left(q\right)\&times;(1+b_1{V}_{22}^2+b_2{V}_{22}^4),V_{21}<0.1---\left(30\right)$

Q＝V₂₂，V₂₂＜0.1 (31)

wherein b is₁＝-0.5，b₂＝-0.1259。

Fig. 15 is a schematic diagram of the phase shifter 16, which comprises 2 adders 105, 108, 2 registers 104, 109 and a multiplier 107 and a constant G, and which functions to shift the signal Q by a phase of θ to obtain the signal Q₂The magnitude of the phase θ is determined by a constant G, and G and θ satisfy the following relationship.

$G=\frac{\sin \left(\frac{\mathrm{\&theta;}-\mathrm{\&omega;}T}{2}\right)}{\sin \left(\frac{\mathrm{\&theta;}+\mathrm{\&omega;}T}{2}\right)}---\left(32\right)$

FIG. 16 is a schematic diagram of the automatic gain controller 15, which includes multiplicationA comparator 110, a comparator consisting of 111 and 118, a frequency doubling tracking trap 112, a phase corrector 113, an amplitude adjuster 1 consisting of 119 and 114, and an integrator consisting of 115, 116 and 117. Constant 118 is 0.5A²A is a circuit design time V₅Constant 119 is around 0.003. The final output signal of the automatic gain controller is aa. The block diagrams of the double frequency tracking trap 112 and the phase corrector 113 are shown in fig. 12 and 13, except that the input and output signals are different.

Fig. 17 is a schematic diagram of the frequency scanning circuit 9, which includes the tracking filter 13, the reference signal generator 17, the multiplier 120, the frequency doubling trap 121, the C0 estimation and compensation 12, and the hardware circuit portion. The value of the module 122 is used to control the frequency of the output signal I, Q of the reference signal generator 17, and in order to implement the frequency sweeping function, the value f in the module 122 is changed and stepped according to a certain time. The value of f in block 122 will be at f_ResonanceThe range of +/-delta f is changed from small to large, the value of delta f is determined by the characteristics of the quartz resonator, the minimum amplitude ratio of the signal V in the frequency sweeping process is ensured to be less than 0.707 than the maximum amplitude, the accuracy of the step length is selected by the test accuracy, the higher the accuracy requirement is, the smaller the change step length is. The reference signal generator 17 generates two signals I, Q with constant amplitude and phase and orthogonal, and the two signals are directly input to the C0 estimation and compensation 12, and the C0 estimation and compensation outputs a signal V after adding an evaluation signal to the signal I₇，V₇Applied to the electrodes of the quartz resonator via a D/a converter 20. Output signal V of quartz resonator₁The signal V is formed via an analog conditioning circuit 10 and an A/D converter 11₄Signal V₄The output signal V is filtered by the tracking filter 13₅The centre frequency of the tracking filter is controlled by the output signal β of the reference generator 17 to ensure that the centre frequency coincides with the frequency of the signal I the output signal V of the tracking filter 13₅The sum signal I is multiplied by a multiplier 120 to obtain a signal V₂₆Signal V₂₆The signal V is obtained through a frequency doubling trap and the correspondence between the signal V and the frequency f in the module 122 is recorded.

FIG. 18 shows the relationship between frequency f and amplitude VffDrawing is shown. Through f_ResonanceCorresponding amplitude V_maxAnd the values of R1 can be calculated by the following equations (5) to (7)Corresponding frequency f₁And f₂And the quality factor Q of the quartz resonator can be calculated by formula (4), and the values of L1 and C1 can be calculated by formula (8) and formula (9).

Claims (2)

1. A system for measuring impedance characteristic parameters of a quartz resonator, which establishes an equivalent circuit of the quartz resonator, is characterized in that: the measuring system comprises a CO measuring and calculating and closed-loop driving circuit (7) and a frequency scanning circuit (9), wherein the CO measuring and calculating and closed-loop driving circuit (7) detects the size of a distributed capacitor CO in an equivalent circuit and performs digital compensation on the distributed capacitor CO, the frequency scanning circuit (9) is started when a driving amplitude value output by the CO measuring and calculating and closed-loop driving circuit (7) is smaller than a driving amplitude threshold value, the frequency scanning circuit (9) performs frequency sweeping on the equivalent circuit of the quartz resonator, and finally equivalent parameters of the equivalent circuit of the quartz resonator are obtained through calculation;

the CO measuring and closed-loop driving circuit (7) consists of an analog conditioning circuit (10), an A/D converter (11), a CO measuring and compensating circuit (12), a tracking filter (13), a phase discriminator (14), an automatic gain controller (15), a phase shifter (16), a reference signal generator (17), a first multiplier (18), a second multiplier (19) and a D/A converter (20), wherein the analog conditioning circuit (10) detects an output signal V of the equivalent circuit (5)₁And to the output signal V₁Filtering and amplifying to obtain signal V₂The A/D converter (11) converts the signal V₂Converted into a digital signal V₃Output to a CO measuring and compensating circuit (12), the CO measuring and compensating circuit (12) is used for measuring and compensating the digital signal V₃After compensation, a signal V is obtained₄Output to a tracking filter (13), and the tracking filter (13) compares the signal V with a reference signal₄Filtering to obtain a signal V₅A phase detector (14) for detecting a reference signal Q₂Sum signal V₅Performing phase comparison, transmitting the comparison result V6 to a reference signal generator (17), adjusting the frequency of an output signal I, Q by the reference signal generator (17) according to the value of the comparison result V6, controlling the center frequency of a tracking filter (13) by an output signal β of the reference signal generator (17), controlling the working frequencies of an automatic gain controller (15) and a phase discriminator (14) by an output signal β 1 of the reference signal generator (17), and changing the output signal Q into a reference signal Q after the phase shifter (16) shifts a certain phase₂The magnitude of the shift phase is equal to the output signal I and the signal V₅By detecting the phase difference of the signal V, the automatic gain controller (15)₅The amplitude value of the driving amplitude signal aa is adjusted, and the driving amplitude signal aa and the output signal I are multiplied by a first multiplier (18) to obtain a signal I₁The CO estimation and compensation circuit (12) is based on the signal I₁Output drive signal V₇The driving amplitude signal aa and the output signal Q are multiplied by a second multiplier (19) to obtain a signal Q₁Driving signal V₇After being converted into an analog signal by a D/A converter (20), the analog signal is applied to the electrode of the quartz resonator;

the frequency scanning circuit (9) consists of an analog conditioning circuit (10), an A/D converter (11), a CO measuring and compensating circuit (12) and a tracking circuitThe analog frequency converter comprises a filter (13), a reference signal generator (17), a D/A converter (20), a multiplier (120), a frequency doubling wave trap (121) and a frequency control module (122), wherein an analog conditioning circuit (10) detects an output signal V of an equivalent circuit (5)₁And to the output signal V₁Filtering and amplifying to obtain signal V₂The A/D converter (11) converts the signal V₂Converted into a digital signal V₃Output to a CO measuring and compensating circuit (12), the CO measuring and compensating circuit (12) is used for measuring and compensating the digital signal V₃After compensation, a signal V is obtained₄Output to a tracking filter (13), and the tracking filter (13) compares the signal V with a reference signal₄Filtering to obtain a signal V₅The frequency control module (122) is used for controlling the frequency of an output signal of the reference signal generator (17), the reference signal generator (17) generates two signals I, Q with constant amplitude and orthogonal phase, the two signals are input to the CO measuring and compensating circuit (12), and the CO measuring and compensating circuit (12) outputs a driving signal V according to the signal I₇Driving signal V₇The signal is converted into an analog signal by a D/A converter (20) and then applied to the electrode of the quartz resonator, the output signal β of the reference signal generator (17) is used for controlling the central frequency of the tracking filter (13), the output signal β 1 of the reference signal generator (17) is used for controlling the frequency doubling wave trap (121), and the output signal V of the tracking filter (13)₅The sum signal I is multiplied in a multiplier (120) to obtain a signal V₂₆Signal V₂₆And obtaining a signal V through a frequency doubling wave trap (121), and finally obtaining the corresponding relation between the signal V and the frequency f in the frequency control module (122).

2. The system for measuring the impedance characteristic of a quartz resonator of claim 1, wherein: the CO measuring and compensating circuit (12) in the CO measuring and closed-loop driving circuit (7) and the frequency scanning circuit (9) comprises a band-pass filter (32), an evaluation signal generator (23), a frequency doubling trap (26), a CO calculating module (27), a first multiplier (25), a second multiplier (30), a third multiplier (31), an I channel compensation parameter (28), a Q channel compensation parameter (29), a first adder (33) and a second adder (34), wherein the evaluation signal generator (23) generates an evaluation deviating from the working frequency of the quartz resonatorSignal V₁₀Evaluating the signal V₁₀And signal I₁After superposition, a driving signal V is obtained₇Digital signal V applied to drive circuit of quartz resonator₃The output and evaluation signal V is filtered by a band-pass filter (32)₁₀Signals V of the same frequency₉The first multiplier (25) is coupled to the signal V₉And an evaluation signal V₁₀Performs demodulation of the output signal V₁₁A frequency-doubling trap (26) for dividing the output signal V of the first multiplier (25)₁₁The second frequency doubling signal in the signal is suppressed to obtain a direct current signal V which is in direct proportion to the distributed capacitance CO₁₂The CO calculating module (27) outputs the signal V₁₂Dividing by the circuit gain to obtain a signal V₁₃Signal V₁₃An I channel compensation parameter (28) and a signal I₁The signal V is obtained after multiplication by a second multiplier (30)₁₄Signal V₁₃Q channel compensation parameter (29) and signal Q₁The signal V is obtained after multiplication by a third multiplier (31)₁₅Signal V₁₄Sum signal V₁₅The signals V are obtained after addition by a first adder (33)₁₆Will signal V₁₆From signal V₃Is subtracted to obtain a compensated signal V₄Wherein the circuit gain is composed of the gain generated when the evaluation signal V10 passes through the hardware circuit and the gain of the frequency doubling trap (26).