RU2488785C1 - Method of measuring amplitude-frequency characteristics of movable elements of micromechanical devices - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: method involves generating harmonic signals with a constant component on fixed capacitor plates, from which compensation current, which is equal to the first harmonic of the sum of currents flowing through the capacitor, is generated. Constant voltage equal to zero is maintained at the movable plate. The compensation current is generated by iteration, while varying the amplitude of the compensation current and optionally the phase to achieve minimum amplitude of the first harmonic of the output signal. The difference between the compensation charge and the sum of charges flowing through the capacitor is converted to proportionally dependent output voltage. A second harmonic is selected in the output signal. The amplitude-frequency characteristic of the micromechanical device is defined by the ratio of the second harmonic of the output voltage to the first harmonic of the signal generated on capacitor plates.

EFFECT: broader functional capabilities, high accuracy of measuring amplitude-frequency characteristics.

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Description

The invention relates to micromechanics and is intended to measure the amplitude-frequency characteristics (AFC) of moving elements of micromechanical devices (MMU), such as accelerometers, pressure sensors, microgyroscopes, micromirrors having capacitive signal pick-up.

Known: a method for measuring the dynamic characteristics of a compensation accelerometer [1], a method for controlling the manufacturing quality of micromechanical devices [2], a method for measuring the amplitude-frequency characteristics of moving elements of micromechanical devices [3].

The dimensions of the parts of the MMU range from hundreds to fractions of microns. In particular, the thickness of the torsion is about 8-10 microns. Visual control is difficult and often the only way to ensure the parameters of micromechanical devices is an indirect control method, namely the measurement of the frequency response of moving (sensitive) elements that characterize the generalized quality criterion for manufacturing MMU. The method [1] is intended for measuring the characteristics of compensation type accelerometers containing a force sensor and a displacement sensor, which does not allow its use for direct conversion micromechanical devices containing only two fixed and one movable differential capacitance plates.

The method [2] is also intended to control the quality of manufacturing of micromechanical devices, which consist of a force generator and a displacement sensor. The electrostatic type force adjuster is made in the form of a differential capacity. As well as the method [1], it requires the presence of both a force adjuster and a displacement adjuster.

The known method [3] is the closest in technical essence to the claimed invention and is intended to measure the amplitude-frequency characteristics of the moving elements of micromechanical devices. This method includes forming harmonic signals with a constant component on the fixed capacitor plates when installing a constant bias of zero on the moving plate of the capacitor. In this case, the second harmonic of the sum of charges flowing through the capacitors formed by the movable and fixed plates of the sensing element is distinguished. The amplitude-frequency characteristic of a micromechanical device is determined by the ratio of the second harmonic of the obtained sum of charges to the first harmonic of the signal formed on the capacitor plates.

In the production of micromechanical devices, there is a technological variation in the capacitance values due to the variation in the gaps, distortions, etc.

The imperfection of technological processes is the cause of various distortions and uneven reproduction of gap values, as a result of which there is a spread in the capacitance values of the sensitive element, which violates the symmetry of the capacitive system as a whole. As a result of the inequality of capacities, the values of the overcharge currents differ from each other. In this case, the difference current of the first harmonic is converted into the output voltage of the first harmonic, the value of which is proportional to the difference in capacitance of the capacitors and the amplitude of harmonic oscillations on them. The amplitude of the oscillations depends on the stiffness of the torsion bars, the magnitude of which is proportional to the measurement range, and on the amplitude of the harmonic signals on the fixed plates of the capacitor. The change in capacitance at the edge of the measuring range (nominal impact) is approximately 20%. As a rule, the frequency response is measured at an amplitude of oscillations of the movable plate, which is 10% of the deviation amplitude at the nominal impact, causing a change in the average value of the capacitance by 2%. Such a change can be obtained only for converters with low torsion stiffness, which is due to the limitation of the amplitude of harmonic signals with a constant component, the value of the breakdown voltage. For a number of MMUs with a rigid suspension, this change can be less than about two orders of magnitude, which is less than 0.02%.

Therefore, even a relatively small difference in the capacitance values in the MMD with rigid torsions can lead to the appearance of a difference current of a sufficiently large magnitude, the amplitude of which can significantly exceed the amplitude of the current of the second harmonic.

Since any charge-sensitive amplifier (charge-voltage converter) has a certain non-linearity of the amplitude characteristic, when converting the difference current of the first harmonic to voltage, the voltage of not only the first but also higher harmonics is generated at the output of the converter, including the second, resulting in thereby distorting the useful signal (second harmonic voltage). For MMUs with high sensitivity (low rigidity of the suspension), a sufficiently large effect can be exerted by gravity, leading to a change in the ratio of capacitance capacities.

In addition, the measurement of the second harmonic in the output voltage against the background of the first, which is many times higher than the amplitude of the second harmonic, can be carried out using fairly expensive measuring instruments. The price of such devices ranges from approximately 80 thousand (spectrum analyzer SK4-56, operating frequency from 10 Hz) to more than one and a half million rubles (spectrum analyzer from Bruhl & Kj типаr type 3560 PULSE, operating frequencies - much less than 1 Hz).

The circumstances discussed above limit the scope, reducing the accuracy of measuring the frequency response in the method [3] and require the use of expensive equipment for its implementation.

The objective of the proposed method is to expand the functionality, increase accuracy and reduce the cost of equipment for its implementation.

To achieve this goal, a constant voltage equal to zero is maintained on the movable lining of the capacitor of a differential variable capacitance, consisting of a movable element and two fixed elements. Harmonic signals of the same frequency and amplitude with a constant component are supplied to the stationary plates in antiphase, from which a compensation current is formed equal to the first harmonic of the sum of the currents flowing through the capacitors.

Formation of the compensation current is carried out by iteration - at the beginning, the compensation current is set equal to zero and the amplitude of the first harmonic is measured in the output voltage. Then, the compensation current is increased, with a decrease in the amplitude of the first harmonic in the output signal, the compensation current is increased until the amplitude of the first harmonic becomes minimum, and with an increase in the amplitude of the first harmonic in the output signal, the phase of the compensation current is changed by 180 degrees, while the amplitude of the first harmonic in the output signal decreases, and the amplitude of the compensation current is increased until the amplitude of the first harmonic becomes minimal; at the same time, during the iteration, it is taken into account that a further increase in the amplitude of the compensation current after reaching the minimum amplitude of the first harmonic of the output signal will lead to its increase.

The sum of the compensation charge and the charges flowing through the capacitors is converted into a proportionally dependent output voltage. In this case, the amplitude-frequency characteristic of the MMD is equal to the ratio of the second harmonic of the output voltage to the first harmonic of the signals formed on the capacitor plates.

Due to the formation of the compensation current and subtraction of it from the sum of the currents flowing through the capacitors, the current of the first harmonic decreases sharply, which is converted to the output voltage, thereby reducing the amplitudes of both the first harmonic and the parasitic harmonics caused by the nonlinearity of the conversion, which increases the measurement accuracy. In this case, it is possible to measure the frequency response of the MMU with torsion bars of both large and very low stiffness, thereby ensuring the expansion of the possibilities of using this method.

The invention is illustrated in graphic materials.

Figure 1 shows a block diagram of a device designed to implement the proposed method, where

1 - midpoint generator;

2 - the midpoint of the generator;

3 - source of constant voltage;

4, 5 - symmetrical conclusions of the generator;

6, 7 - fixed electrodes of MMU;

8 - movable electrode MMU;

9 - input charge-sensitive amplifier;

10 - resistor;

11 - capacitor;

12 - operational amplifier;

13 - output charge-sensitive amplifier;

14 - spectrum analyzer or selective microvoltmeter.

15 - compensator;

16 - potentiometer;

17 - capacitor.

A device for implementing the proposed method, the structural diagram of which is presented in figure 1, includes a generator 1 with a balanced output and a midpoint. A constant bias voltage (of the order of 20-70 V) is supplied to the midpoint 2 of the generator 1 from the voltage source 3, and the symmetrical terminals of the generator 4, 5 are connected to the stationary electrodes 6, 7 of the MMU and to the first and second inputs of the compensator 15. The movable electrode 8 and the output of the compensator is connected to the input 9 of the charge-sensitive amplifier formed by the resistor 10, the capacitor 11, the operational amplifier 12. The first output of the resistor 10, the first output of the capacitor 11 and the negative input of the operational amplifier 12 are closed and form the input 9 of the charge-sens powerful amplifier. The second conclusions of the resistor 10, the capacitor 11 and the output of the operational amplifier 12 are closed and form the output 13 of the charge-sensitive amplifier. The positive input of the operational amplifier 12 is connected to zero potential. The output 13 is connected to the input of the spectrum analyzer 14.

The compensator 15 can be made in the form of a potentiometer 16 and a capacitor 17, the first output of which is the output of the compensator 15, and the second output is connected to the movable slider of the potentiometer 16, the other two outputs of which are the inputs of the compensator 15.

In the case of capacitance inequality when applying a pulsating voltage to the plates of an alternating capacitor, the differential current of the first harmonic recharge is converted into the output voltage of the first harmonic using a charge-sensitive amplifier and is measured using a selective voltmeter.

Moving the slider of the potentiometer leads to a change in the voltage applied to the capacitor, and, consequently, to a change in the compensation charge, leading to a decrease or increase (depending on the phases of the difference and compensation currents) of the amplitude of the output voltage of the first harmonic. Moreover, the voltage at the output of the potentiometer in the middle position of the slider is zero, and in the two extreme positions it is maximum, but the phase shift is 180 °.

The proposed method for measuring the frequency response is based on the electrostatic interaction between the movable (Fig. 1, pos. 8) and fixed plates (Fig. 1, pos. 6, 7) of the CE, forming a differential capacitor of variable capacitance. Harmonic signals U ₁ and U _{2 of} frequency w with a constant component U ₀ (FIGS. 2-A and 2-B, respectively) are fed to the fixed plates of this capacitor, and a zero voltage is maintained on the moving electrode:

U ₁ = U ₀ + U _g sin (wt),

U ₂ = U ₀ -U _g sin (wt), where

voltage U ₀ corresponds to the voltage at the point pos.2 of figure 1;

voltage U ₁ corresponds to the voltage at the point 4 of figure 1;

voltage U ₂ corresponds to the voltage at the point 5 of FIG. 1.

The value of the constant component U ₀ must be not less than the amplitude U _{g of the} harmonic component U ₀ ≥U _G , thus setting the condition U ₁ , U ₂ ≥0.

The resulting variable component due to the force of the Coulomb interaction between the movable and two stationary electrodes is shown in Fig.2c, due to the influence of which the movable electrode of the SE oscillates.

In the absence of voltage on the capacitor plates (the device is turned off), the electric capacitance of capacitors C ₁ , C ₂ are equal to:

C ₁ = C _o + ΔC

C ₂ = C _o -ΔC

The deviation ΔС of the capacitance value from the value of C _о can be the result of both technological variation and the effect of the Earth's gravity. Moreover, the value of ΔC reaches a value of 0.1C _about due to technological variation. The effect of gravity can cause an even greater deviation, depending on the sensitivity of the MMU.

When operating voltage is applied, the deflection of the movable plate is proportional to the applied force and inversely proportional to the torsion stiffness.

In the General case, the electric capacitance of the capacitors C ₁ , C ₂ formed by the plates of the SE and the common electrode is expressed as follows:

C ₁ = (C _o + ΔC) · (1 + A _mech · sin (wt)),

C ₂ = (C _o -ΔC) · (1-A _mech · sin (wt)),

the electric capacitance C _{1 is} formed by the plates of pos.6 and pos.8 of figure 1;

the electric capacitance C _{2 is} formed by the plates of pos.7 and pos.8 of figure 1;

the change in capacitances C ₁ , C ₂ is shown in FIGS. 2d and 2e, respectively.

Coefficient A _mech depends on the amplitude U _g and the amplitude of the mechanical vibrations of the movable element MMU, and With _{about the} electrical capacitance of the capacitors in the absence of asymmetry, when C ₁ = C ₂ = C _about .

The transfer coefficient of the charge-sensitive amplifier (formed by the resistor pos.11, capacitor pos.10, operational amplifier pos.12 of figure 1) for the signal U _{1 is} calculated as follows

, где U_вых - напряжение на выходе зарядо-чувствительного усилителя. $${\mathrm{TO}}_{PeR}=\frac{U_{\mathrm{at}sx}}{U_{\mathrm{one}}}=\frac{X_{Coo}}{X_{C\mathrm{one}}}=\left(\frac{\mathrm{one}}{j\cdot w\cdot C_{oc}}\right)÷\left(\frac{\mathrm{one}}{j\cdot w\cdot C_{\mathrm{one}}}\right)=\frac{C_{\mathrm{one}}}{C_{oc}}$$

where U _o - voltage at the output of the charge-sensitive amplifier.

The values of R _a (the ohmic resistance of the resistor 1, item 11) and the C _axes (electric capacity of the condenser 1, item 10) are chosen such that R _os in the operating range of frequencies was much more reactance X _Sos capacitance C _a.

The voltage U ₁ generates a signal at the output of the charge-sensitive amplifier:

$$\begin{array}{l}{U}_{\mathrm{at}sx\mathrm{one}}=U_{\mathrm{one}}\cdot {\mathrm{TO}}_{PeR}=U_{\mathrm{one}}\cdot \frac{C_{\mathrm{one}}}{C_{oc}}=U_{\mathrm{one}}\cdot \frac{\left(C_o+\Delta C\right)\cdot \left(\mathrm{one}+A_{mex}\cdot \sin \left(wt\right)\right)}{C_{oc}}\\ =U_{\mathrm{one}}\frac{C_o}{C_{oc}}\left(\mathrm{one}+A_{mex}\cdot \sin \left(wt\right)\right)+U_{\mathrm{one}}\frac{\Delta C}{C_{oc}}\left(\mathrm{one}+A_{mex}\cdot \sin \left(wt\right)\right)=\\ k\left(U_o+U_g\cdot \sin \left(wt\right)\right)\cdot \left(\mathrm{one}+A_{mex}\cdot \sin \left(wt\right)\right)+k_{\mathrm{one}}\left(U_o+U_g\cdot \sin \left(wt\right)\right)\cdot \left(\mathrm{one}+A_{mex}\cdot \sin \left(wt\right)\right)\end{array}$$

, $$k_1=\frac{\Delta C}{C_{oc}}$$

.Where $$k=\frac{C_o}{C_{oc}}$$

, $$k_{\mathrm{one}}=\frac{\Delta C}{C_{oc}}$$

.

Due to symmetry, the voltage U ₂ creates a signal at the output of the amplifier

$$\begin{array}{l}{U}_{\mathrm{at}sx2}=U_2\cdot {\mathrm{TO}}_{PeR}=U_2\cdot \frac{C_2}{C_{oc}}=U_2\cdot \frac{\left(C_o-\Delta C\right)\cdot \left(\mathrm{one}-A_{mex}\cdot \sin \left(wt\right)\right)}{C_{oc}}=\\ U_2\frac{C_o}{C_{oc}}\left(\mathrm{one}-A_{mex}\cdot \sin \left(wt\right)\right)-U_2\frac{\Delta C}{C_{oc}}\left(\mathrm{one}-A_{mex}\cdot \sin \left(wt\right)\right)=\\ k\left(U_o-U_g\cdot \sin \left(wt\right)\right)\cdot \left(\mathrm{one}-A_{mex}\cdot \sin \left(wt\right)\right)-k_{\mathrm{one}}\left(U_o-U_g\cdot \sin \left(wt\right)\right)\cdot \left(\mathrm{one}-A_{mex}\cdot \sin \left(wt\right)\right)\end{array}$$

Assuming that the slider of the potentiometer 16 is in the middle position, and the alternating voltage on it is zero, and taking into account the principle of superposition, we get:

U _{o out} = U _{o out1} + U _{o out2} =

k (U _o + U _g · sin (wt)) · (1 + A _mech · sin (wt)) + k ₁ (U _o + U _g · sin (wt)) · (1 + A _mech · sin (wt )) +

k (U _o -U _g · sin (wt)) · (1-A _mech · sin (wt)) - k ₁ (U _o -U _g · sin (wt)) · (1-A _mech · sin (wt )))

After the conversion, taking into account the fact that 1-2sin ² (wt) = cos (2wt), we get the final expression for U _o :

U _O = 2kU _o + kU _G A _T A _fur -kU _fur · cos (2wt) + 2k ₁ (U _o + U A _{fur T)} · sin (wt)

The voltage U _o corresponds to the voltage at point 13 of FIG. 1. The amplitude of the second harmonic of the output signal depends on the coefficients k, U _G , A _mech . The values of k, U _Г are constant, this means that the amplitude A of the _mech , which characterizes the amplitude of the mechanical vibrations of the moving element of the IMC, affects the amplitude of the second harmonic of the output signal. The analysis of the amplitude of the second harmonic using a spectrum analyzer (pos. 14 of Fig. 1) when the frequency changes on the master oscillator (pos. 1 of Fig. 1) implements the task - measuring the frequency response of the moving element of the MMU.

Consider the ratio of the amplitudes of the first and second harmonics in the output signal. The amplitudes of the first and second harmonics U _A1 and U _{A2 are} respectively equal:

, при условии U_Г>>U_oA_мех получим $$U_{A1}\approx 2\frac{\Delta C}{Coc}{U}_{Г}$$

$$U_{A\mathrm{one}}=2\frac{\Delta C}{Coc}\left(U_o{A}_{mex}+U_G\right)$$

, under the condition U _Г >> U _o A _fur we get $$U_{A\mathrm{one}}\approx 2\frac{\Delta C}{Coc}{U}_G$$

$$U_{A2}=2\frac{Co}{Coc}{U}_2{A}_{mex}$$

We write the ratio of the amplitudes U _A1 and U _A2 :

$$\frac{U_{A\mathrm{one}}}{U_{A2}}=\frac{2U_2\Delta C}{C_{oc}}\cdot \frac{C_{oc}}{2C_o{U}_2{A}_{mex}}=\frac{2\Delta C}{C_o{A}_{mex}}$$

As mentioned earlier, the value of ΔC can reach 0.1C _about , and the coefficient A _{fur is} approximately 0.02. Thus, the amplitude of the first harmonic exceeds the amplitude of the second measured harmonic by 10 times. Moreover, for MMU with a rigid suspension, the value of this ratio can increase by about two orders of magnitude.

With such large ratios of the spurious harmonic to the measured one, the nonlinearity of the charge-sensitive amplifier begins to affect, thereby reducing the measurement accuracy and limiting the functionality of this method. In addition, the implementation of the method requires expensive equipment.

The amplitude of the first harmonic in the output signal can be significantly reduced due to the presence of a compensator and its adjustment. By measuring the amplitude of the first harmonic in the output voltage, we change the position of the slider of the potentiometer 16 in such a way as to minimize the amplitude of the first harmonic in the output voltage, up to zero, thereby increasing the accuracy and expanding the functionality of the method.

To implement this method in practice, a measuring device was assembled. The selective voltmeter and the master oscillator were implemented on the basis of the MAX7490 microcircuit, which is a two-channel universal filter on switched capacitors. Moreover, the cost of the chip did not exceed 150 rubles.

An experimental check showed that the first harmonic in the output signal decreased by 47 dB (about 200 times). Incomplete suppression is due to the influence of the active resistance of the potentiometer on the phase shift in the compensator circuit. If necessary, it can be reduced by complicating the compensator device using a decoupling amplifier (voltage follower). Although in our case, for all practical tasks, this complication was not required.

LFs were measured both using an expensive SK4-56 spectrum analyzer and a tunable active filter based on MAX7490. Deviations of the results were within the measurement error.

The experimental verification fully confirmed the expected results.

Information sources

1. USSR patent 1839835

2. RF patent 2244271

3. RF patent 2377508 - prototype

Claims (1)

A method for measuring the amplitude-frequency characteristics of sensitive elements of micromechanical devices containing a movable element, which is a common lining of a differential capacitor of variable capacitance, which consists in forming harmonic signals with a constant component on the fixed plates of the capacitor and installing a constant bias of zero on the moving lining, the frequency response of the micromechanical device is calculated by the ratio of the second harmonic of the output voltage pressure to the first harmonic of the signal formed on the capacitor plates, characterized in that the compensation current, which is in antiphase but equal in amplitude to the first harmonic of the sum of the currents flowing through the capacitors, is formed from harmonic signals on the fixed capacitor plates and the compensation charge is converted and charges flowing through the capacitors into a proportionally dependent output voltage, and the formation of the compensation current is carried out by iteration - at the beginning of The current current is set equal to zero and the amplitude of the first harmonic is measured in the output voltage, then the compensation current is increased, when the amplitude of the first harmonic decreases in the output signal, the compensation current is increased until the amplitude of the first harmonic becomes minimal, and when the amplitude of the first harmonic is increased in the output the signal changes the phase of the compensation current by 180 °, while the amplitude of the first harmonic in the output signal decreases, and the amplitude of the compensation current is increased until the amplitude the first harmonic there will not be minimal; at the same time, during the iteration, it is taken into account that a further increase in the amplitude of the compensation current after reaching the minimum amplitude of the first harmonic of the output signal will lead to its increase.