DE102018218249A1 - Micromechanical component and method for frequency tuning of a parametrically amplified micromechanical component - Google Patents

Abstract

A method for frequency tuning of a micromechanical component is proposed, the micromechanical component having an oscillatable structure, a drive structure, a detection structure, a feedforward structure and a control system, the drive structure being configured to excite a drive mode of the oscillatable structure, the detection structure being for detection a detection mode of the vibratable structure is configured, the vibratable structure with respect to the detection mode having a spring constant that increases or decreases due to a coupling between the drive mode and the detection mode with a deflection of the drive mode, the positive feedback structure being configured to increase or decrease the natural frequency of the detection mode , wherein the detection mode is excited with a first and a second pilot tone, the amplitude ratio of the first and second pilot tone depending The strength of the coupling between the drive mode and the detection mode is set, the natural frequency of the detection mode being regulated via the central coupling structure in such a way that the first output amplitude is equal to the second output amplitude , a detection structure, a feedforward structure and a control system, the drive structure, the detection structure and the control system being configured to carry out the method for frequency tuning.

Description

State of the art

The invention is based on a method according to the preamble of claim 1 and a micromechanical component according to the preamble of claim 6.

Micromechanical components (microelectromechanical systems, MEMS) with vibratable structures are known from the prior art in a variety of embodiments. One of the areas of application for such components is, for example, use as rotation rate sensors in the automotive sector or in entertainment and consumer electronics. The measurement of a rotation rate is based on the exploitation of the Coriolis effect. The rotation rate sensors consist of one or two frame structures of mass m _c coupled via springs. Comb electrodes are used for electrostatic actuation of the frame structures and detection of the deflections. Two vibration modes, the so-called drive and detection modes, with the same or different resonance frequency are used to record a rotation rate. The drive mode is excited to oscillate by an alternating voltage. The detection mode remains at rest without external rotation rate. When an external rotation rate Ω is applied, the detection mode is deflected due to the Coriolis force F _c . The Coriolis force F _c is proportional to the external rate of rotation Ω and the speed, ie to the time derivative q̇ _{A of} the vibration amplitude of the drive mode q _A with Coriolis mass m _c : $$F_c=\mathrm{2nd}{m}_c\mathrm{\Omega }{\dot{q}}_A$$

The deflection q _{D of} the detection mode can be read out via the change in capacitance between the detection comb electrodes.

wobei k_AD die Stärke der Kopplung zwischen Antriebs- und Detektionsmode quantifiziert. Typischerweise ist das Quadratursignal ein bis drei Größenordnungen größer als das Coriolis-Signal. Das Quadratur-Signal ist um 90° phasenversetzt zum Coriolis-Signal, wie aus Gleichungen (1) und (2) ersichtlich ist. Die Separierung zwischen Quadratur- und Coriolis-Signal erfolgt mittels Demodulationstechnik basierend auf dem 90°-Phasenunterschied.A challenge with MEMS rotation rate sensors is that a small asymmetry in the component leads to crosstalk of the drive vibration. This causes a parasitic signal, the so-called quadrature, in the detection signal. The quadrature force F _Q is proportional to the drive amplitude $$F_Q=k_{AD}{q}_A,$$

where k _AD quantifies the strength of the coupling between the drive and detection modes. Typically, the quadrature signal is one to three orders of magnitude larger than the Coriolis signal. The quadrature signal is 90 ° out of phase with the Coriolis signal, as can be seen from equations (1) and (2). The quadrature and Coriolis signals are separated using demodulation technology based on the 90 ° phase difference.

$${\ddot{q}}_D+\frac{{\omega }_D}{Q_D}{\dot{q}}_D+{\omega }_D^2{q}_D=F_c/m_c+F_Q/m_c$$

The equations of motion for the drive and detection mode of a conventional rotation rate sensor are as follows: $${\ddot{q}}_A+\frac{{\omega }_A}{Q_A}{\dot{q}}_A+{\omega }_A^{\mathrm{2nd}}{q}_A=F_{drive}/m_c$$

$${\ddot{q}}_D+\frac{{\omega }_D}{Q_D}{\dot{q}}_D+{\omega }_D^{\mathrm{2nd}}{q}_D=F_c/m_c+F_Q/m_c$$

Here ω _A and ω _D or Q _A and Q _D denote the resonance frequency or the quality factor of the drive and detection mode. The electrostatic driving force is called F _drive . The Coriolis force F _c is proportional to the speed of the drive mode according to equation (1), so that this term (together with the undesired quadrature term F _Q ) creates a coupling between the drive and detection modes. The Coriolis force acts as an external driving force for the detection mode, the energy transfer being determined by the quality factor Q _D and the ratio of natural frequency ω _{A of} the drive mode and natural frequency ω _{D of} the detection mode. In order to achieve the highest possible energy transfer between the drive and detection modes, it is therefore advantageous to coordinate these drive and detection frequencies with one another (mode matching).

mit Anlagen einer DC Spannung U_DC an den dafür vorgesehen Elektroden beeinflussen, wobei C die Kapazität bezeichnet und x der Abstand zwischen den Elektroden. Durch Änderung der effektiven Steifigkeit kann die Detektionsfrequenz variiert werden ${\omega }_D^{eff}={\omega }_D-{\omega }_{em}\left(U_{DC}\right),$

wobei ${\omega }_{em}{\left(U\right)}_{DC}\sim U_{DC}^2$

Es lässt sich dann eine sogenannte Mitkoppelspannung U_DC bestimmen, bei der die Frequenzen ω_A und ω_D im Wesentlichen zusammenfallen. An exact setting of the drive and detection frequencies based solely on design measures is not possible in practice due to the process uncertainties. The operating principle of electrostatic positive feedback is therefore often used. The effective stiffness can be $k_{eff}=\frac{{\partial }^{\mathrm{2nd}}\mathrm{C.}}{\partial x^{\mathrm{2nd}}}{U}_{D\mathrm{C.}}^{\mathrm{2nd}}$

influence with systems of a DC voltage U _DC at the electrodes provided, where C denotes the capacitance and x the distance between the electrodes. The detection frequency can be varied by changing the effective stiffness ${\omega }_D^{eff}={\omega }_D-{\omega }_{em}\left(U_{D\mathrm{C.}}\right),$

in which ${\omega }_{em}{\left(U\right)}_{D\mathrm{C.}}\sim U_{D\mathrm{C.}}^{\mathrm{2nd}}$

A so-called positive feedback voltage U _DC can then be determined, at which the frequencies ω _A and ω _D essentially coincide.

gegeben. In vielen praktischen Anwendungen wird ein Amplitudenverhältnis von $$r\equiv \frac{{\alpha }_1}{{\alpha }_2}=1$$

gewählt. Dadurch wird jedoch bei MEMS-Sensoren hoher Güte nur ein vernachlässigbar kleiner Fehler verursacht.The pilot tone method is an efficient and inexpensive method for determining the positive feedback voltage for the lowest possible frequency detuning between the drive and detection modes (see C. Ezekwe, Readout Techniques for high-Q micromachined vibratory rate gyroscope, University of California, Berkeley: PhD thesis, 2007 ). The method is based on the following basis: The dynamics of the detection mode can be characterized by an amplitude transfer function, the position of the maximum of this function corresponding to the resonance frequency of the detection mode. The frequency tuning aims to set up the positive feedback voltage in such a way that ω _A and ω _D coincide, so that the maximum of the transfer function (the resonance peak) is at ω _A. For this purpose, two frequency signals, so-called pilot tones, are fed into the control circuit containing the MEMS component. The pilot tones are referenced to the drive frequency and outside the desired signal bandwidth, the frequency ω ₁ = ω _A - ω _{cal of} a pilot tone below and the other frequency ω ₂ = ω _A + ω _cal above the drive frequency ω _A. Let α ₁ and α _{2 be} the input amplitudes of the pilot tones at frequencies ω ₁ and ω ₂ . The response signal of the MEMS component to the pilot tones is demodulated in phase with the pilot tones and evaluated with a low-pass filter (see 1 ). In this way, the ratio of response amplitude and input amplitude for the pilot frequencies ω ₁ and ω ₂ can be determined, which corresponds to an evaluation of the (complex) transfer function of the system for these two frequencies. The amplitude transfer function (as a real part of the transfer function) causes a change in the amplitude of the input signal, while the phase transfer function (as an imaginary part of the transfer function) causes a phase shift of the signal. In the phase-in-phase demodulation of the pilot tane, the phase shifts ϕ ₁ and ϕ _{2 of} the first and second pilot tones lead to a reduction in the corresponding response amplitudes by the factor cos (ϕ ₁ ) or cos (ϕ ₂ ). However, since the difference ϕ ₁ - beträgt ₂ is close to π, both pilot tones are reduced in the same way, whereby the factors cos (wobei ₁ ) and cos (ϕ ₂ ) additionally cause a change in the relative sign. In the pilot tone method, the transfer function is regulated by the positive feedback voltage so that the resonance peak is at ω _A and ω ₁ and ω ₂ are arranged symmetrically left and right of the maximum of the amplitude transfer function. In the pilot tone process, the asymmetry of the transfer function is taken into account in that the input amplitudes are selected differently and the positive feedback voltage is regulated in such a way that the difference between the two response amplitudes disappears. If the input amplitudes are matched to the asymmetry of the transfer function, this method leads to the maximum of the amplitude transfer function being exactly ω _A. The required amplitude ratio of the pilot tones is through $$\frac{{\alpha }_{\mathrm{<figure-callout\; id="1"\; label="2nd\; \alpha "\; filenames="DE102018218249A1\_0031.png"\; state="\{\{state\}\}">2nd\; </figure-callout>}}}{{\alpha }_{}}=\frac{\mathrm{2nd}{\omega }_A-{\omega }_{cal}}{\mathrm{2nd}{\omega }_A+{\omega }_{cal}}\equiv \frac{1}{r}$$

given. In many practical applications, an amplitude ratio of $$r\equiv \frac{{\mathrm{<figure-callout\; id="1"\; label="\alpha "\; filenames="DE102018218249A1\_0031.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_1}{{\alpha }_{\mathrm{2nd}}}=1$$

chosen. However, this only causes a negligibly small error in high-quality MEMS sensors.

In conventional, linear oscillators, which are driven by an external force, the dynamic excess of the vibration amplitude and thus the signal is determined by the quality factor. Parametric amplification also enables the detection signal to be amplified in a sensor. With parametric amplification, the energy input into the oscillating system does not take place via an external driving force, but rather via a periodic variation of a system parameter, for example the stiffness of the springs. While an external drive can also be used to excite a stationary system, the parametric amplification only amplifies an existing vibration, which in turn can be excited by an external force. With a parametric amplification of the detection mode, the effect of the (external) Coriolis force is amplified in this way and the detection signal is thus increased.

When generating parametric gain, a distinction is made between externally induced and intrinsically induced parametric gain. Both types of parametric amplification are used to increase sensitivity in open loop yaw rate sensors. An externally induced parametric amplification can be achieved, for example, by applying an alternating voltage to the detection electrodes, the frequency of which corresponds to twice the resonance frequency of the detection mode (see also C. Ahn, S. Nitzan, E. Ng, V. Hong, Y. Yang, T. Kimbrell, D. Horsley and T. Kenny, "Encapsulated high frequency (235kHz), high-Q (100k) disk resonator gyroscope with electrostatic parametric pump, “Appl. Phys. Lett, Vol. 105, p. 243504, 2014 ). Intrinsically generated parametric amplification of the detection mode is based on the exploitation of an intrinsic mechanical non-linearity of the rigidity or the mechanical tension of the vibrating structure. The mechanical non-linearity of the rigidity or the mechanical tension in the silicon chip is used in MEMS sensors at high deflections. One possible mechanism is that the temporally oscillating deformation of the resonator associated with the excitation of the drive mode changes the stiffness of the resonator with respect to the detection mode by means of a non-linear coupling between the drive and detection modes. With a suitable choice of the resonator shape or the symmetry of the drive and detection mode, a stiffness can be achieved which oscillates at twice the drive frequency (see also SH Nitzan, V. Zega, M. Li, CH Ahn, A. Corigliano, T. Kenny and D. Horsely, "Selfinduced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope," Sci. Rep., Vol. 5, p. 9036, 2015 ). In this way, energy is transferred from the drive mode vibrating with a large amplitude (a few micrometers) to the detection mode vibrating with a very small amplitude (a few nanometers), and the detection signal is thus amplified.

The pilot tone method described above is specially designed for frequency tuning of linear or harmonic rotation rate sensors. For angular rate sensors with parametric amplification, the conventional pilot tone method does not lead to the desired disappearing frequency detuning but on the contrary leads to a significant frequency detuning. With this detuning, the MEMS oscillator only leads to a response function that corresponds to a linear or harmonic transfer function and any parametric gain is suppressed. In other words, the parametrically amplified rotation rate sensor with a positive feedback voltage determined by the conventional pilot tone method is just as good as a linear or harmonic rotation rate sensor without parametric amplification.

Disclosure of the invention

Against this background, it is an object of the present invention to provide a parametrically amplified micromechanical component and a method for frequency tuning of the component, with which the frequency tuning can be carried out in an efficient and cost-effective manner.

In the method according to the main claim, a pilot tone method modified compared to the prior art is carried out, in which the input amplitudes of the two pilot tones are set as a function of the strength of the coupling between the drive and detection modes. The choice of the ratio of the two input amplitudes takes place on the basis of the transfer function of the structure capable of oscillation. The amplitude ratio is preferably obtained by a mathematical modeling, as is carried out below by way of example for a preferred embodiment of the invention.

The coupling between the drive mode and the detection mode can, for example, be such that when the drive mode is excited, the spring constant of the detection mode oscillates at twice the drive frequency. However, designs are also conceivable in which the detection mode oscillates by utilizing higher eigenmodes with a more general integer multiple, such as three or four times the drive frequency.

Such a modified pilot tone process makes the use of parametric amplification in micromechanical sensors possible, which opens up a variety of technical advantages. Parametric amplification leads to an increase in sensitivity in the fully resonant open loop operation of the Yaw rate sensor compared to conventional yaw rate sensors without parametric amplification. Furthermore, there is an improved signal-to-noise ratio in closed-loop rotation rate sensors compared to conventional rotation rate sensors. Using parametric amplification, lower drive amplitudes are sufficient to achieve the same signal-to-noise ratio as with conventional rotation rate sensors. The smaller drive amplitudes reduce the risk of unwanted or uncontrolled nonlinear effects, and the lower drive voltages enable the application-specific integrated circuit (ASIC) to be reduced in cost. By using the parametric gain, the distance between the electrodes can still be increased and still achieve the same signal-to-noise ratio as with conventional rotation rate sensors. A larger distance between the electrodes is closely linked to an improved robustness of the sensor against external vibrations. The desired signal-to-noise ratio can also be achieved with a smaller sensor core, which enables a reduction in manufacturing costs.

According to a preferred embodiment of the method according to the invention, the detection mode is quadrature compensated by the control system.

According to a further preferred embodiment, the ratio of the first and second input amplitude is set as a function of the difference between the first pilot frequency and the second pilot frequency.

According to a further preferred embodiment, the ratio of the first and second input amplitude is set as a function of the drive frequency.

According to a further preferred embodiment, the ratio of the first and second input amplitude is set as a function of the quality factor of the detection mode.

$$\begin{array}{l}{\ddot{q}}_D+\frac{{\omega }_D}{Q_D}{\dot{q}}_D+{\omega }_D^2{q}_D+\lambda {\omega }_D^2{q}_D+\lambda {\omega }_D^2\text{cos}\left(2{\omega }_{A}t\right)q_D\\ =F_c/m_c+F_Q/m_c\end{array}$$

Another object of the present invention is a micromechanical component according to claim 6, with which the inventive method can be carried out.
In the following, the determination of the ratio of the first and second input amplitude for the pilot tone method according to the invention is outlined using a system in which the spring constant of the detection mode oscillates at twice the drive frequency. Including parametric amplification, the equations of motion for drive and detection modes are as follows: $${\ddot{q}}_A+\frac{{\omega }_A}{Q_A}{\dot{q}}_A+{\omega }_A^{\mathrm{2nd}}{q}_A=F_{drive}/m_c$$

$$\begin{array}{l}{\ddot{q}}_D+\frac{{\omega }_D}{Q_D}{\dot{q}}_D+{\omega }_D^{\mathrm{2nd}}{q}_D+\lambda {\omega }_D^{\mathrm{2nd}}{q}_D+\lambda {\omega }_D^{\mathrm{2nd}}\text{cos}\left(\mathrm{2nd}{\omega }_{A}t\right)q_D\\ =F_c/m_c+F_Q/m_c\end{array}$$

in Gleichung (4) bestimmt die Überhöhung bzw. Unterdrückung der Detektionsamplitude aufgrund von parametrischer Verstärkung. Neben der Amplitudenänderung bewirkt der Term $\lambda {\omega }_D^2{q}_D$

in Gleichung (4) eine Frequenzverschiebung aufgrund der parametrischen Verstärkung. Der nichtlineare Steifigkeitsparameter $\lambda =\frac{V{a}_A^2}{2{\omega }_D^2}$

ist proportional zu dem von der Geometrie abhängigen nichtlinearen Kopplungskoeffizienten V, proportional zum Amplitudenquadrat $a_A^2$

der Antriebsmode und invers proportional zum Frequenzquadrat ${\omega }_D^2$

der Detektionsmode. Der nichtlineare Steifigkeitsparameter λ definiert den Arbeitspunkt in Relation zum kritischen Schwellwert λ_crit. Der kritische Schwellwert ist gegeben durch: $${\lambda }_{crit}=\frac{2}{Q_D}\sqrt{\frac{4Q_D^2{\delta }^2}{{\omega }_D^2}+1}$$

Hierbei bezeichnet $\delta ={\omega }_p\sqrt{1+\lambda }-{\omega }_{drive}$

die Frequenzverstimmung zwischen der Frequenz ω_drive der äußeren Kraftanregung und Frequenz der Detektionsmode ${\omega }_p\sqrt{1+\lambda }$

bei parametrischer Verstärkung. Für perfekte Frequenzabstimmung δ → 0 ist der kritische Schwellwert λ_crit → 2/Q_D minimal (vgl. 2). Je größer die Frequenzverstimmung zwischen Antriebs- und Detektionsmode, desto größer ist der kritische Schwellwert λ_crit (siehe 2). Die nichtlineare Steifigkeit λ in Bezug auf den kritischen Schwellwert λ_crit bestimmt den Verstärkungsfaktor G (engl. Gain) des Detektionssignals. Der Verstärkungsfaktor G ist definiert als Verhältnis der Detektionsamplituden a_D eines parametrische verstärkten Drehratensensors (λ/λ_crit ≠ 0) im Vergleich zu einem konventionellen Drehratensensors ohne parametrische Verstärkung (λ/λ_crit = 0): $$G=\frac{a_D\left(\lambda /{\lambda }_{crit}\ne 0\right)}{a_D\left(\lambda /{\lambda }_{crit}=0\right)}$$

The driving force in fully resonant operation of the drive mode is defined as F _drive = f ₀ sin (ω _A t). The non-linear stiffness parameter λ is a measure of the parametric amplification of the detection signal and determines the coupling between the drive and detection modes. For q _A >> q _D , the feedback of the detection mode to the drive mode can be neglected. In the case of a quadrature-compensated rotation rate sensor, the coupling k _AD can be neglected. The term $\lambda {\omega }_D^{\mathrm{2nd}}\text{cos}\left(\mathrm{2nd}{\omega }_{A}t\right)q_D$

Equation (4) determines the increase or suppression of the detection amplitude due to parametric amplification. In addition to the change in amplitude, the term causes $\lambda {\omega }_D^{\mathrm{2nd}}{q}_D$

in equation (4) a frequency shift due to the parametric gain. The nonlinear stiffness parameter $\lambda =\frac{V{a}_A^{\mathrm{2nd}}}{\mathrm{2nd}{\omega }_D^{\mathrm{2nd}}}$

is proportional to the geometry-dependent non-linear coupling coefficient V, proportional to the square of the amplitude $a_A^{\mathrm{2nd}}$

the drive mode and inversely proportional to the frequency square ${\omega }_D^{\mathrm{2nd}}$

the detection mode. The nonlinear stiffness parameter λ defines the working point in relation to the critical threshold λ _crit . The critical threshold is given by: $${\lambda }_{crit}=\frac{\mathrm{2nd}}{Q_D}\sqrt{\frac{\mathrm{4th}{Q}_D^{\mathrm{2nd}}{\delta }^{\mathrm{2nd}}}{{\omega }_D^{\mathrm{2nd}}}+1}$$

Inscribed here $\delta ={\omega }_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="DE102018218249A1\_0031.png"\; state="\{\{state\}\}">p</figure-callout>}}\sqrt{1+\lambda }-{\omega }_{drive}$

the frequency detuning between the frequency ω _{drive of} the external force excitation and the frequency of the detection mode ${\omega }_p$${}_{}\sqrt{1+\lambda }$

with parametric gain. For perfect frequency _tuning δ → 0, the critical threshold λ _crit → 2 / Q _{D is} minimal (cf. 2nd ). The greater the frequency _detuning between drive and detection _mode , the greater the critical threshold λ _crit (see 2nd ). The non-linear stiffness λ in relation to the critical threshold value λ _crit determines the gain _factor G (English Gain) of the detection signal. The gain factor G is defined as the ratio of the detection _amplitudes a _{D of} a parametric amplified rotation rate sensor (λ / λ _crit ≠ 0) compared to a conventional rotation rate sensor without parametric amplification (λ / λ _crit = 0): $$G=\frac{a_D\left(\lambda /{\lambda }_{crit}\ne 0\right)}{a_D\left(\lambda /{\lambda }_{crit}=0\right)}$$

abgestimmt ist, d.h. $\delta ={\omega }_D\sqrt{1+\lambda }-{\omega }_{drive}=0.$

Es lässt sich dann eine sogenannte Mitkoppelspannung U_DC bestimmen bei der die Frequenzverstimmung $\delta ={\omega }_p\sqrt{1+\lambda }-{\omega }_{drive}-{\omega }_{em}\left(U_{DC}\right)=0$

ergibt.As in 2nd shown, the parametric gain factor decreases G with increasing critical threshold value λ _crit and with increasing frequency _detuning δ . The result of this is that a noteworthy parametric gain factor G >> 1 can only be achieved if the frequency of the external drive matches the frequency of the detection mode with parametric gain ${\omega }_D$${}_{}\sqrt{1+\lambda }$

is coordinated, ie $\delta ={\mathrm{<figure-callout\; id="1"\; label="\omega \; D"\; filenames="DE102018218249A1\_0031.png"\; state="\{\{state\}\}">\omega \; </figure-callout>}}_D\sqrt{1+\lambda }-{\omega }_{drive}=0.$

A so-called positive feedback voltage U _DC can then be determined at which the frequency detuning $\delta ={\omega }_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="DE102018218249A1\_0031.png"\; state="\{\{state\}\}">p</figure-callout>}}\sqrt{1+\lambda }-{\omega }_{drive}-{\omega }_{em}\left(U_{D\mathrm{C.}}\right)=0$

results.

festgelegt, wobei hier $p=\frac{{\omega }_{cal}}{{\omega }_D}$

ist. Mit diesem Amplitudenverhältnis ist das Ausgangssignal des Pilottonverfahrens genau dann bei Null, wenn die Mitkoppelspannung so gesetzt ist, dass δ = 0 gilt. Dies gilt für jeden nichtlinearen Steifigkeitsparameter λ. Dadurch wird die parametrische Verstärkung in Drehratensensoren, bei denen die Mitkoppelspannung mithilfe des Pilottonverfahrens bestimmt wird, möglich gemacht.To use the pilot tone method on a rotation rate sensor with parametric gain, the pilot tone method must be adapted. This in 1 The diagram shown is still to be used, but the form of the transfer function must be taken into account when choosing the ratio of the first and second input amplitudes. In particular, in contrast to the purely harmonic case, the approximation ϕ ₁ ≈ ϕ ₂ + π no longer applies to the phase shifts ϕ ₁ and ϕ _{2 of} the first and second pilot tone caused by the phase transfer function. In order to take into account both the influence of the amplitude transfer function and the phase transfer function, the amplitude ratio is determined by the dynamics given by equations (3) and (4) $$r\equiv \frac{{\mathrm{<figure-callout\; id="1"\; label="\alpha "\; filenames="DE102018218249A1\_0031.png"\; state="\{\{state\}\}">\alpha </figure-callout>}}_1}{{\alpha }_{\mathrm{2nd}}}=1+\frac{\mathrm{2nd}\lambda \left(Q_D^{\mathrm{2nd}}\left(16p^{\mathrm{2nd}}+{\lambda }^{\mathrm{2nd}}\right)-\mathrm{4th}\right)}{64Q_D^{\mathrm{2nd}}{p}^{\mathrm{3rd}}+\mathrm{4th}\lambda -16Q_D^{\mathrm{2nd}}{p}^{\mathrm{2nd}}\lambda -Q_D^{\mathrm{2nd}}{\lambda }^{\mathrm{3rd}}+\mathrm{4th}p\left(\mathrm{4th}+Q_D^{\mathrm{2nd}}{\lambda }^{\mathrm{2nd}}\right)}$$

fixed, being here $p=\frac{{\omega }_{cal}}{{\omega }_D}$

is. With this amplitude ratio, the output signal of the pilot tone process is at zero if and only if the positive feedback voltage is set such that δ = 0. This applies to every nonlinear stiffness parameter λ . This enables parametric amplification in yaw rate sensors, in which the positive feedback voltage is determined using the pilot tone method.

Figure list

• 1 shows schematically the signal chain of the pilot tone process.
• 2nd shows in the course of the gain factor G depending on the non-linear stiffness parameter λ for three different values of the frequency detuning δ .
• 3a and 3b show the course of the amplitude and phase of the detection mode depending on the frequency detuning δ for four different values of the stiffness parameter λ .

Embodiments of the invention

In 1 the signal chain of the pilot tone process is shown schematically. The signal consisting of two pilot tones α ₁ cos (ω ₁ t) + α ₂ cos (ω ₂ t) 10th With input amplitudes α ₁ and α ₂ , the detection mode (characterized by the transfer function 11 ), where the frequency ω ₁ = ω _A - ω _{cal of} the first pilot tone below and the second frequency ω ₂ = ω _A + ω _cal above the drive frequency ω _{A is} selected. The resulting response signal is demodulated 12th with cos (ω ₁ t) + cos (ω ₂ t) and a low pass filter 13 isolating the system's response to pilot frequencies ω ₁ and ω ₂ . The first and second amplitudes of the response signal belonging to ω ₁ and ω ₂ go into the output signal 14 on the basis of which the control system regulates the feedforward structure. The output signal is such that it disappears if and only if the two response amplitudes are the same. In the pilot tone method according to the prior art, the ratio of the input amplitudes α ₁ and α _{2 is set} to one and the control carried out with it leads (to a very good approximation) to a disappearing frequency detuning. In the case of a parametrically amplified rotation rate sensor, in which the amplification is induced by a non-linear coupling between the drive and detection modes, this method leads to a significant frequency detuning. In the method according to the invention, the amplitude ratio is set as a function of the strength of the coupling, so that the modified method achieves precise frequency coordination between the drive and detection modes.

abgebildet. Als mathematisches Modell liegen dabei die Gleichungen (3) und (4) zugrunde. Der Gütefaktor wurde auf den Wert Q_D = 800 festgelegt. Auf der horizontalen Achse 1 ist der Wert des nichtlinearen Steifigkeitsparameters λ in der Kombination λQ_D/2 aufgetragen, d.h. die Position 1.0 entspricht dem Wert λ = 2/Q_D. Auf der vertikalen Achse 2 ist der Verstärkungsfaktor G aufgetragen und die Kurven 3a, 3b und 3c zeigen den Verlauf von G als Funktion von λQ_D/2 für die Werte $\frac{\delta }{2\pi }=0\text{ Hz},$

-10 Hz und -30 Hz. In allen drei Kurven 3a, 3b, 3c wächst der Verstärkungsfaktor mit steigendem λ monoton an und divergiert bei einem kritischen Schwellwert λ_crit . Für λ < λ_crit ist G > 1, wobei die Verstärkung erst mit Annährung an den kritischen Wert λ_crit erheblich größer als Eins wird. Der kritische Wert λ_crit verschiebt sich mit zunehmender Frequenzverstimmung δ nach rechts, d.h. für ein festes λ nimmt die Verstärkung mit zunehmender Frequenzverstimmung ab. Um eine möglichst hohe Verstärkung zu erreichen ist es deshalb erstrebenswert, die Frequenzverstimmung möglichst gering zu halten. Optimale Bedingungen, d.h. ein minimaler Wert λ_crit = 2/Q_D wird für eine verschwindende Frequenzverstimmung δ = 0 erreicht (Kurve 3a).In 2nd is the course of the gain factor G depending on the non-linear stiffness parameter λ for three different values of the frequency detuning $\delta ={\mathrm{<figure-callout\; id="1"\; label="\omega \; D"\; filenames="DE102018218249A1\_0031.png"\; state="\{\{state\}\}">\omega \; </figure-callout>}}_D\sqrt{1+\lambda }-{\omega }_{drive}$

pictured. Equations (3) and (4) are used as the mathematical model. The quality factor was set at Q _D = 800. On the horizontal axis 1 is the value of the nonlinear stiffness parameter λ in the combination λQ _D / 2 plotted, ie the position 1.0 corresponds to the value λ = 2 / Q _D. On the vertical axis 2nd is the gain factor G plotted and the curves 3a , 3b and 3c show the course of G as a function of λQ _D / 2 for the values $\frac{\delta }{\mathrm{2nd}\pi }=0\text{Hz},$

-10 Hz and -30 Hz. In all three curves 3a , 3b , 3c the gain factor increases monotonically with increasing λ and diverges at a critical threshold λ _crit . For λ <λ _crit is G > 1, whereby the reinforcement only with approximation to the critical value λ _crit becomes significantly larger than one. The critical value λ _crit shifts to the right with increasing frequency detuning δ, ie for a fixed λ the gain decreases with increasing frequency detuning. In order to achieve the highest possible amplification, it is therefore desirable to keep the frequency detuning as low as possible. Optimal conditions, ie a minimum value λ _crit = 2 / Q _D is achieved for a vanishing frequency _detuning δ = 0 (curve 3a ).

d.h. im Verhältnis zur Amplitude der treibenden Kraft F(t) aufgetragen. Die Kurve 6a entspricht dem Wert λ = 0, d.h. einem linearen Oszillator ohne parametrische Verstärkung. Die Kurven 6b, 6c, 6d entsprechen den Werten λQ_D/2 = 0.8, 0.9 und 0.98. Mit Annäherung an den kritischen Wert λ_crit = 2/Q_D (d.h. λQ_D/2 = 1) steigt die Höhe des Maximums immer stärker an, wobei bei jeder Kurve (d.h. bei einem festem Wert von λ) das Maximum und damit die größte Erhöhung der Amplitude für eine verschwindende Frequenzverstimmung δ = 0 erreicht wird. In 3b ist die zugehörige Phase der Detektionsmode dargestellt. Auf der horizontalen Achse 4 ist, wie in 3a die Frequenzverstimmung δ in der Kombination δ/2π aufgetragen, während auf der vertikalen Achse 7 die Phasenverschiebung Φ_D/2π zwischen der Schwingung der Detektionsmode und der treibenden Kraft aufgetragen ist. Die Kurve 8a entspricht dem Fall λ = 0 ohne parametrische Verstärkung und die Kurven 8b, 8c und 8d entsprechen den Werten λQ_D/2 = 0.8, 0.9 und 0.98. Es lässt sich zeigen, dass das konventionelle Pilottonverfahren zu einer signifikanten Frequenzverstimmung von $\delta =\frac{{\omega }_D\lambda }{4}$

führt. In der 3b ist der entsprechende Bereich 9 der Breite $\frac{{\omega }_D\lambda }{2}$

um den Wert δ = 0 herum eingezeichnet.In 3a the course of the amplitude of the detection mode is depicted as a function of the frequency detuning δ for four different values of the stiffness parameter λ. The mathematical model is based on equations (3) and (4), the detection mode being driven with an external force of the form F (t) = F _c sin (ω _drive t). The quality factor was set at Q _D = 800. On the horizontal axis 4th is the frequency detuning δ in the combination δ / 2π plotted on the vertical axis 5 is the detection amplitude a _D in the combination $a_D{\omega }_D^{\mathrm{2nd}}/F_c,$

ie plotted in relation to the amplitude of the driving force F (t). The curve 6a corresponds to the value λ = 0, ie a linear oscillator without parametric amplification. The curves 6b , 6c , 6d correspond to the values λQ _D / 2 = 0.8, 0.9 and 0.98. As the critical value λ _crit = 2 / Q _D (ie λQ _D / 2 = 1) approaches, the height of the maximum increases more and more, with the maximum and thus the largest for each curve (ie with a fixed value of λ) Increasing the amplitude for a vanishing frequency detuning δ = 0 is achieved. In 3b the associated phase of the detection mode is shown. On the horizontal axis 4th is like in 3a the frequency detuning δ in combination δ / 2π plotted while on the vertical axis 7 the phase shift Φ _D / 2π is plotted between the vibration of the detection mode and the driving force. The curve 8a corresponds to the case λ = 0 without parametric amplification and the curves 8b , 8c and 8d correspond to the values λQ _D / 2 = 0.8, 0.9 and 0.98. It can be shown that the conventional pilot tone method leads to a significant frequency detuning of $\delta =\frac{{\omega }_D\lambda }{\mathrm{4th}}$

leads. In the 3b is the corresponding area 9 the width $\frac{{\omega }_D\lambda }{\mathrm{2nd}}$

for value δ = 0 drawn in.

QUOTES INCLUDE IN THE DESCRIPTION

This list of documents listed by the applicant has been generated automatically and is only included for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Non-patent literature cited

• C. Ahn, S. Nitzan, E. Ng, V. Hong, Y. Yang, T. Kimbrell, D. Horsley and T. Kenny, "Encapsulated high frequency (235kHz), high-Q (100k) disk resonator gyroscope with electrostatic parametric pump, “Appl. Phys. Lett, Vol. 105, p. 243504, 2014 [0010]
• S. H. Nitzan, V. Zega, M. Li, C. H. Ahn, A. Corigliano, T. Kenny and D. Horsely, "Selfinduced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope," Sci. Rep., Vol. 5, p. 9036, 2015 [0010]

Claims (6)

Method for frequency tuning of a micromechanical component, the micromechanical component having an oscillatory structure, a drive structure, a detection structure, a coupling structure and a control system, wherein the drive structure is configured to excite a drive mode of the oscillatable structure, the detection structure being used to detect a detection mode of the oscillatory structure Structure is configured, wherein the vibratable structure with respect to the detection mode has a spring constant that increases or decreases due to a coupling between the drive mode and the detection mode with a deflection of the drive mode, the positive feedback structure being configured to increase or decrease the natural frequency of the detection mode, characterized in that that the method comprises the following steps: excitation of the drive mode with a drive frequency by the drive structure, excitation of the detectors Onsmode with a first and second pilot tone by the control system, wherein the first pilot tone has a first input amplitude and a first pilot frequency and the second pilot tone has a second input amplitude and a second pilot frequency, the first pilot frequency being less than the drive frequency and the second pilot frequency being greater when the drive frequency and the ratio of the first and second input amplitude is set as a function of the strength of the coupling between the drive mode and the detection mode, - measurement of a time-dependent deflection of the excited detection mode by the detection system, - determination of a first response amplitude at the first pilot frequency and one second response amplitude at the second pilot frequency by the control system, the first and second response amplitudes being determined on the basis of the time-dependent deflection of the excited detection mode, - regulation of the natural frequency of the detector Ionsmode over the coupling structure by the control system, the control being carried out such that the first response amplitude is equal to the second response amplitude. Procedure according to Claim 1 , with a quadrature compensation of the detection mode by the control system. Method according to one of the preceding claims, wherein the ratio of the first and second input amplitude is set as a function of the difference between the first pilot frequency and the second pilot frequency. Method according to one of the preceding claims, wherein the ratio of the first and second input amplitude is set as a function of the drive frequency. Method according to one of the preceding claims, wherein the ratio of the first and second input amplitude is set as a function of the quality factor of the detection mode. Micromechanical component, comprising a vibratable structure, a drive structure, a detection structure, a feedforward structure and a control system, the drive structure being configured to excite a drive mode of the vibratable structure, the detection structure being configured to detect a detection mode of the vibratable structure, the vibratable structure has a spring constant with respect to the detection mode, which increases or decreases due to a coupling between the drive mode and the detection mode with a deflection of the drive mode, the positive feedback structure being configured to increase or decrease the spring constant of the detection mode, characterized in that the drive structure, the detection structure and the Control system for carrying out a method for frequency tuning according to one of the Claims 1 to 5 are configured.

Images