Characterization and driving method based on the second harmonic, which is enhancing the quality factor and reducing the feedthrough current in varying gap electrostatic MEMS resonators

Abstract

A method of an open loop characterization of an electrostatic MEMS based resonator with a varying gap, the method including: converting, via a trans-impedance amplifier circuit, an output current signal of the resonator into a voltage; multiplying the output current signal converted into the voltage, by means of a multiplier circuit, with an AC signal or with a different signal at a frequency of the resonator and carrying a second harmonic signal to a main tone; and measuring a frequency response of a signal cleared of frequencies apart from the main tone using a network analyzer.

Claims

1. A method of an open loop characterization of an electrostatic MEMS based resonator with a varying gap, the method comprising: converting, via a trans-impedance amplifier circuit, an output current signal of the resonator into a voltage; multiplying the output current signal converted into-the voltage, by means of a multiplier circuit, with an AC signal or with a different signal at a frequency of the resonator and carrying a second harmonic signal to a main tone; and measuring a frequency response of a signal cleared of frequencies apart from the main tone using a network analyzer.

2. A method for closed loop operation (drive) of an electrostatic MEMS based resonator with a varying gap, the method comprising: converting an output current signal of the resonator into a voltage via a trans-impedance amplifier circuit; multiplying the output current signal converted into the voltage, by means of a multiplier circuit, with an AC signal or with a different signal at a frequency of the resonator and obtaining a second harmonic signal to a main tone; eliminating frequencies apart from the main tone of the resonator of the multiplied signal with a frequency eliminator circuit to form a clear signal; adjusting gain and phase values of the clear signal by using an amplifier to form an amplified signal; and feeding back the amplified signal to a resonator drive electrode.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Below, the figures that have been prepared to further describe the characterization/drive method based on a second harmonic reading that reduces feedthrough current and increases the quality factor in electrostatic MEMS resonators that has been developed by means of this invention are described.

(2) FIG. 1 shows a mechanical model of a resonator;

(3) FIG. 2 shows a schematic view of the electrostatic varying gap MEMS resonator;

(4) FIG. 3 shows a diagram showing the open loop characterization of the electrostatic varying gap MEMS based resonator structures;

(5) FIG. 4 shows a diagram showing the closed loop operation of electrostatic varying gap MEMS based resonator structures;

(6) FIG. 5 shows effect of the capacitive feedthrough currents to the proposed and present characterization methods;

(7) FIG. 6 shows resonance simulation results carried out in air and water medium using the present and proposed characterization methods; and

(8) FIG. 7 shows resonance measurements carried out with the traditional method and our method: The information that has not been processed (a) is shown and the information relating to the fault currents obtained by means of a computer (b) is shown.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(9) In this detailed description, the novelty provided by the invention is described with non-limiting examples which should not be deemed to limit the scope of the invention but which are rather used to further explain the invention. The characterization/drive method, operation, its aspects and aims based on a second harmonic reading, which reduces feedthrough current and increases the quality factor in electrostatic MEMS resonators (1) is described below in detail.

(10) The parts in the figures have each been numbered and the references of each number has been listed below. 1. Resonator 2. Spring, (k) 3. Damping, (B) 4. Moveable proof mass, (m) 5. DC polarization electrode 6. Drive electrode 7. Sense electrode 8. Varying gaps 9. Trans-impedance amplifier 10. Mixer 11. Network analyzer 12. High harmonic elimination circuit 13. Phase and gain regulation amplifier

(11) Electrostatic varying gap MEMS based resonator structures (1) are used as transducers, which convert input voltage into output current. In FIG. 1, the mechanical modeling of a typical resonator has been shown and in FIG. 2, the diagram of the electrostatic varying gap MEMS based resonator structure has been shown. The AC voltage applied to the input electrode (6) causes generation of an electrostatic force by means of the DC voltage applied from the DC polarization electrode (5) to the moveable proof mass (4). The gap (8) of the capacitor located between the sense electrode (7) and the moveable proof mass (4) which starts moving by means of this force is changed and this in turn leads to the generation of an electric current. The forces generated in varying gap resonators (1) also comprise other harmonic elements; however, by means of the bandpass structure of the resonator, the effect of higher harmonic elements will not influence motion. As the relationship between the change of the capacitance and the change of gap during the conversion of motion into current is nonlinear, the output current comprises other harmonic components besides drive frequency (main tone).

(12) Two new methods have been proposed within the scope of the invention, which are the open loop characterization method of electrostatic variable spacing MEMS based resonator structures and the closed loop driving method of electrostatic variable spacing MEMS based resonator structures.

(13) In the open loop characterization method of electrostatic varying gap MEMS resonator structures (FIG. 3), the second harmonic component of the output current is used for resonator characterization. The output current is converted into voltage using a trans-impedance amplifier (9).

(14) The output voltage obtained is multiplied with another signal having the same frequency or with the input signal using a mixer (10). Following this multiplication, the main tone is transferred to DC and 2nd harmonic frequencies, and the 2nd harmonic tone is transferred to the main tone and 3rd harmonic frequencies. By this means, the second harmonic component in the output current can be examined at the main tone frequency.

(15) As the capacitive (or resistive) feedthrough current is formed on drive voltage due to the parasitic capacitance, it is at the same frequency with the main tone. This method converts the second harmonic component, which comprises less parasitic current of the output current into main tone, and the main tone output of the resonator, which carries the feedthrough current is conveyed to other harmonics and therefore these are eliminated.

(16) The closed loop driving method of electrostatic variable spacing MEMS based resonator structures (FIG. 4) enables the resonator structures to self-oscillate. Closed loop driving is another method, which enables to reach resonance frequency. In this method the voltage at the output of the mixer (10) (output signal) is filtered with a higher harmonic elimination circuit (12), and the frequencies beside the resonance frequency (main tone) of the signal are also eliminated. It is required for the gain of the system at resonance frequency to be at least 1 and the phase response to be zero by means of the amplifier circuits (13) that regulate phase and gain, in order to meet the Barkhausen criteria. After this condition is provided, the system continues to oscillate at the resonance frequency. The resonance frequency of the system can be detected by tracking the signal that drives the resonator with a frequency meter.

(17) The functions of the electronic circuit components used in the application of the two new methods have been described below.

(18) Trans-impedance amplifier is an electronic circuit, which converts by means of a feedback resistance the input current into output voltage. The voltage/current gain is determined by resistance values.

(19) The mixer (e.g. voltage mixer), is an electronic circuit, which multiplies the two input signals. This is used in order to multiply the AC voltage or another signal having the same frequency that is used to drive the resonator with the output voltage of the current voltage converter.

(20) The network analyzer is a device that is used in order to determine the open loop characteristic of the system. The output voltage of the network analyzer is applied to the open loop input of the system, the open loop output of the system, is connected to the network analyzer input. The network analyzer applies voltages at the desired frequencies and the desired magnitudes and the device obtains the magnitude and phase response of the system by checking the phase and the magnitude in accordance with the voltage applied to the system output voltage. By this means in resonance systems, the device provides resonance frequency and quality factor information.

(21) The higher harmonic elimination circuit eliminates the high frequency components of the input signal using various methods. The most frequently used method is filter structures; however, it is possible to design special circuits for each application.

(22) As can be seen in FIG. 5, the dominant feedthrough current in the present characterization method corrupts the resonance characteristics; however, with the proposed method, the resonance characteristics in high damping coefficient mediums such as air and water can be obtained.

(23) As it can be seen in FIG. 6, the simulations carried out in water and air mediums according to the proposed method, provides higher resonance peaks when compared with the quality factors obtained from the present system.

(24) In FIG. 7A and FIG. 7B, the characteristics, which we have observed by testing the same resonator, has been given. In FIG. 7A, reduction in the feedthrough current has been shown. In the characterization carried out with the traditional method, 0.2 dB resonance peak has been obtained; however, when our novel method is used, the magnitude of this peak has been increased to 6 dB. When the quality factor measurement is carried out, as it can be seen in FIG. 7B, the quality factor that was calculated to be 821 when the traditional method was used has increased to 1363 when our method was used. These results also show that compliance with the simulations is obtained.