Q-controlled microresonators and tunable electronic filters using such resonators

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CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to a co-pending, commonly-owned application entitled "Microelectromechanical Signal Processors," Ser. No. 07/990,582, filed on Dec. 11, 1992. The entire disclosure of this application is hereby incorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to resonant microstructures, and more particularly to Q-control for resonant microstructures and electronic filters using such microstructures.

The need for high-frequency bandpass filters with high selectivity for telecommunication systems has stimulated interest in integrated versions of such filters wherein entire systems may be integrated onto a single silicon chip. Examples of systems requiring these filters include radio-frequency (RF) receiver systems, mobile phone networks, and satellite communication systems.

Previously, intermediate frequency (IF) filtering in frequency modulated (FM) receivers has been performed at 10.7 Mega-Hertz (MHz) IF frequency, using highly selective inductive-capacitance (LC) ceramic or crystal filters. Recently, integrated versions using integrated circuit (IC) switched-capacitor techniques have been attempted. However, designs based upon a coupled biquad filter architectures suffer from dynamic range reduction introduced when attempting high-Q operational simulation of LC stages. (Q is a figure of merit equal to reactance divided by resistance. The Q of a system determines the rate of decay of stored energy. ) Modulation filtering techniques, such as N-path designs, suffer from the generation of extraneous signals, such as image and clock components inside the signal band, resulting from the remodulation process.

Recent advances in micromachining offer another analog, high frequency, high-Q, tunable integrated filter technology that can enhance filter performance over that of previous integrated versions while maintaining design characteristics appropriate for bulk fabrication in very large-scale integrated (VLSI) systems. Specifically, micromachined mechanical resonators or resonant microstructures may be used. These microresonators are integrated electromechanical devices with frequency selectivity superior to integrated resistance-capacitance (RC) active filtering techniques. Using integrated micromechanical resonators, which have Q-factors in the tens of thousands, microelectromechanical filters with selectivity comparable to macroscopic mechanical and crystal filters may be fabricated on a chip.

Since the passband shape of these filter designs depends strongly on the Q of the constituent resonators, a precise technique for controlling resonator Q is required to optimize the filter passband. Such a Q-control technique would be most convenient and effective if the Q was controllable through a single voltage or an element value, e.g., a resistor, and if the controlled value of Q was independent of the original Q.

An object of the present invention is thus to provide feedback techniques for precise control of the Q-factor of a micromechanical resonator.

Another object of the present invention is to provide very high Q microelectromechanical filters constructed of Q-controlled microresonator biquads in biquad filter architectures. In addition, the invention provides a means for passband correction of spring-coupled or parallel micromechanical resonators via control over the Q-factor of the constituent resonators.

Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the claims.

SUMMARY OF THE INVENTION

The present invention is directed to a resonator structure. The resonator structure comprises a first electrode at which an input signal may be applied and a second electrode at which an output signal may be sensed. The resonator structure further includes a feedback means for applying the output signal to the first electrode for controlling the Q of the resonator structure.

The equivalent circuit series resistance (R.sub.x) of the resonator of the present invention is proportional to the inverse of the Q of the resonator. As such, the controlled value of Q is independent of the original Q of the resonator. Rather, it is dependent only on the control voltage (V.sub.Q) or some other controlling factor such as resistance values.

Additionally, the gain of the resonator (v.sub.0 /v.sub.i) is equal to the number of input fingers divided by the number of feedback fingers. This is advantageous in that it offers very precise gain values. This enables construction of bandpass biquads with precisely settable gains. Also, the gain will stay constant as the Q is changed.

Dimensions of a microresonator of the present invention may be: a length between about 5 microns(.mu.m) and 1000 .mu.m, a width between about 5 .mu.m and 100 .mu.m, and a thickness from between about 0.1 and 100 .mu.m.

High-Q tunable electronic filters based upon the Q-controlled microresonators of the present invention are suitable for batch fabrication using standard complementary metal-oxide semiconductor (CMOS) integrated circuit and micromachining technologies. The Q-controlled microresonators may serve as adjustable biquad stages in various filter architectures such as coupled (or cascaded) biquad, follow-the-leader feedback (FLF), or other multiple-loop feedback techniques. Frequency and bandwidth are independently voltage-controllable. This permits adaptive signal processing.

Noise analysis determines that the dynamic range of a proposed high-Q filter is much higher than that of its high-Q active RC counterparts, i.e., switched-capacitor MOSFET-C, and g.sub.m -C filters. Specifically, a dynamic range in excess of 90 decibels (dB) is predicted for a filter centered at 10.7 MegaHertz (MHz) with a bandwidth of 56 KiloHertz (kHz).

With the resonators of the present invention, temperature insensitivity can be achieved through micro-oven control, which, on a micron scale, provides orders of magnitude improvement in power dissipation and thermal time constant over equivalent macroscopic methods.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute a part of the specification, schematically illustrate a preferred embodiment of the invention and, together with a general description given above and the detailed description of the preferred embodiment given below, will serve to explain the principles of the invention.

FIG. 1A is a schematic representation of a Q-control scheme for a three-port electrostatic-comb driven microresonator.

FIG. 1B is a schematic cross-section along lines 1B--1B of FIG. 1A.

FIG. 2 is a system block diagram for the circuit of FIG. 1A.

FIG. 3 is a schematic representation of a Q-control scheme for a two-port microresonator.

FIG. 4 is a system block diagram for the circuit of FIG. 3.

FIG. 5 is a schematic representation of a scheme for raising the Q of a three-port microresonator.

FIG. 6 is an equivalent circuit diagram for a three-port microresonator biased and excited as shown in FIG. 1A.

FIG. 7 is a schematic representation of a balanced Q-control scheme for a four-port microresonator using two balanced amplifiers (one of them transimpedance) and metal oxide semiconductor (MOS) resistors.

FIG. 8 is a schematic representation of a balanced Q-control scheme for a six-port microresonator using one balanced transimpedance amplifier.

FIG. 9 is a schematic representation of a Q-controlled microresonator filter using a balanced FLF architecture.

FIG. 10A is a system block diagram for a general FLF filter.

FIG. 10B is a single-ended noise block diagram for the circuit of FIG. 3 or 6.

FIG. 11 is a graphical representation of simulated responses for the filter of FIG. 9.

FIG. 12 is a graphical representation of the measured transconductance spectra of the embodiment of FIG. 1A using different values of R.sub.amp and demonstrating control of the Q-factor through control of

FIG. 13 is a graphical representation of the transconductance spectra for the microresonator of FIG. 1A subjected to Q-control with R.sub.amp =3.3 mega-ohms and with varying ambient pressure.

FIG. 14A is a schematic representation of a microresonator including sloped drive fingers, which allow resonance frequency-pulling.

FIG. 14B is an enlarged schematic representation of the relationship between the sloped and straight drive fingers.

FIG. 15A is a schematic representation of a microresonator including a third polylayer to introduce a nonlinear variation in the voltage-to-force transfer function of the resonator and thus allow frequency-pulling.

FIG. 15B is a view along lines 15B--15B of FIG. 15A.

FIG. 16A is a schematic representation of a microresonator including spring-pulling electrodes for frequency tuning.

FIG. 16B is a graphical representation of resonance frequency versus frequency pulling voltage for the microresonator of FIG. 16A.

FIG. 17A is a schematic representation of feedback control circuitry for a micro-oven controlled resonator fabricated on a microplatform for thermal and mechanical isolation.

FIG. 17B is a scanning electron micrograph of a resonator fabricated on top of a thermally-isolated microplatform.

FIG. 18 is a circuit diagram of a high gain transresistance amplifier which may be used in the present invention.

FIGS. 19A and 19B are graphical representations of filter passband correction.

FIG. 20 is a circuit diagram showing the implementation of passband correction for a parallel microresonator filter.

FIG. 21 is a circuit diagram for Q control of a resonator structure with a single port.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be described in terms of a number of different embodiments. It is directed to Q-control for microresonators. These resonators may be used to build very high Q microelectromechanical filters. The filters may be constructed of coupled, Q-controlled microresonator biquads, spring-coupled resonators or resonators electrically connected in parallel. Spring-coupled resonators and resonators electrically connected in parallel are described in the above-identified, co-pending application entitled "Microelectromechanical Signal Processors," which has been incorporated by reference.

A basic Q-control architecture for a microresonator 20 is shown in FIG. 1. The microresonator is of the type shown in U. S. Pat. No. 5,025,346, issued Jun. 18, 1991, which is hereby incorporated by reference.

The resonator shown in U. S. Pat. No. 5,025,346 is preferred in the context of the present invention. However, the principles of the present invention equally apply to other types of resonators, and the Q-control scheme discussed herein may be used with those resonators. Also the filter architectures, frequency-pulling schemes and micro-oven schemes discussed below may be applied to these other types of resonators. Such resonators include, but are not limited to, those which use piezoelectric, piezoresistive, parallel-plate electrostatic, or magnetic drive and sense, and to resonators with arbitrary geometries, such as cantilevers or double-ended tuning forks.

As shown in FIG. 1, resonator 20 has three ports, comprising a drive electrode 22, a sense electrode 23, and a feedback electrode 24. The resonator is driven electrostatically by the drive electrode and capacitive motional current is sensed at the sense electrode. Signals are fed back to the microresonator via the feedback electrode.

The electrodes comprise interdigitated finger (comb) structures 25 and 27. The fingers 25 are stationary, being anchored to a substrate 29a, which may be a silicon wafer substrate, or anchored to passivation layers, which may be a nitride layer 29b over an oxide layer 29c, over the substrate. The darkly shaded region 28 represents the anchor point for the drive electrode 22 and its associated fingers 25. The fingers 27 are attached to a suspended, movable shuttle 27a; thus, they are movable. The shuttle 27a and fingers 27 are spaced above the substrate, and are allowed to move laterally relative to the substrate overlayers and stationary fingers 25. A folded-beam suspension arrangement, represented generally by reference numeral 30, allows shuttle 27a and attached fingers 27 to move.

The folded beam suspension 30 comprises folded beams 31a, 31b, 31c, and 31d, and truss support beam 31f, all of which are suspended above the substrate 29a and associated overlayers 29b and 29c. Motivations for this truss suspension are its large compliance and its capability for relief of built-in residual strains in the structural film. The cantilever beams 31b and 31d are anchored at one end to a ground plane 29d, which is fabricated over the substrate 29a and substrate overlayers 29b and 29c, near a center point 31e (a darkly shaded region) and attached at the other end to the folding truss beam 31f. Cantilever beams 31a and 31c are attached at one end to the folding truss beam 31f and at the other to the shuttle 27a. The folded beam suspension 30 allows expansion or contraction of the four beams along the y-axis, increasing the linear range of operation of the resonator 20. The folded beam suspension 30; comprising 32a, 32b, 32c , 32d, and 32f, is anchored through beams 32b and 32c to ground plane 29d and/or overlayers 29b and 29c at location 32e, and the suspension operates like beams 31a-31f.

The long effective support length of beams 31a-31d and 32a-32d result in a highly compliant suspension for movable fingers 27 of the drive, sense, and feedback electrodes. In an alternate arrangement, the substrate overlayers may be eliminated. The anchor points would then be formed on the substrate, and the substrate would serve as the ground plane.

The motion of the movable fingers is sensed by detecting the motional current through the time-varying interdigitated finger capacitor formed by the movable and stationary fingers of the sense electrode 23 with a direct current (dc) bias voltage V.sub.P applied to ground plane 29b, which is attached to the shuttle 27a and movable fingers 27 through anchor points 31e and 32e. The driving force F.sub.x and the output sensitivity are proportional to the variation of the comb capacitance C with the lateral displacement x, .differential.c/.differential.x, of the structure.

A key feature of the electrostatic-comb drive is that .differential.c/.differential.x is a constant, independent of the displacement x, so long as x is less than the finger overlap. Note that .differential.c/.differential.x for a given port is a function of the number of overlaps between movable and stationary fingers 27 and 25, respectively, of the port in question. Thus, it can be different for drive port or drive electrode 28, sense port or sense electrode 23, and feedback port or feedback electrode 24. To distinguish these values, (.differential.c/.differential.x).sub.d, (.differential.c/.differential.x).sub.s, and (.differential.c/.differential.x).sub.fb may be used for the drive, sense, and feedback ports, respectively.

At sense electrode 23, harmonic motion of the structure results in a sense current I.sub.s which is represented by: ##EQU1## At drive electrode 22, the static displacement is a function of drive voltage v.sub.D given by: ##EQU2## where F.sub.x is the electrostatic force in the x direction and k.sub.sys is the system spring constant.

For a drive voltage V.sub.D (t)=V.sub.P +V.sub.d sin (.omega.t) the time derivative of x is ##EQU3## where v.sub.d is the amplitude of the input ac signal, V.sub.P is the previously-mentioned dc-bias applied to the resonator, and where the fact that (.differential.c/.differential.x).sub.d is a constant for the inter-digitated-finger capacitor 23 or 24 is used. The second-harmonic term on the right-hand side of Equation (3) is negligible if v.sub.d<<V.sub.P. Furthermore, if a push-pull (differential) drive is used, this term results in a common-mode force and is cancelled to the first order. At mechanical resonance, the magnitude of the linear term in Equation (3) is multiplied by the Q-factor, from which it follows that the magnitude of the transfer function T(j.omega..sub.r)=X/v.sub.D relating the phasor displacement X to phasor drive voltage V.sub.d at the resonant frequency .omega..sub.r is: ##EQU4##

The transconductance of the resonant structure is defined by Y(j.omega.)=I.sub.s /V.sub.d. Its magnitude at resonance can be found by substitution of Equation (4) into the phasor form of Equation (1): ##EQU5##

Planar electrode or ground plane 29d (FIGS. 1A and 1B) can be grounded or set to a dc potential in order to minimize parasitic capacitive coupling between the drive, feedback and sense ports. An additional function of this electrode is to suppress the excitation of undesired modes of the structure.

As noted, the motional current output from the resonator is electronically sensed by means of sense electrode 23. The motional current is applied to a transimpedence or transresistance amplifier 34, where it is converted to a voltage v.sub.o. The voltage v.sub.o is fed back to the microresonator via feedback electrode 24. The drive voltage v.sub.d is applied to the resonator via drive electrode 22. The microresonator sums the drive voltage and the negative feedback signal, v.sub.fb =v.sub.o, closing the loop and reducing its own original Q. The Q of the microresonator is effectively controlled by the gain of amplifier 34, which can be made voltage controllable through the voltage V.sub.Q.

The equivalent system block diagram for the architecture of FIG. 1A is shown in FIG. 2, where Y.sub.d..sub.s (j.omega.) and Y.sub.fb..sub.s (j.omega.) correspond to the microresonator drive port-to-output and feedback port-to-output transfer functions, respectively. Using FIG. 2, and modelling the resonator n port to m port transfer functions Y.sub.m..sub.n (j.omega.) with the form ##EQU6## where R.sub.xm..sub.n is the equivalent series resistance of the resonator from any port m to any port n, and .omega..sub.0 is the natural resonance frequency. The equivalent series resistance is discussed below in relation to FIG. 5. In the equations that follow, any port m or n may be d, s, or fb, corresponding to drive, sense, or feedback ports, respectively. Direct analysis of FIG. 2 yields ##EQU7## where R.sub.amp is the value of the transresistance or transimpedence of amplifier 34 and where ##EQU8## is the controlled value of the Q-factor. For large loop gain, the gain of Equation (7) reduces to (R.sub.xfb.s /R.sub.xd.s), which, as will be seen, is determined by the number of input and feedback fingers, and stays constant as Q is varied. The Q can be changed, as noted, by adjusting the gain of amplifier 34 through the voltage V.sub.Q.

A schematic of the Q-control architecture for a two-port resonator 40 is shown in FIG. 3. Although FIG. 3 shows a resonator with equal numbers of drive and sense fingers, the number of fingers need not be equal. This resonator includes only a drive electrode 22 and a sense electrode 23. A summing amplifier 42 is provided to sum the input and feedback signals v.sub.d and v.sub.o, respectively, which in FIG. 1A were summed by the multi-port resonator itself. The resistances R.sub.k and R.sub.f are variable. These resistances and R.sub.sum provide gain factors for signals applied to amplifier 42. Thus, they directly determine the Q and gain of the Q-control circuit.

FIG. 4 shows the single-ended system block diagram equivalent of the circuit of FIG. 3. Referring to FIGS. 3 and 4, gain factor ##EQU9## and gain factor ##EQU10## Using FIG. 4, and modeling the resonator with the transfer function ##EQU11## where R.sub.xd.s is the equivalent drive-to-sense series resistance of the resonator. Direct analysis yields ##EQU12## is the controlled value of the Q-factor. For large loop gain, the gain of Equation (10) reduces to ##EQU13## which in turn reduces to ##EQU14## In addition, Q' can be varied by changing R.sub.f, with R.sub.k tracking this change.

The discussion of Q-control has so far concentrated on the lowering of Q through the application of a negative feedback voltage. By using a positive feedback, however, the Q of a resonator can be raised. Positive feedback implementations of Q-control can be realized by merely changing the amplification of amplifier 34 from positive to negative on the architectures of FIGS. 1A and 3.

Alternatively, and more conveniently, positive feedback may be obtained by interchanging finger connections as shown in FIG. 5. Specifically, the connections to microresonator 20 of FIG. 1A are reversed so sense electrode 23 becomes drive electrode 22' in the embodiment of FIG. 5. Similarly, drive electrode 22 of FIG. 1A becomes sense electrode 23', and the feedback electrode 24' is at the input or drive side of microresonator 20 where the input voltage v.sub.i is applied. The equation for controlled Q under positive feedback is: ##EQU15##

To design for a specific Q and voltage gain ##EQU16## for the architecture of FIG. 1A, the equivalent drive-to-sense and feedback-to-sense series resistances, R.sub.xd.s and R.sub.xfb..sub.s, respectively, of the resonator are required. To calculate these resistances, reference may be made to an equivalent circuit for a three-port micromechanical resonator. The equivalent circuit, as shown in FIG. 6, is biased and excited as in the circuit of FIG. 1A. The equations for the circuit elements are as follows: ##EQU17## where n corresponds to the port of the resonator (drive, sense, or feedback) in question, C.sub.on is the overlap capacitance across the motionless shuttle and electrode fingers, and the .PHI.'s represent multiplication factors for the current-controlled current sources shown in the figure. Typical element values for high-Q (Q=50,000) operation of a microresonator are f.sub.0 =20 kHz, C.sub.0 =15 fF, C.sub.x =0.3 fF, L.sub.x =100 KH, and R.sub.x =500K .OMEGA..

The equivalent drive-to-sense resistance of the microresonator may be calculated from the following equation: ##EQU18## Driving the equivalent circuit of FIG. 6 at the input port d and grounding the other ports, the output motional current i.sub.s at resonance is: ##EQU19## Applying Equation (15) to (14), gives: ##EQU20## A similar analysis yields ##EQU21## To maximize the range of Q-control afforded by a given amplifier 34, the loop gain of the circuit, A=(R.sub.amp /R.sub.xfb..sub.s), should have a wide range. Thus, R.sub.xfb..sub.s should be minimized, which in turn requires that R.sub.xfb be minimized and .PHI..sub.sfb be maximized. Reduction in R.sub.xfb can be achieved by increasing the number of feedback fingers, decreasing the gaps between these fingers, and increasing finger thickness. .PHI..sub.sfb is increased with similar modifications to the output fingers.

The number of input and feedback fingers also determines the gain of the Q-control circuit. Using Equation (17) and (18), the equation for gain at resonance is: ##EQU22## where N.sub.d and N.sub.fb are the number of input and feedback fingers, respectively. The last equality assumes identical finger gaps and thicknesses for both ports. Thus, the gain is determined by resonator geometry and is independent of variables which determine the controlled Q.

FIG. 3 presented a schematic of Q-control using a two-port microresonator, two amplifiers, and linear resistors. In order to implement variability of Q through voltage control, metal oxide semiconductor resistors (MOS) can replace the linear resistors of FIG. 3. The value of resistance realized by an MOS resistor can be varied through variation of the gate voltage of such devices. However, MOS resistors suffer from the drawback that they are less linear than their passive counterparts. In order to linearize MOS resistors, a balanced architecture must be used.

Such a balanced architecture is shown in FIG. 7, which illustrates Q-control using MOS resistors and a four-port microresonator 50. The microresonator 50 is similar in construction to microresonator 20 in that it includes movable and stationary, interdigitated fingers forming differential drive and sense electrodes 52 and 54, respectively. As in the embodiment of FIG. 1A, stationary electrode fingers 55 are anchored to the overlayers 29b and 29c (see FIG. 1B) at the darkly shaded regions or anchor points 56. The movable fingers 57 are suspended above the ground plane by means of the folded beam suspension arrangement 58.

Drive voltages v.sub.i(-) and v.sub.i(+) are applied to the drive electrodes. The output voltages v.sub.o-(-) and v.sub.0+) represent amplifications of the signals sensed by sense electrodes 54. Since the shuttle and its fingers are electrically connected to the ground plane, they are at the same voltage, V.sub.P, as the ground plane.

The architecture of FIG. 7 also utilizes metal oxide semiconductor (MOS) resistors M.sub.Q1, M.sub.Q2, M.sub.K1, M.sub.K2, M.sub.sum1, and M.sub.sum2. Such resistors are normally nonlinear, unless operated in a fully balanced architecture, such as that depicted in FIG. 7. Fully balanced operation minimizes the even ordered harmonics of the MOS resistor voltage-to-current response, thus greatly reducing the total nonlinearity in such devices. In FIG. 7, MOS resistors M.sub.Q1 and M.sub.Q2 serve to feed back the output signal v.sub.o with the appropriate gain factor f=R.sub.sum /R.sub.Qn =(W/L).sub.Qn /(W/L).sub.sumn, (see FIG. 4) where n is either 1 or 2, to the summing amplifier composed of balanced operational amplifier 62 and shunt-shunt MOS resistors M.sub.sum1 and M.sub.sum2. Note that gain factor f is determined by a ratio of MOS W/L's, which are the width over length ratios, and thus can be accurately set to a 0.2% or better tolerance using integrated circuit processes. MOS resistors M.sub.K1 and M.sub.K2 direct the input signal v.sub. i with the appropriate gain factor K=R.sub.sumn /R.sub.Kn =(W/L).sub.Kn /(W/L).sub.sumn to the summing amplifier to be summed with the negative feedback signal from MOS resistors M.sub.Q1 and M.sub.Q2. This summation completes the feedback loop for Q-control as in the block diagram for the equivalent single-ended version given in FIG. 3. The equations dictating Q-control for the balanced version of FIG. 7 are similar to those for FIG. 3, Equations (9) through (11), except for changes in the drive-to-sense resistance R.sub.xd.s, which must now account for the four-port nature of the resonator, and can be easily obtained using an analysis similar to that of Equations (13) through (18).

The circuitry further includes a balanced transimpedance or transresistance amplifier 60, which may or may not be variable. As shown, it is voltage-controllable via V.sub.R.

For large loop gain, the gain in the scheme of FIG. 7 is determined by a ratio of MOS resistor gate width over gate length ratios ##EQU23## specifically ##EQU24## wherein K=R.sub.sum /R.sub.k =(W/L).sub.Kn /(W/L).sub.sumn and f=R.sub.sum /R.sub.Q =(W/L).sub.Qn /(W/L).sub.sumn. The gain of the stage in FIG. 7 stays constant with changing Q, since the channel resistances of M.sub.Q and M.sub.K track with V.sub.Q.

Any Q may be realized using the embodiment discussed herein; thus, any bandpass biquad transfer function may be implemented. Since both the Q and gain of the stage of the embodiment of FIG. 7 depend mainly on ratios