Abstract:
A circuit component has an elastically deformable first structure, a second structure, and a support structure coupling the first and second structures, wherein the first structure can be variably deformed in response to a variable force, to provide either a variable capacitor or a variable tank circuit having a variable capacitor and an inductor. In one particular embodiment, a piezoelectric element is laminated to the surface of the first elastically deformable structure thereby providing the capability to deform the first structure. A method of making a circuit component includes forming an elastically deformable first structure, forming a second structure, and joining the first and second structures, to provide either a variable capacitor or a variable tank circuit having a variable capacitor and an inductor.

Description:
PRIORITY CLAIM 
       [0001]    This is a Continuation Application of U.S. patent application Ser. No. 11/392,980, filed on Mar. 28, 2006, and entitled, “A Variable Electrical Circuit Component.” 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates generally to electronic circuit components, and more particularly to variable capacitors and variably tunable tank circuits. 
       BACKGROUND OF THE INVENTION 
       [0003]    Many high frequency electronic systems benefit from the use of tunable passive elements such as capacitors and resonators. However, the performance of these tunable elements is typically limited by linearity, intermodulation products, loss and power handling. For example, a varactor diode is commonly used to provide a variable capacitance, however, a varactor often suffers from a limited tuning range (20%), high loss, poor intermodulation performance, and limited power handling. In other circuits, ferroelectric devices are used as tuning elements in place of varactor diodes. In yet other instances, microelectromechanical variable capacitors are used as tuning elements. However, all of these techniques suffer from poor linearity, which is an especially relevant constraint under high RF signal power conditions. 
         [0004]    As is known, resonators with a variable resonant frequency can be constructed by assembling discrete variable capacitor and inductor elements. However, these resonant circuits typically suffer from a poor quality factor (Q), resulting in diminished narrowband performance such as increased insertion loss in the case of a filter. It is desirable to construct a resonant cavity wherein the unloaded Q is very high, thus allowing the implementation of a low insertion-loss narrowband tunable filter, or a low-phase noise tunable oscillator. Generally speaking, the quality factor is limited by the Q of the discrete elements that comprise a circuit. Losses in either an inductor element or a capacitor element will have the effect of reducing the overall system Q. A circuit design which minimizes the losses associated with these reactive elements, and minimizes the interconnection and parasitic losses is very desirable. 
         [0005]    Given the breadth of applications for tunable passive elements such as capacitors, inductors and resonantors, it would be desirable to overcome the aforesaid and other disadvantages, and to provide an electronic circuit component capable of providing a relatively wide tuning range and a relatively high Q, low intermodulation, high linearity and thermal stability. 
         [0006]    A radio receiver is but one example of a wide variety of electronic devices that require the ability to tune to selected frequencies. Other examples include, but are not limited to, radio transmitters, power amplifiers, wireless telephones (voice and data), wireless modems, cable modems, radar systems, and scientific instrumentation, and all would make use of and be based upon the design and construction and operation disclosed in earlier U.S. Pat. No. 5,964,242 to Alexander H. Slocum, who is a co-applicant herein, and U.S. Pat. No. 6,914785 to Alexander H. Slocum et al, the contents of both of which are herein incorporated by reference. 
         [0007]    Many electronic devices require the ability to selectively tune one or more circuits to receive or transmit a selected one of a variety of radio signals, each associated with a relatively narrow band of frequencies about a corresponding center frequency. For example, a conventional radio receiver is designed to manually or automatically tune to enable reception of a selected radio signal from among many radio signals. By selectively tuning the radio receiver, any selected one of the many of radio signals can be received, down-converted to an audio signal, and presented to a user for listening. As is known, the many radio signals span a relatively wide frequency range, while each individual radio signal spans a relatively narrow frequency range, each having a different center frequency. 
         [0008]    While the conventional radio receiver has selective tuning to tune near selected ones of the many radio signals, i.e. with selective “coarse” tuning, it should also be appreciated that the conventional radio receiver also has selective “fine” tuning, to tune within a narrower frequency range. Such fine tuning can variably move a tuned center frequency, first selected by the coarse tuning, to more accurately select a particular center frequency. 
         [0009]    As is known, fixed electrical components typically suffer from component value drift with time and temperature, which can result in drift of a tuned circuit. With the selectable tuning described above, tuning drift can be overcome, and a tuning circuit, regardless of component drift, can still tune to a desired center frequency. 
         [0010]    Some characteristics that are important in determining the effectiveness of an electronic tuning circuit include a total frequency span over which the selective tuning can tune, i.e., a coarse tuning range, an accuracy of the tuning, i.e. a fine tuning range and accuracy, and a selectivity of the tuning. The selectivity will be understood to be characterized by a quality or Q factor (or more simply “Q”), associated with the relative amplitude of a resonant peak and hence the minimum filter bandwidth capabilities. 
         [0011]    Conventional electronic circuits are known which can provide selective coarse tuning over a wide range of frequencies, but with only a relatively low Q. For example, a phase locked loop (PLL), having a programmable divider, can provide selective tuning in a relatively wide range of frequencies. Conventional electronic circuits are also known which can provide selective tuning over only a small range of frequencies, but with a high Q on the order of several hundred. For example, a varactor diode is known to provide a variable capacitance, which can be used in conjunction with a fixed inductor and other electronic components in a resonant tank circuit to provide selective fine tuning. To this end, there also exist other passive components used in tank circuits (e.g. crystals, surface acoustic wave (SAW) devices, and bulk acoustic mechanical resonators), which provide relatively high Q (on the order of a thousand), low noise, and high stability necessary for highly-selective, low-loss fine tuning at radio frequencies (RF) and intermediate frequencies (IF). While a high Q is obtained with tank circuits, if used in a radio receiver without coarse tuning circuitry, the tank circuit could not tune over the full AM and FM frequency bands. Therefore, it should be understood that with conventional circuits a tradeoff must typically be made between total tuning frequency range and Q. 
         [0012]    In order to achieve both a wide range of tuning and a high Q, many conventional electronic circuits incorporate both coarse tuning circuits, which conventionally have a wide tuning range but low Q, and fine tuning circuits, which conventionally have a low tuning range but a high Q. It will, however, be understood that the coarse tuning circuits and fine tuning circuits in combination represent a relatively complex and expensive electronic structure. 
         [0013]    To replace the circuits described above, researchers have sought to develop micro electromechanical systems (MEMS) to provide on-chip voltage-tunable capacitors, low-loss inductors, and on-chip mechanical resonators. MEMS capacitors with a tuning range of approximately 6:1 at radio frequencies (RF) are known, but their robustness and Q have not met requirements. In addition, very low-loss inductors have yet to be demonstrated by other research groups. 
         [0014]    It would, therefore, be desirable to overcome the aforesaid and other disadvantages, and to provide an electronic circuit component capable of providing a relatively wide tuning range and a relatively high Q. 
       SUMMARY OF THE INVENTION 
       [0015]    The present invention provides a tunable capacitor and/or a tunable tank circuit capable of tuning at relatively high signal frequencies, over a relatively wide range of frequencies, and with a relatively high Q factor, fabricated using electroforming, ceramic printed circuit board, and joining technology. 
         [0016]    In accordance with the present invention, a circuit component has a first structure provided from an elastically deformable material. The circuit component also has a second structure with a surface proximate a surface of the first structure. The first and the second structures are coupled with a support structure which also acts as an elastic constraint to the first structure. The first structure can be elastically deformed, causing a portion of the surface of the first structure to move relative to the surface of the second structure, varying a gap. In one particular embodiment, the gap can range from microns to nanometers in size and is controllable with nanometer resolution. In one particular embodiment, the surface of the first structure and the surface of the second structure which are in proximity, each have a first conductive region, forming a first capacitor, the capacitance of which varies in proportion to the movement of the first structure relative to the second structure. In another embodiment, the surface of the first structure and the surface of the second structure which are in proximity, each also have at least one other conductive region, forming an inductor in parallel with the capacitor, and therefore, forming a tank circuit. In yet another embodiment, the circuit component includes a piezoelectric disk laminated or otherwise attached to the elastically deformable region of the first structure to form a piezoelectric bimorph actuator. In yet another embodiment, a flexible circuit element comprised of insulating and conducting layers may be disposed on the upper surface of the resonator or on the lower surface of the piezoelectric disc to electrically insulate the piezoelectric actuator from the elastically deformable metal structure, and to provide an electrical contact to the bottom surface of the piezoelectric disc. 
         [0017]    To simplify the manufacturing process and reduce manufacturing costs, an inventive fabrication process for the production of the variable electrical circuit components of the present invention, incorporating metal electroforming techniques known for use in other applications was developed. The first elastically deformable structures of the inventive variable electrical circuit components may advantageously be fabricated by electroplating one or more thin layers of conductive material onto a mandrel having a complementary shape, polishing the surface of the electroplated layer until it exhibits a fine surface finish, dicing the electroplated layer into individual components and then releasing the electroplated layer from the mandrel using standard techniques, resulting in thin free-standing metal structures. This first metal structure may then be joined to a second structure having a conductive circuit topography patterned onto its surface. The first and second structures may be joined by means of an intervening conductive adhesive, or by direct joining techniques such as ultrasonic welding or thermocompression bonding. In one particular embodiment, a piezoelectric ceramic may be laminated onto the top surface of the first elastically deformable structure, providing a means of deforming the first structure in response to an applied electric field, and thus electronically controlling the capacitor gap. In another embodiment, the piezoelectric ceramic may be incorporated into the electroforming mandrel and is intimately joined to the first elastically deformable structure without intervening adhesives. This provides a significant advantage in reducing mechanical hysteresis associated with the deformation of the adhesive layer, and assembly complexity. By creating multiple such features on a larger mandrel, many such devices may be made in a single batch process. 
         [0018]    With this particular arrangement of the present invention, a MEMS capacitor having a selectably variable capacitance value is provided. The capacitor can be provided as part of a variable tank circuit having a relatively wide tuning range and a relatively high Q. 
         [0019]    In another arrangement, a stripline circuit pattern may be disposed upon the second substrate wafer forming the second structure of the variable electrical circuit component of the present invention, such that a variable input coupling capacitor, a variable tank capacitor and a variable ouput coupling capacitor may be formed between the second substrate and the top deformable conductive region of the first structure. In such an arrangement, the input and output capacitors have the effect of transforming the resonator impedance to the impedance of the input and output striplines respectively. Adjusting the size of the coupling capacitors allows the designer to adjust the electrical bandwidth of the resonator. In another embodiment, a circuit pattern may be disposed upon the second substrate wafer such that a fixed inductive input coupling structure and a fixed inductive output coupling structure are formed. Thus, either magnetic or capacitive coupling circuits can be formed to couple electromagnetic energy into and out of the variable tunable element. 
         [0020]    With this particular arrangement, the method provides a variable capacitor and/or a variable tank circuit having a relatively wide tuning range and a relatively high Q. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0021]    The foregoing features of the invention, as well as the invention itself may be more fully understood from the following detailed description of the drawings, in which: 
           [0022]      FIG. 1  is a cross-sectional schematic view through a version of the device showing the inductor cavity, the central capacitor and a piezoelectric element for tuning; 
           [0023]      FIG. 2  is a cross-sectional schematic view of the resonator with a tuning voltage applied to the piezoelectric actuator. 
           [0024]      FIG. 3  is an exploded view that shows the assembly of the cavity; 
           [0025]      FIG. 4  is an isometric view of the system with a piezoelectric bimorph actuator; 
           [0026]      FIG. 5  shows the dependence of the actuator displacement on the diaphragm dimensions; 
           [0027]      FIG. 6  shows a cross-sectioned view of a device with principal dimensions labeled; 
           [0028]      FIG. 7  shows a schematic plan view of the fixed ceramic substrate including coupling capacitor and tank capacitor regions with principal dimensions labeled; 
           [0029]      FIG. 8  shows the lumped-parameter equivalent circuit for the device; 
           [0030]      FIG. 9  shows the frequency response (S 21 ) of a typical two-port device tuned to resonate at 1.41 Ghz, 2.30 Ghz and 3.50 Ghz by varying the applied piezoelectric tuning voltage; 
           [0031]      FIG. 10  shows the center frequency versus piezo tuning voltage; 
           [0032]      FIG. 11  shows the resonant frequency vs center frequency of a typical device; 
           [0033]      FIG. 12  shows the quality factor (Q) vs center frequency of a typical device; 
           [0034]      FIG. 13  shows the insertion loss vs. center frequency of a typical device. 
           [0035]      FIG. 14  shows a four-port tunable capacitor device; 
           [0036]      FIG. 15  shows an equivalent circuit for the four-port tunable capacitor. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0037]    Before describing the circuit components of the present invention, mention is made as to the format of some of the figures. Those figures shown and described as cross-sectional figures are drawn without some hidden lines representing features behind the section region. Those lines behind the section region, if drawn, would add unnecessary complexity to the drawings and obscure the features which are described. In effect, the cross-sectional figures may be thought of as “slice” figures, representing a slice of an apparatus. 
         [0038]    Referring now to  FIG. 1 , an exemplary circuit component  100 , includes a first (or upper) structure  101 , provided from an elastically deformable material, having a first surface  101   a a  nd a second surface  101   b . In one particular embodiment, the circuit component  100  is symmetrical about the axis  170 . In another embodiment, the circuit component  100  can be provided having circular symmetry about the axis  170 , and thus the circuit component  100  is essentially round. In another embodiment, the structure could be shaped in the form of a polygon or other shape. The first structure  101  may be fabricated from a conductive material such as a conductive metal. The first structure  101  may have a thin layer of conductive adhesive  110  disposed upon the surface  101   b , which bonds the thin piezoelectric disc  300  to the deformable material  121  creating a piezoelectric bending bimorph actuator. The second structure  200  has a top surface  205   a  and a bottom surface  205   b.  In some embodiments, a conductive layer disposed upon the top surface  205   a  may be patterned to form independent variable input and output coupling capacitors  210   a  and  210   b,  and a variable tank capacitor  220  between the surfaces  230  and  130 . In one implementation, a dielectric layer  131 , for example parylene-N, may be disposed upon the inner surface of the element  101 , preventing conductive surfaces  230  and  130  from touching. The conductive regions  101   a,    140  and  205   a  form the periphery of a single-turn toroidal inductor  150  that is electrically connected to the bottom plate  220  of the variable tank capacitor. Structure  101  may be anchored to surface  205   a  with thin film attachment means  201 , such as an adhesive, or alternatively it may be laser welded or ultrasonically welded, eliminating the film  201 . 
         [0039]    Referring now also to  FIG. 2 , an exemplary circuit component  100  includes a first (or upper) structure  101 , provided from an elastically deformable material, having a first surface  101   a  and a second surface  101   b.  The first structure  101  has a central region  120 , which in an alternative embodiment (not shown) may be thicker than the flexible diaphragm region  121 . The upper circuit component  101  may be electrically connected to “ground,”  119 , while the conductive surface  301  of the piezoelectric element  300  may be electrically coupled by a wire  117  connected to a high-voltage power supply  118  capable of adjusting the electric field across the piezoelectric disk. This piezoelectric bimorph structure, as is known in the art, creates an effective force F acting upon the central region  120 , thereby varying the gap δ between surfaces  130  and  230  in the direction of axis  170 . It should be noted that the sidewall  140  of the inductor cavity  150  also acts as an elastic fulcrum to support the outer edge of the flexible diaphragm  101  so the force F can produce reasonable capacitance changes. Sidewall  140  can be very short, even just a rim if the inductor cavity  150  is machined into the substrate  200 , for example. 
         [0040]    The exemplary circuit component  100  also includes a second (or lower) structure  200 , having a first surface  205   a  and a second surface  205   b.  The conductive material disposed upon the first surface  205   a  of the lower structure  200  is structured to provide an input coupling capacitor plate  210   a,  a tank capacitor plate  220  and an output coupling capacitor plate  210   b.  Thus, three parallel-plate capacitors may be formed between the input plate  210   a,  the tank plate  220  and the output plate  210   b  and the movable top plate  120 . Conductive vias  211   a  and  211   b  provide an electrical contact path to the second conductive layer  205   b.  Input and output striplines,  212   a  and  212   b  respectively, are used to couple electrical power into and out of the coupling capacitor plates  210   a  and  210   b.  A bottom conductive material is disposed upon the surface  205   b  and patterned to define input and output striplines  212   a  and  212   b,  respectively, and a ground plane  215 . The tank capacitor plate  220  may preferably be electrically grounded. Additional ground vias (not shown) may couple the top ground plane regions  209   a,    209   b  and  220  to the bottom ground plane  215 , thereby decreasing any parasitic coupling between input and output striplines  212   a  and  212   b  respectively. 
         [0041]    In one exemplary embodiment, the force F can be provided by piezoelectric element  300  coupled to the second surface  101   b  of the first structure  101 . In such an embodiment, in response to a signal provided thereto, the piezoelectric element may provide a force upon the first structure  101  in the lever regions formed by the side structure  140 . While the piezoelectric element  300  is shown, in other embodiments, an external piezoelectric stack or any suitable electrostatic or electromechanical actuator can be provided in place of, or in addition to, the piezoelectric element  300  to provide the force F upon the second surface  130 . 
         [0042]    In one particular embodiment, the first structure  101  may be made from metal, for example copper metal, using electroforming techniques, and the second structure  200  may be made from ceramic, such as for example, Aluminum Nitride, Aluminum Oxide, or Pyrex™ with conductive regions disposed and patterned thereupon using conventional circuit processing techniques that are widely known in the art. In another embodiment, the first structure  101  may be made from a metal alloy, for example “Alloy 42”, whose composition of Nickel and Iron may be adjusted such that the metal alloy has a coefficient of thermal expansion that is closely matched to the ceramic of the second structure  200 . Furthermore, the inner surface  101   a  of the first structure  101  can have a thin layer (1-3 microns) of non-ferromagnetic material such as copper or gold disposed upon it to desirably reduce the level of third-order intermodulation at RF frequencies. 
         [0043]      FIG. 2  shows the effective deflection force F, generated by the action of the exemplary piezo actuator  300  on the central region  120 , causing separation of the first and second conductive layers  130 ,  230  respectively, forming a gap  6 . It will be understood that the size of the gap  6  is influenced by the magnitude of the force F and the stiffness of the structures  101  and  140 . Therefore, the layers  130  and  230  form a variable capacitor having a capacitance that varies in proportion to the force F. As the force F increases, the gap δ tends to increase, therefore reducing the capacitance. Furthermore, the direction of the force F can be reversed by reversing the direction of the electric field applied across the piezoelectric actuator  300 . In this case, the gap δ decreases in size, thereby increasing the capacitance. In addition, there can be an initial gap between conductive layers  130  and  230  due to bow and warp of the surfaces, or residual thermal stresses produced during component manufacturing. 
         [0044]    As described above, in other embodiments, the force F can equally well be applied with another type of actuator in place of or in addition to the piezoelectric element  300 . For example, in other embodiments, the force F can be applied with an external electromechanical actuator or piezoelectric stack actuator (not shown). 
         [0045]    Because the gap δ of the circuit component  100  has a high aspect ratio, i.e., a major axis or a diameter d much greater than the gap δ, which can be precisely controlled, the circuit component  100  can form a capacitor having a relatively wide range of achievable capacitance values. A tuning ratio can be defined as the largest capacitance value which can be achieved divided by the smallest capacitance value which can be achieved, and the capacitor  100  is provided having a relatively high tuning ratio. In one particular embodiment, the tuning ratio may be 10, although values up to at least about 100 may be achieved. With addition of an integral inductor as described more fully below, a tunable LC resonator circuit, or LC tank circuit, may operate from, for example, UHF (Ultra-High Frequency) to SHF (Super-High Frequency) and may be capable of band selection over a wide frequency range. It should, however, be appreciated that the structures and techniques described herein may also be applied to frequency ranges which are lower than and higher than UHF and SHF. 
         [0046]      FIG. 3  shows a metal resonator cavity  101  which may be formed by advantageously adapting conventional electroforming techniques such as by electroplating one or more thin layers of conductive material onto a mandrel having a complementary shape, polishing the surface of the electroplated layer until it exhibits a fine surface finish, dicing the electroplated layer into individual components and then releasing the electroplated layer from the mandrel using standard techniques, resulting in the resonator cavity  101 , or by other known means for producing a thin-walled conductive geometry. A ceramic circuit board  200  having patterned metal interconnections, for example  212   a  and  212   b,  and through-hole vias, for example  211   a  and  211   b,  may be fabricated by advantageously adapting conventional ceramic circuit-board techniques known in the art. A thin adhesive layer  201  may be applied around the periphery of the ceramic tile. Subsequently, the resonator cavity  101  may be pressed against the thin adhesive layer  201 , and the adhesive may be allowed to cure, thereby electrically and mechanically joining resonator cavity  101  and the patterned ceramic circuit board  200 . A second layer of conductive adhesive  102   a  and  102   b  may be disposed upon the top surface  101   b  of the resonator cavity  101 , and a piezoelectric disk element  300  may be pressed against the adhesive layer. Care must be taken to avoid applying excess conductive adhesive, or the excess can squeeze out from the interface and short-circuit the top and bottom surfaces of the thin piezoelectric disk. In an alternate embodiment, the adhesive  102   a  and  102   b  may be a non-conductive adhesive, for example cyanoacrylate, thin enough to still allow electrical interconnections between asperities on the surface  302  of the piezoelectric disk and surface  101   b  of the electrical resonator. 
         [0047]    Referring now to  FIG. 4 , in which like elements from  FIG. 1  are shown with like reference designations, an exemplary circuit component  100  having circular symmetry is shown in an isometric view. A piezoelectric disk  300  is bonded to the top surface  101   a  of the resonator  101 . Rectangular coaxial feed-throughs  105   a  and  105   b  are formed in the side  140  of the resonator allowing for lateral electrical interconnections into the resonator cavity if desired. The resonator  101  may be bonded to the ceramic substrate  200  such as by using adhesive or welding means, as described previously. 
         [0048]    Referring now to  FIG. 5 , the maximum actuator displacement, for a given 3.5×10 5  V/m electric field across an exemplary piezoelectric actuator, and for a piezo disk thickness of 100 microns, and a metal diaphragm thickness of 75 microns, is plotted as a function of the relative diameters of the piezoelectric disk and the metal diaphragm. The maximum displacement is 5.9 microns for an exemplary piezoelectric disk diameter of 10 mm and a metal diaphragm diameter of 11.6 mm. 
         [0049]    Referring now to  FIG. 6 , in which like elements from  FIG. 1  are shown with like reference designations, an exemplary tunable tank circuit  100  includes a first structure  101  preferably made of highly conductive metal, and having a central axis  170 . The tunable tank circuit  100  also includes a second structure  200  having a conductive region  205 , and conductive regions  210   a  and  210   b.  The conductive region  205  may be joined to the structure  101  by a flexible conductive structure  140  such as by using conductive epoxy  201  or a direct joining technique. The conductive regions  160  and  220  form a variable capacitor having a capacitance related to the area and width of a variable gap δ, and the conductive regions  205 ,  140  and  180  form an inductor  190  having an inductance that is substantially fixed as determined by the dimension H as well as the dimensions of conductor  205 . The conductive region  160  and  220 , each have a radius R 1 , and the conductive regions  180  have inner and outer radii R 1  and R 2  respectively. The area of region  220  may be decreased by the coupling structures  210   a  and  210   b.  Region  220  may be electrically connected to region  205 . An insulating layer  131  may be disposed on the conductive region  160 , having a fixed thickness δ 1 . 
         [0050]    The electrical response characteristics of the circuit component  100  may be analyzed by first assuming that a current flows into the conductive region  160  and out the conductive region  220 , by also assuming that current distributes evenly, forming a surface current K f  in the closed conductor  190 , by also assuming that magnetic flux lines (not shown) are contained inside the effective toroid  150  formed by the conductive regions  190  and  180  respectively, and by assuming that an H field is zero directly outside of the closed conductor. A boundary condition, n×(H a -H b )=K f , may be used, where H a  is inside the toroid and H b  is outside. Therefore, in such case, the H field inside the toroid is H a =K f . 
         [0051]    The surface current K f  is a function of the radius r is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       K 
                       f 
                     
                     = 
                     
                       H 
                       = 
                       
                         I 
                         
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                   , 
                 
               
               
                 
                   ( 
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         [0052]    The flux density is thus 
         [0000]    
       
         
           
             
               
                 
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         [0053]    To calculate inductance, the total flux in the toroid may be calculated. This is done by integrating the flux density across a cross-sectional area of the toroid. Dividing the flux-linkage by the current gives the inductance, 
         [0000]    
       
         
           
             
               
                 
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         [0054]    Capacitance between the conductive regions  160  and  220  respectively, derived by inspection, is written below, taking into account the effect of a higher permittivity, ε 1 , of the oxide layer  131  and the thickness δ 1  of the oxide layer  131 : 
         [0000]    
       
         
           
             
               
                 
                   
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         [0055]    The resistance of the toroid, i.e., effective resistance in series with the inductor formed by the conductive regions  190  and  180  respectively, is calculated below. A skin depth w Au  is a function of resonant frequency. The calculated resistance below does not take into account dielectric hysteresis, radiation, charge relaxation time constants, and leakage through first structure  101 , all of which tend to reduce the Q of the tank circuit. 
         [0000]    
       
         
           
             
               
                 
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                           2 
                            
                           
                               
                           
                            
                           ln 
                            
                           
                             
                               R 
                               2 
                             
                             
                               R 
                               1 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     w 
                     Au 
                   
                   = 
                   
                     
                       2 
                       
                         ω 
                          
                         
                             
                         
                          
                         
                           μ 
                           o 
                         
                          
                         
                           σ 
                           Au 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0056]    Referring now to  FIG. 7 , conductive regions  210   a  and  210   b  may be disposed on the fixed ceramic substrate  200 , thereby forming structures that couple RF energy into an out of the resonant cavity. The capacitance of the coupling circuit corresponding to  210   b  may be represented by: 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                      
                     
                       ( 
                       δ 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             ɛ 
                             1 
                           
                            
                           
                             δ 
                             1 
                           
                         
                         + 
                         
                           
                             ɛ 
                             0 
                           
                            
                           δ 
                         
                       
                       
                         
                           
                             ( 
                             
                               
                                 δ 
                                 1 
                               
                               + 
                               δ 
                             
                             ) 
                           
                           2 
                         
                          
                         
                             
                         
                       
                     
                      
                     
                       W 
                       1 
                     
                      
                     
                       L 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    and the capacitance corresponding to the coupling circuit  210   a  may be represented by: 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                      
                     
                       ( 
                       δ 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           
                             ɛ 
                             1 
                           
                            
                           
                             δ 
                             1 
                           
                         
                         + 
                         
                           
                             ɛ 
                             0 
                           
                            
                           δ 
                         
                       
                       
                         
                           
                             ( 
                             
                               
                                 δ 
                                 1 
                               
                               + 
                               δ 
                             
                             ) 
                           
                           2 
                         
                          
                         
                             
                         
                       
                     
                      
                     
                       W 
                       2 
                     
                      
                     
                       
                         L 
                         2 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0057]    Referring now to  FIG. 8 , an equivalent lumped-parameter circuit is shown. Input stripline  212   a  couples energy into the resonant tank  400  through capacitor C i    173 . Output stripline  212   b  couples energy out of the resonant tank  400  through capacitor C o    172 . Tank capacitor C t    171  varies in concert with coupling capacitors C i    173  and C o    172 , thus the ratio of tank and coupling capacitors may be held constant even as the capacitor spacing is varied. 
         [0058]    In one particular embodiment R 1  is 2.5 mm, R 2  is 5.8 mm, d is 3 mm, the thickness of the insulating layer  131  is 100 nm, the variable gap δ can be varied in a range between about 1 μm and 20 μm (although the desired range could be from about 100 μm to 10 nm), the closed conductor  191  may comprised of gold having a skin depth of 1.61 μm, a calculated inductance of the toroid  150  is 505 pico-Henries (pH), a calculated equivalent series resistance of the toroid is 8.2 mΩ, a capacitance of the capacitor formed by the conductive regions  160 ,  170 , respectively, varies between 173 pico-Farads (pF) and 8.69 pF as the variable gap is varied in the above range. The coupling capacitor regions are each 0.75 mm×0.5 mm, thus the coupling capacitance varies between 0.16 pF and 3.3 pF. The resonant frequency of resonant cavity varies between 534 Mhz and 2.38 GHz as the variable gap is varied in the above range, and the loaded Q varies between 26.7 and 198 as the variable gap is varied in the above range, and the 3 dB bandwidth of the resonance, given 50-Ohm input and output coupling, is between 20 Mhz and 12 Mhz as the variable gap is varied in the above range. However, in other embodiments, other dimensions and characteristics can be selected in order to provide a circuit component having another capacitance range, another inductance, another bandwidth, another range of resonant frequencies, and another range of Qs. 
         [0059]    Referring now to  FIG. 9 , curves  501   a,    501   b  and  501   c  represent S 21 , i.e. the power transmitted between the input and output ports of the tunable resonator for a range of applied tuning voltages. The transmitted power S 21  (in dB) is shown along axis  502 . The frequency, in Ghz, is shown on axis  503 .  FIG. 9  shows that the insertion loss of a two-port one-pole resonator device is between −3.0 dB at 1.41 Ghz and −2.1 dB at 3.50 Ghz, for a fixed resonator bandwidth of 25 Mhz. 
         [0060]      FIG. 10  shows the dependence of the resonator center frequency on the tuning voltage applied to the piezoelectric bimorph actuator. Curve  601  represents the center frequency of the exemplary resonator as a function of the tuning voltage applied to the piezoelectric bimorph. The center frequency, in Ghz, is shown along axis  602 , and the applied piezo voltage, in Volts, is shown along axis  603 . 
         [0061]      FIG. 11  shows the dependence of the measured resonator bandwidth on the resonator center frequency. The curve  606  shows the variation of resonator bandwidth between 15 Mhz at 1.41 Ghz to 38 Mhz at 2.80 Ghz center frequency. Axis  605  gives the resonator bandwidth in Mhz. Axis  606  gives the resonator center frequency in Ghz. 
         [0062]      FIG. 12  shows the variation of the resonator unloaded Q with center frequency. Curve  611  represents the unloaded Q as a function of the resonator center frequency. Axis  610  shows the unloaded Q, a dimensionless number, which varies from 270 to 350. Axis  612  shows the center frequency of the resonator which in this case varies from 1.41 Ghz to 2.80 Ghz, as a function of the applied tuning voltage. The unloaded Q is readily calculated from the measured loaded Q and the insertion loss (IL) using the following relation: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       Q 
                       u 
                     
                     = 
                     
                       
                         
                           Q 
                           l 
                         
                         · 
                         
                           10 
                           
                             IL 
                             / 
                             20 
                           
                         
                       
                       
                         
                           10 
                           
                             IL 
                             / 
                             20 
                           
                         
                         - 
                         1 
                       
                     
                   
                   , 
                   
                       
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     Q 
                     l 
                   
                   = 
                   
                     
                       f 
                       0 
                     
                     BW 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0063]      FIG. 13  shows the variation of resonator insertion loss with center frequency. Axis  903  shows the center frequency of the resonator which was tuned between 1.41 Ghz and 2.80 Ghz. Axis  902  shows the measured insertion loss in dB. Curve  901  represents the insertion loss as a function of resonator center frequency, which in this case varies from −3.5 dB at 1.41 Ghz to −2.1 dB at 2.80 Ghz. 
         [0064]      FIG. 14  shows a cross-section of an embodiment of an inventive four-port tunable capacitor based on a modification of the tunable resonator structure disclosed above. An exemplary circuit component  700 , includes a first (or upper) structure  701 , provided from an elastically deformable material. In one particular embodiment, the circuit component  700  is symmetrical about the axis  870 . In another embodiment, the circuit component  700  may be provided having circular symmetry about the axis  870 , and thus the circuit component  700  may be substantially round. In yet another embodiment, the structure could be formed in the shape of a polygon or other shape. The first structure  701  may be fabricated from a conductive metal. The first structure  701  may have a thin layer of conductive adhesive  810  disposed upon the surface  701   b,  which bonds the thin piezoelectric disc  300  to the deformable material  721  creating a piezoelectric bending bimorph actuator. The second layer  800  has a top surface  805   a  and a bottom surface  805   b.  A conductive layer disposed upon the top surface  805   a  may be patterned to form independent variable input and output capacitors, formed between the surfaces  730  of conductive plates  710   a  and  710   b,  and the surface  830 . In one implementation, a dielectric layer  731 , for example parylene-N, may be disposed upon the inner surface of the element  701 , preventing conductive surfaces  730  and  830  from touching. 
         [0065]    To electrically isolate the variable capacitor from the actuation circuitry, an RF choke  815  may be connected between the conductive structure  701  and the ground  816 , with a wire  817 . Likewise, an RF choke  811  may be connected with a wire  813  to the top surface  301  of the piezoelectric element  300 . The RF choke  811  may be connected to the variable voltage supply  812 , which provides a control voltage to the piezoelectric bimorph actuator, thus varying the gap δ, in a manner similar to that employed in the tunable resonator device described earlier. 
         [0066]      FIG. 15  shows an equivalent circuit model for the exemplary four-port tunable capacitor disclosed in  FIG. 14 . The variable capacitors  842  and  841  are connected by striplines  712   a  and  712   b.  The node  890  is a common terminal for the piezoelectric actuator  300  and the variable capacitors  842  and  841 . At RF frequencies, for example frequencies above 50 Mhz, the RF choke inductors  811  and  815  have a high impedance and thus may be modeled as an “open circuit.” Thus at high RF frequencies, the voltage on the node  890  may not be fixed to the ground  816 . Conversely, at audio frequencies, for example the typical 0-30 kHz actuation frequency of the piezoelectric bimorph  300 , the RF choke may be modeled as a short circuit, and the node  890  may be held at ground. Thus, the high-frequency variable capacitor circuit path and the low-frequency actuator circuit path may be isolated from each other. 
         [0067]    The variable capacitors  841  and  842  are electrically connected in series, thus their equivalent capacitance is: 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                     eq 
                   
                   = 
                   
                     
                       
                         
                           C 
                           1 
                         
                          
                         
                           C 
                           2 
                         
                       
                       
                         
                           C 
                           1 
                         
                         + 
                         
                           C 
                           2 
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0068]    All references cited herein are hereby incorporated herein by reference in their entirety. 
         [0069]    Having described preferred embodiments of the invention, it will now become apparent to one of ordinary skill in the art that other embodiments incorporating their concepts may be used. It is felt therefore that these embodiments should not be limited to disclosed embodiments, but rather should be limited only by the spirit and scope of the appended claims.