Abstract:
A micromechanical variable/tunable inductor is disclosed. The present inductor comprises at least two elements capable of supporting spatial electromagnetic coupling and means for varying a geometrical relationship thereof. Varying the geometrical relationship between such elements varies the inductance of the inductor. In some embodiments, the geometrical relationship that is varied is the spacing between the two elements. The spacing is varied by creating a differential movement between such elements. In further embodiments, the present invention comprises resonant circuits incorporating such variable inductors, and oscillators including such resonant circuits.

Description:
STATEMENT OF RELATED CASES 
     The present case is related to the following U.S. patent applications Ser. Nos. 09/152,185 and 09/152,189, both of which were filed Sep. 12, 1998. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to inductors. More particularly, the present invention relates to a micromechanical variable inductor and circuits for use therewith. 
     BACKGROUND OF THE INVENTION 
     Inductors and variable inductors are useful and/or required circuit elements in a variety of important applications and products. For example, inductors and variable inductors are necessary elements of many RF-wireless products. In particular, they are used for matching and loading low noise amplifiers, power amplifiers and mixers, as well as for providing frequency- selective resonant circuits in variable-frequency oscillators in such RF-wireless products. 
     In a typical cellular telephone, inductors, and other “passive” components (e.g., capacitors and resistors) may occupy over 90 percent of the circuit-board space, and outnumber active devices by more than ten-to-one. As the functionality of such a telephone continues to be integrated into progressively fewer chips, the passive components that are not easily integrated have come to dominate the board-level design. Thus, it would be desirable to fabricate semiconductor-integrable passive components. 
     Several difficulties have impeded the development of such semiconductor-integrable passive components. Regarding inductors, important performance parameters for RF applications include the “quality factor,” Q, (i. e., the relative absence of resistive losses) and obtaining a suitably high self-resonant frequency. Unfortunately, a performance improvement in one of such parameters is typically obtained at the expense of the other parameter. For example, increasing the size of an inductor will typically reduce resistive losses, but it will also lower its resonant frequency. 
     In the prior art, active circuits are typically used to “tune” or vary inductance in integrated circuits. Such an approach has several disadvantages, including degraded phase noise, relatively high power requirements and limited dynamic range. 
     A prior-art implementation of variable inductor that is described to be useful for silicon-based RF integrated circuit applications has been disclosed by Pehlke, et al in “Extremely High-Q Tunable Inductor for Si-Based RF Integrated Circuit Applications,” 1997 IEEE Int&#39;l Electron Devices Meeting, at 3.4.1-3.4.4., Washington, D.C., Dec. 7-10, 1997. That tunable inductor uses a variable-phase shifter to vary Q and inductance. While reported performance was good, the presence of the phase shifter is undesirable. 
     SUMMARY OF THE INVENTION 
     A variable/tunable inductor is disclosed wherein the geometry of the inductor is altered to vary inductance. More particularly, in accordance with the illustrated embodiments and in contrast with the prior art, the present inductors comprise at least two elements that support spatial electromagnetic coupling and means for varying a geometrical relationship thereof. Varying the geometrical relationship between such elements varies the inductance of the inductor. 
     In one embodiment, a variable inductor in accordance with the present teachings comprises a ground plane, an electrically-conductive planar loop spaced therefrom, and means for varying a geometrical relationship between the ground plane and the loop. In another embodiment, a variable inductor comprises two electrically-conductive planar loops that are spaced from each other and means for varying a geometrical relationship between the two loops. 
     In the illustrated embodiments, the geometrical relationship that is varied is the spacing between the loop and the ground plane or the spacing between the two loops. In various embodiments, the spacing is varied by creating a differential movement between the relevant elements. 
     In the illustrated embodiments, such differential movement is generated (1) by restraining the movement of one of the elements or (2) by varying a parameter/property of the two elements such that the elements respond differently to an actuating stimulus. The varied parameter may include, without limitation, element (e.g., loop) thickness, material of fabrication, and structural implementation. In the illustrated embodiments, the actuating stimulus includes temperature, electrostatic force, electromechanical impulsion and magnetic force. 
     In further embodiments, the present invention comprises resonant circuits incorporating such variable inductors, and oscillators including such resonant circuits. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 depicts a first embodiment of a variable inductor in accordance with the present teachings. 
     FIG. 2 depicts a second embodiment of a variable inductor in accordance with the present teachings. 
     FIGS. 3A and 3B depict a third embodiment of a variable inductor in accordance with the present teachings. 
     FIGS. 4A-4C depict a fourth embodiment of a variable inductor in accordance with the present teachings. 
     FIG. 5 depicts an illustrative arrangement for thermal actuation. 
     FIG. 6 depicts an illustrative arrangement for electrostatic actuation. 
     FIG. 7 depicts an illustrative arrangement for electromechanical actuation. 
     FIGS. 8A-8I depict an illustrative fabrication method. 
     FIG. 9 depicts an arrangement for generating a positive mutual inductance term. 
     FIG. 10 depicts an arrangement for generating a negative mutual inductance term. 
     FIG. 11 is a conceptual depiction of a one-port negative resistance oscillator in the prior art. 
     FIG. 12 is a conceptual depiction of a conventional amplifer-based variable-frequency oscillator. 
    
    
     DETAILED DESCRIPTION 
     The present invention provides a variable inductor, and circuits utilizing same. Such variable inductors are advantageously fabricated on an “integrable” support, such as, without limitation, silicon, germanium and the like. It should be understood, however, that there are applications in which it is desirable to fabricate the present passive variable inductors on a “non-integrable” support, such as glass or other non-conducting or low-dielectric-constant substrates. Applications for non-integrable supports include, for example, “drop in” replacement of existing inductors. The present variable inductors are suitable for use in conjunction with such non-integrable supports, as well as with applications using integrable supports. 
     Several illustrative resonant circuits in accordance with the present teachings are described later in this Specification after the present variable inductor is described. 
     The total inductance, L RF , of a passive inductor is given by: 
     
       
           L   RF   =L   SELF   +M   [1] 
       
     
     The two contributions to total inductance include (1) a self inductance term, L SELF , and (2) a mutual inductance term, M. The self inductance term derives from the geometry of segments of the inductor. The mutual inductance term derives from the geometry, spatial separation and relative phase of currents carried by different segments comprising the inductor. The impact of such geometric and phase relationships on inductance is well understood. Inductance is varied or “tuned” by changing the self inductance term, or the mutual inductance term, M. In accordance with the present teachings, inductance is changed by varying the geometry/spatial separation of the segments of the inductor. 
     FIGS. 1-4B depict several illustrative embodiments of a variable inductor in accordance with the present teachings. In all of such illustrative embodiments, inductance is changed by varying the geometry/spatial separation of various elements or segments of the inductor. It will be understood that the elements or segments must comprise a material that supports spatial electromagnetic coupling. Suitable materials include, without limitation, electrically-conductive materials, magnetic materials that are not electrical conductors (e.g., ferromagnetic glasses), and super conductors. 
     In the illustrated embodiments, some of the inductive elements that exhibit electromagnetic coupling are referred to as “loops” and depicted as having a “u” shape. It should be understood that such inductive elements can have an arbitrary shape. That is, they need not be loops, need not be “u-” shaped or have any particular shape at all. In fact, in some embodiments, such inductive lines are straight. As used herein, the term “loop,” when referring to elements that exhibit electromagnetic coupling, is meant to indicate an arbitrary geometry, including spirals, loops (including ellipsoidal, circular, rectangular, etc. loops), straight lines and any other suitable configuration. 
     For clarity of illustration, the means or stimuli by which such geometry is altered (e.g., an actuator, an actuating stimulus) is not depicted in FIGS. 1-4B nor described in conjunction therewith. Actuation devices/stimuli are described later in this Specification. 
     In the embodiment depicted in FIG. 1, illustrative variable inductor  100  comprises “loop”  110 , ground plane  104  and support  102 , interrelated as shown. Inductor  100  is configured so that a differential motion can be generated between loop  110  and ground plane  104 . In the illustrated embodiment, loop  110  is “fixed” to support  102 , while ground plane  104  is movable at free end  105  along direction vector  106  but is restrained at fixed end  103 . Since loop  110  is restrained from moving, movement of ground plane  104  causes a differential motion between that loop and the ground plane. A signal, such as an RF signal, is delivered to loop  110  at contacts  116   a  and  116   b.  Support  102  can suitably be semiconductor-integrable, or not, as desired. 
     The presence of ground plane  104 , which in some embodiments comprises a metal, affects mutual inductance between inductor segments  118  and  119 . As previously noted, the inductance of an inductor, such as inductor  100 , is a function of such spacing, among other factors. 
     When free end  105  of ground plane  104  is raised off of support  102  (e.g., rotated about fixed end  103 ) such that the ground plane is not co-planar with loop  104 , the distance x between ground plane  104  and inductor segments  118  or  119  varies along the direction vector  107 . As such, the mutual inductance term between segments  118  and  119  varies along direction vector  107 . 
     As ground plane  104  is moved along direction vector  106 , the distance x between the ground plane and any point along inductor segments  118  and  119  changes, increasing or decreasing depending upon the ground plane&#39;s direction of motion. As a result of such movement, effective electrical spacing  117  changes, so that self inductance is changed between different segments of loop  110  (e.g., any point along segments  118  and  119 ), thereby changing the inductance of inductor  100 . 
     In an alternate embodiment (not depicted), loop  110  is movable, while ground plane  104  is non movable. In such an embodiment, loop  110  can be fixed to support  102  at anchors, such as anchors  112  and  114 , about which loop  110  can rotate. As described later in this Specification, movement generated in ground plane  104  (or in loops, such as loop  110 ) may, as a function of the actuation method, arise from a “warping” of the ground plane (or loop), rather than a true rotation about a fixed end thereof. In this Description and the appended Claims, the terms “movement,” “movable,” “rotation” or the like, when used to describe motion of an unrestrained ground plane or loop, includes warping and/or rotation about a fixed point. 
     In some embodiments, ground plane  104  comprises a magnetic material, or is otherwise rendered magnetic. Relatively larger changes in inductance can be realized for a given movement along direction vector  106  when ground plane  104  is magnetic. 
     It will be understood that while loop  110  (and loops shown in other Figures depicting other embodiments) has a single turn, loops having multiple turns may suitably be used in conjunction with the present invention. Additional turns will result in higher values of inductance for the inductor. 
     A second illustrative embodiment of a variable inductor  200  is depicted in FIG.  2 . Inductor  200  comprises two loops—outer loop  210  and inner loop  220 . Both loops are anchored at anchors  212 ,  214 . Loop  210  is movable at free end  211  as indicated by direction vector  216 , and loop  220  is movable at free end  221  as indicated by direction vector  222 . A signal, such as an RF signal, is delivered to loops  210  and  220  at contacts  216   a  and  216   b.    
     The loops are suitably arranged, actuated, etc., as described later in this Specification, such that a differential motion between loops  210  and  220  can be generated. In other words, the loops move relative to one another such that a change in geometry/spacing results with such movement. As previously described, such a change results in a change in inductance. 
     Illustrative variable inductor  300  depicted in FIGS. 3A and 3B includes two-loops like inductor  200 . Inductor  300  differs from inductor  200  in that outer loop  210  of illustrative inductor  300  is restrained from moving by hooks  302 . Hooks  302  maintain loop  210  in a position relatively near to support  102 . Inductance is varied as unrestrained inner loop  220  is moved upwardly or downwardly. FIG. 3B shows inner loop  220  moving downwardly along direction vector  322  towards restrained outer loop  210 . When the inner and outer loops are co-planar, self-inductance is maximized. 
     Illustrative variable inductor  400  depicted in FIGS. 4A-4C also has two-loops. In inductor  400 , outer loop  210  is supported by supports  402 . Members  418  depending from outer loop  210  rest on supports  402  (FIG.  4 B). In such manner, downward motion of loop  210  is substantially prevented. In contrast to inductor  300 , supports  402  raise loop  210  to a position relatively distant from support  102 . Inductance is varied as unrestrained inner loop  220  is moved upwardly or downwardly. FIG. 4A depicts the inner and outer loops disposed in co-planar relation. FIG. 4C shows inner loop  220  moving downwardly along direction vector  422  away from restrained outer loop  210 . 
     The present variable inductors utilize a differential motion between inductor segments (or inductor segments and a ground plane) to vary inductance. The manner in which such differential motion is developed is now described. 
     In one embodiment, a change in temperature can be used as an actuation stimulus. For example, to create such a change in temperature, the inductor can be disposed in a micro-sized oven or a cooler. To generate differential movement between inductor segments, etc., the segments must respond differently to temperature. Such different responses can be achieved, for example, by varying the thickness of the inductor segments, utilizing different metals, and varying the mechanical design, such as by corrugating the surface of one of the segments. 
     Alternatively, a DC bias can be applied to one of the loops to selectively heat that loop. For example, as depicted in FIG. 5, bias is applied to loop  220 , such that loop  220  will be selectively heated. 
     The movement generated by thermal actuation is typically a “warping” of the loop or ground plane. Such warping is depicted, for the case of fixed inductors, in Gammel et al., “Design, Test and Simulation of Self-Assembled, Micromachined RF Inductors,” Symposium on Design, Test and Microfabrication of MEMS and MOEMS, Paris, France, March-April 1999, reprinted in SPIE vol. 3680 at pp. 582-591. 
     Inductor  300  depicted in FIGS. 3A and 3B, and inductor  400  depicted in FIGS. 4A-4C, are well adapted for use in conjunction with thermal actuation. For example, as temperature is reduced, an unrestrained loop tends to “warp,” rising away from support  102 . As temperature increases, the loop lends to assume a planar form. 
     In another embodiment, the movable member(s) is electrostatically actuated. FIG. 6 depicts an arrangement for electrostatic actuation wherein electrodes  630  and  632  are disposed beneath the “free end” of loop  210 , and electrodes  640  and  642  are disposed beneath free end of loop  220 . A DC bias is applied to the electrodes generating an electrostatic force that attracts the associated loop. The magnitude of the bias voltage controls the electrostatic force and the amount of movement (i.e., deflection) of the loop. 
     In a further illustrative embodiment depicted in FIG. 7, loops  210  and  220  are electromechanically actuated. In particular, loop  210  is actuated via actuator  758  that mechanically engages that loop via linkage  152   a.  The action of illustrative actuator  758  causes member  759  to move along direction vector  707  in a substantially “horizontal” or “in-plane” motion. Such in-plane movement is converted to a “vertical” lifting or “out-of-plane” motion via the operation of linkage  152   a.  Illustrative linkage  152   a  comprises rigid arm  752  that connects to loop  210  via hinge  754  and connects to actuator  758  via hinge  760 . Loop  220  is similarly actuated via an actuator (not shown for clarity) that is mechanical connected thereto via linkage  752   b.    
     Actuators suitable for use in conjunction with the present invention include, for example, well known scratch drives, comb drives and any of a variety of other suitable configurations for electromechanical actuation well known in the art. 
     The present variable inductors can be fabricated with standard micromachining techniques, such as, for example, the multi-user MEMS (micro electromechanical systems) process, “MUMPs” available from MEMS Microelectronics Center of North Carolina (MCNC) in Research Triangle Park, N.C. 
     One of MCNC&#39;s MUMPs technology is a three-polysilicon layer surface micromachining process. That process allows for a first deposited layer, referred to as “POLY0,” that is “non-releasable” and is typically used for patterning address electrodes and local wiring on a support. Thus, the POLY0 layer can be used to form, for example, electrodes  630 ,  632 ,  640  and  642  (see FIG. 6) that are useful for electrostatic actuation of inductor loops. The upper two polysilicon layers, referred to as “POLY1” and “POLY2,” are “releasable” and so can be used to form mechanical structures such as elements of an actuator or movable loops and ground planes. The POLY1 and/or POLY2 layers are released by etching away sacrificial oxide layers that are deposited between the polysilicon layers during fabrication. 
     The polysilicon layers POLY0, POLY1 and POLY2 have nominal thicknesses of 0.5, 2 and 1.5 microns, respectively. The polysilicon and oxide layers are individually patterned, and unwanted material from each layer is removed by reactive ion etching before the next layer is added. Optionally, a layer of metal, nominally 0.6 to 1.3 microns thick, may be deposited on the POLY2 layer. 
     MCNC&#39;s three-layer process, as well as other MEMS fabrication processes, are now quite familiar to those skilled in the art. 
     An illustrative method for fabricating an inductor loop, such as illustrative loops  110 ,  210  and  220 , based on the MCNC three-layer process is described below and depicted in FIGS. 8A-8I. The Figures are depicted as side-views for clarity of illustration, such that only a portion of the structure of the inductor loop (e.g., for inductor  100 , only anchor  114  and segment  119 ) is illustrated. Certain layers of material that are deposited when using the MCNC process are not utilized when forming the present structure. To the extent that such unnecessary layers are deposited on the present structure during fabrication, they are completely removed in later lithographic steps. Such non-utilized layers are omitted for clarity of presentation. In the following description and the accompanying Figures, the MCNC designations for the various polysilicon layers will be used. 
     As depicted in FIG. 8A, a first layer POLY0 of polysilicon is deposited on an insulating layer IN, such as silicon nitride. The layer POLY0 is then patterned, using an appropriate mask. The as-patterned layer POLY0 p , which will function as an “anchor” for one “end” of inductor loop, is shown in FIG.  8 B. 
     Subsequently, a layer OX of oxide is deposited over the layer IN and the layer POLY0 p , as depicted in FIG.  8 C. Next, layer OX of oxide is patterned as shown in FIG.  8 D. 
     In FIG. 8E, a layer POLY2 of polysilicon is deposited on the patterned layers OX p  and POLY0 p . The inductor loop and supports are formed from the layer POLY2. As such, the layer POLY2 is patterned, using an appropriately configured mask, into such structures. The patterned layer POLY2 p  is depicted in FIG.  8 F. 
     After patterning the layer POLY2, a layer M of metal is deposited on layer POLY2 p , and then patterned. The metal is deposited over the supports, as well as the loop, and provides a conductive surface. FIG. 8G depicts the patterned layer M on the patterned layer POLY2 p . Finally, the layer OX of oxide is etched, such as with HF, releasing the patterned layer POLY2 p , as is depicted in FIG.  8 H. 
     In some embodiments, two layers of metal, as opposed to a single layer, are deposited everywhere on inductor  102  to reduce electrical resistance as compared to a single layer. In still other embodiments, three or more layers of metal are used to further reduce electrical resistance. Any one of a variety of metals may suitably be used for such purpose, including for example, aluminum, copper, silver or gold. As is known to those skilled in the art, gold is typically not used in conjunction with CMOS processes. As such, in embodiments in which the present variable inductor is to be incorporated into a CMOS chip, the other metals listed above should be used in preference to gold. 
     In some embodiments, such as for variable inductor  400 , it is desirable to have at least one of the inductor loops elevated above the substrate. One way to do so is to cause patterned layer POLY2 p  to “warp” as it is released, such that the non-anchored end moves upwardly away from the layer IN disposed on the support, as depicted in FIG.  8 I. 
     Such upward warping can be caused by depositing a “stressed layer” over the structural layer (e.g., the patterned layer POLY2 in the previous example) of the structure that is to be warped. The stressed layer comprises a layer of material that is deposited such that it has a high level of intrinsic stress. 
     For example, as described above, metal is deposited on the POLY2 layer to provide a conductive surface. That metal is typically gold (for non-CMOS applications). Gold does not, however, adhere well to polysilicon. As such, a thin adhesion layer is often deposited on the POLY2 layer before depositing gold. In one embodiment, the adhesion layer is the stressed layer. 
     The adhesion layer is advantageously chromium or refractory metals like titanium or tungsten, since a high intrinsic stress is associated with deposited chromium, titanium, tungsten, etc. When the sacrificial oxide layer is etched away to release the patterned layer POLY2 p , the chromium, etc., layer contracts to minimize strain. Upon such contraction, an upwardly-directed force is imparted to the non-anchored end of patterned layer POLY2 p , causing it to warp in an “upwards” direction. 
     In an alternative embodiment (not shown), patterned layer POLY2 p  is fabricated with compressive stress, and an overlying layer (e.g., metal) is deposited with low stress. Upon release, the POLY2 p  layer expands, causing the same upwardly directed warp. 
     In the aforedescribed illustrative fabrication method, the POLY1 layer of the MCNC process is not used; rather the POLY2 layer is used. There are several reasons for this. First, since the POLY2 layer, at 1.5 microns, is thinner than the POLY1 layer (2 microns), the POLY2 will be more amenable to “warping.” Second, to impart the requisite conductivity to the loop, metal is advantageously deposited on the structural (e.g., polysilicon) layer comprising those structures. In the MCNC process, metal cannot be deposited on the POLY1 layer, but can be deposited on the POLY2 layer. 
     While the above-described method utilized MCNC&#39;s three-polysilicon layer MEMS fabrication technology, it should be understood that inductor loops can be fabricated using other surface micromachining processes. 
     As previously described, the total inductance, L RF , of a passive inductor is given by: 
     
       
           L   RF   =L   SELF   +M,   [1] 
       
     
     where: L SELF  is self inductance and M is mutual inductance term. 
     In a further embodiment, total inductance is influenced by the direction of current flow through the inductor. When parallel currents flow in a concurrent direction in adjacent lines, as illustrated by currents I 210  and I 220  in respective inductor loops  210  and  220  depicted in FIG. 9, a positive mutual inductance results. When parallel currents flow in a countercurrent direction in adjacent lines, as illustrated by currents I 310  and I 320  in respective inductor loops  210  and  220  depicted in FIG. 10, a negative mutual inductance results. 
     For countercurrent flow, the two inductor loops  210  and  220  are electrically isolated from one another at at least one end of the loops, such as end  950  in FIG.  10 . At end  950 , loop  210  terminates with electrical contact  916   a  and loop  220  terminates with electrical contact  916   b.  The contacts  916   a  and  916   b  are physically separated. 
     The variable inductors depicted in FIGS. 1-4 c  are configured for concurrent flow. It will be appreciated that in other embodiments, the present inductors can be readily configured for countercurrent flow. 
     By virtue of its small size, and compatibility with CMOS processing, the present variable inductor can advantageously be monolithically integrated into a number of important circuits via commercial-scale processing. At a most basic circuit level, the present variable inductor can be used to provide an improved version of the well-known tunable LC circuit. A tunable LC circuit in accordance with the present teachings comprises a signal generator and a capacitor that are electrically connected to a variable inductor in accordance with the present teachings. Such a circuit may be arranged in either a series or parallel configuration, as is well known in the art. 
     Such tunable LC circuits are used to provide improved variable-frequency oscillators, filters, and other important circuits in wireless telecommunications and other applications. In one embodiment, the present invention provides a radio-frequency oscillator. In that context, an oscillator is a device or circuit that converts DC power to RF power. Improved oscillators in accordance with the present teachings include the present variable inductor in a variety of well-known configurations. 
     One such configuration is a one-port negative resistance oscillator, which is conceptually depicted in FIG.  11 . Such an oscillator can be conceptualized as including load L and negative-resistance input device IN. Typically, the negative resistance device is a Gunn or IMPATT diode, which is biased to create a negative resistance. In accordance with the present teachings, the load comprises a resonant structure, such as an LC circuit including the present variable inductor. 
     Another oscillator configuration implements the function of negative resistance using an amplification device. FIG. 12 depicts a conventional amplifier-based variable-frequency oscillator. Such an oscillator includes a frequency-dependent or resonant structure RS and an amplification device A. The power output port can be on either side of amplification device A, which is commonly implemented as a transistor. 
     In an improved amplifier-based variable-frequency oscillator in accordance with the present teachings, resonant structure RS comprises an LC circuit including the present variable inductor. The amplifier is implemented such that it is operable, at an input, to monitor the rf signal in the resonant structure, and is further operable, at an output, to inject an amplified signal into the resonant structure in a manner best suited to sustain oscillations in the resonant structure. Those skilled in the art will be able to design an amplification device suitable for providing the above-described functions. 
     In some of the embodiments described above, it is advantageous or necessary to integrate methods for making the present variable inductor with CMOS processing. Integrating methods are commercially available, and are generally readily adaptable to meet the needs of a particular application. One such process is the “BiMOSIIe®” process available from Analog Devices, Inc. of Norwood, Mass. The BiMOSIIe® process integrates a surface micromachining process suitable for forming MEMS structures with a CMOS process suitable for forming devices useful for analog applications. Information concerning the BiMOSIIe® process is provided on Analog Devices/MCNC server pages at http://imems.mcnc.org. See also, U.S. Pat. Nos. 5,326,726 and 5,620,931 to Tsang et al., incorporated by reference herein. 
     Additionally, method for monolithically integrating MEMS structure in a CMOS chip are offered by the University of California at Berkeley, and Sandia National Labs of Albuquerque, N. Mex. 
     It is to be understood that the embodiments described herein are merely illustrative of the many possible specific arrangements that can be devised in application of the principles of the invention. Other arrangements can be devised in accordance with these principles by those of ordinary skill in the art without departing from the scope and spirit of the invention. It is therefore intended that such other arrangements be included within the scope of the following claims and their equivalents.