Abstract:
Flexible force/pressure sensors for producing electrical output signals proportional to forces or pressures exerted on the sensor include a thin, elastically deformable foam pad laminated between a pair of electrically conducive fabric sheets. A piezocapacitive embodiment of the sensor utilizes an elastically deformable perforated open-cell polyurethane foam pad preferably saturated with glycerin to increase the capacitance of the sensor. The piezocapacitive sensor section is preferably stacked onto a piezoresistive section having a second open-cell foam pad containing piezoresistive carbon particles to form a hybrid piezocapacitive/piezoresistive sensor. A third, “leaky dielectric” embodiment of a sensor includes a single open-cell foam pad which contains both a dielectric liquid and conductive particles. A low frequency such as d.c. to a few hertz is applied to a sensor to determine piezoresistive response of the sensor to forces or pressures and a higher frequency such as 30 KHz is applied to determine piezocapactive response.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    A. Field of the Invention 
         [0002]    The present invention relates to sensors for measuring forces or pressures exerted on a surface. More particularly, the invention relates to novel flexible hybrid force sensors which vary both in resistance and capacitance in response to forces or pressures applied to the sensors, and a pressure measurement apparatus which includes a novel hybrid force/pressure sensor and circuitry for measuring electrical impedances of the sensor at different frequencies. 
         [0003]    B. Description of Background Art 
         [0004]    There are a wide variety of situations which require the accurate measurement of forces or pressures exerted at various parts of the surface of an object. For example, when a human body is supported by an object such as a chair or bed, normal and shear forces produced in reaction to the weight of an individual are transmitted from the supporting surface through the skin, adipose tissues, muscles, etc. to the skeleton. Forces exerted on body parts by support surfaces, which are equal and opposite to body weight forces, can in some cases cause damage to tissues. This is because forces on body parts can compress internal blood vessels and occlude nutrients from the tissue; the product of the magnitude and duration of these forces determine whether tissue damage or morbidity will occur. 
         [0005]    High pressures alone are generally not sufficient to deleteriously affect tissue. Deep-sea divers for example, are subjected to high, but evenly distributed normal forces and do not suffer from tissue damage. If, however, there is a sufficiently large external pressure gradient on a body part, resulting from, for example, a low-pressure area adjacent to a high-pressure area, internal body fluids can migrate to the area of lower pressure. 
         [0006]    Tangential or shear forces exerted externally on a body part as a result of uneven normal forces or pressure gradients exerted thereon can also collapse internal capillaries and blood vessels by distorting them along their longitudinal axes. It is therefore extremely important to know both the surface force gradient (pressure gradient) and the externally applied shear force exerted on tissue, because it is the combination of these factors that leads to tissue strain and subsequent tissue death. Thus, even relatively small external shear and normal forces, which may be independent of one another, can combine to produce damagingly large shear stresses on internal tissue. The areas of the human body which are most at risk of developing tissue damage such as a pressure sore are: heel, ischial tuberosities, greater trochanter, occiput and sacrum. 
         [0007]    There are available a variety of pressure/force sensors, shear sensors and sensor arrays which are useable for measuring normal and shear forces exerted on human tissues. Such sensors typically consist of a transducer which covers pressure or force variations into electrical signals. For example, the present inventor&#39;s U.S. Pat. No. 5,751,973, Nov. 5, 1996, Multi-Directional Piezoresistive Shear And Normal Force Sensors For Hospital Mattresses And Seat Cushions discloses thin, planar sensors for measuring reaction forces exerted by mattresses or chair pads on the body of a recumbent or seated patient. One embodiment of the invention disclosed in the specification of the &#39;973 patent includes a sensor comprised of a two-dimensional array of isolated sensor element pads, each consisting of a thin, flat layer formed of a non-conductive elastomeric polymer matrix filled with electrically conductive particles. A matrix of upper and lower conductive elements in electrical contact with upper and lower sides of each sensor pad enables separate measurements to be made of the electrical resistance of each pad. Pressure exerted on each pad, e.g., in response to a normal force exerted on the sensor matrix by a person&#39;s body, reduces the thickness of the sensor pad, and therefore its electrical resistance by a bulk or volume piezoresistive effect. 
         [0008]    The present inventor also disclosed a novel method and apparatus for measuring pressures exerted on human feet or horses&#39; hooves in U.S. Pat. No. 6,216,545, Apr. 17, 2001, Piezoresistive Foot Pressure Measurement. The novel apparatus disclosed in the “545 patent includes a rectangular array of piezoresistive force sensor elements encapsulated in a thin, flexible polymer envelope. Each sensor element includes a polymer fabric mesh impregnated with conductive particles suspended in an elastomeric matrix such as silicone rubber. The piezoresistive mesh layer is sandwiched between an array of row and a column conductor strip laminations, preferably made of a nylon mesh impregnated with printed metallic paths. Each region of piezoresistive material sandwiched between a row conductor and column conductor comprises an individually addressable normal force or pressure sensor in a rectangular array of sensors, the resistance of which varies inversely in a pre-determined way as a function of pressure exerted on the sensors, and thus enabling the force or pressure distribution exerted by an object contacting the array to be mapped. 
         [0009]    In U.S. Pat. No. 6,543,299, Apr. 8, 2003, Pressure Measurement Sensor With Piezoresistive Thread Lattice, the present inventor disclosed a transducer sensor array for measuring forces or pressures exerted on a surface, the array including a fabric-like, two-dimensional lattice of individual force or pressure sensor transducer elements comprising intersecting regions of pairs of elongated, flexible threads, each consisting of a central electrically conductive wire core covered by a layer of piezoresistive material which has an electrical resistivity that varies inversely with pressure exerted on the material. 
         [0010]    In U.S. Pat. No. 7,201,063, Apr. 10, 2007, Normal Force Gradient/Shear Force Sensors And Method Of Measuring Internal Biological Tissue Stress, the present inventor disclosed a normal force gradient/shear force sensor device and measurement method for measuring internal stresses in tissues of a person supported by a chair or bed. The device includes a planar matrix array of peripheral normal force sensors radially spaced from central shear force sensors, each including an electrically conductive disk located within a circular opening bordered by circumferentially spaced apart peripheral electrodes. The disk and peripheral electrodes are located between upper and lower cover sheets made of a stretchable material such as polyurethane, one cover sheet being adhered to the disk and the other sheet being adhered to a support sheet for the electrodes. Motion between the cover sheets in response to shear forces exerted on the array causes the disk to press more or less tightly against the peripheral electrodes, thus varying electrical conductance between the disk and electrodes proportionally to the magnitude and direction of the shear force. Each normal force sensor includes an electrically conductive film pressed between row and column conductors. Measurements of conductance values of pairs of sensors, which vary proportionally to normal forces exerted on the sensor, are used to calculate gradient vectors of normal forces exerted by a body part on the sensor array, which is combined with the shear force vectors in an algorithm to calculate internal reaction shear forces, e.g., on flesh near a bony prominence. 
         [0011]    In co-pending U.S. patent application Ser. No. 12/075,937, filed Mar. 15, 2008, the present inventor disclosed an Adaptive Cushion Method And Apparatus For Minimizing Force Concentrations On A Human Body. That apparatus included an adaptive cushion for placement on a mattress or chair, the cushion having a matrix of air bladder cells which are individually pressurizable to variable pressures by means of an air compressor and valves. The apparatus disclosed in that application also included a flexible, stretchable planar array of force sensor transducers of novel construction, which is preferably positioned on the upper surface of the cushion, the array having at least one sensor in vertical alignment with each air bladder cell of the cushion. 
         [0012]    The sensor array disclosed in the above-cited patent application included stretchable fabric row and column conductors which have sandwiched between inner facing conductive surfaces thereof a stretchable fabric sheet coated with a piezoresistive material. Thus constructed, the planar sensor array is elastically deformable in response to forces exerted on the array by the weight of a human body supported on the upper surface of the sensor array overlying the air bladder cells. Preferably, the sensor array is placed on the upper surfaces of the air bladder cells and maintained in that position by a form-fitting, waterproof, contour sheet. The fabric matrices for both row and column conductors, as well as the central piezoresistive layer, are all made of a material which is elastically deformable in any direction within the plane of the material. In a preferred embodiment, the fabric matrices or the row conductor sheet and column conductor sheet are plated with a copper base coat and nickle cover coat. The central piezoresistive sheet consists of a synthetic fabric matrix coated with piezoresistive coating. The sensor array also has an upper cover sheet which is made of a fabric such as Lycra which has a two-way stretch characteristic, i.e., is elastically stretchable in orthogonal directions. 
         [0013]    To avoid cross-talk between measurements of the resistance of individual sensors in the array, by which measurements forces exerted on the sensors are determined, the sensors were constructed in a novel way which gave them non-bilateral, asymmetric current-versus-voltage impedance characteristics. Asymmetric impedance was produced by modifying the sensors to have a diode-like characteristic, by altering either the upper or lower surface of the central piezoresistive sheet to form thereon a P-N, semiconductor-type junction, by a novel method described in detail in the disclosure of that application. 
         [0014]    The flexible force sensor arrays described above have proven highly effective in performing their intended functions. However, there were situations in which it would be desirable to have available force sensor arrays with somewhat different characteristics not offered by prior sensor arrays. 
         [0015]    For example, if typical previously existing flexible sensor arrays are used to measure pressures exerted on a human body by a very form-fitting, conformal wheelchair seat cushion or extremely low pressure bed mattress or cushion, such sensor arrays often interfere with the function of the cushion or bed support surface, and give erroneous force measurements which are used to map the way the bed or chair supports a person. Such errors result from a “hammocking” effect, in which a flexible but not drapable sensor array deployed between fixed support positions cannot conform precisely to the shape of a patient. This effect can occur for example, using sensor arrays that use wire core sensing elements which make the arrays essentially non-stretchable. The lack of conformability of a sensor array alters the way a cushion or bed supports a patient, and also frequently results in forces or pressures exerted on individual sensors in the array being larger than a patient would actually encounter in the absence of the sensor array. 
         [0016]    Another situation in which previous force sensor arrays for measuring and mapping forces exerted on human body parts are less than satisfactory occurs when attempting to make such measurements in a non-obtrusive, non-interfering manner on body parts which have complex shapes such as the feet. 
         [0017]    For example, people who have diabetes often lose feeling sensation in their feet. Since they cannot feel when an ill-fitting shoe is exerting excessive pressure on parts of the foot, the pressure spots can lead to ulcers, which may in turn necessitate amputation of the foot. Accordingly, to prevent such undesirable results, it would be desirable to have a sensor array which could be used to identify such problems, so that corrective actions such as changing the size or shape of a shoe may be taken in a timely manner. 
         [0018]    To address the problem of measuring and mapping forces exerted on complex shapes having compound curves, such as a human foot, the present inventor disclosed in co-pending application Ser. No. 12/380,845 force or pressure sensor arrays which have elastically stretchable electrically conductive polymer threads disposed in parallel rows and columns that contact at intersections thereof a piezoresistive material which has an electrical resistivity which varies inversely with pressure or force exerted thereon to form a matrix array of force or pressure sensor elements. The threads are fixed to a single one or pair of flexible elastically stretchable substrate sheets made of thin sheets of an insulating polymer such as PVC, or for greater elasticity and conformability to irregularly-shaped objects such as human body parts, an elastically stretchable fabric such as LYCRA or SPANDEX. Elastic stretchability of the sensor arrays is optionally enhanced by disposing either or both row and column conductive threads in sinuously curved, serpentine paths rather than straight lines. 
         [0019]    The present invention was conceived of to provide highly flexible force/pressure sensors which have a wide dynamic range. at least partially in response to the unavailability of present sensor arrays to fulfill the requirements described above. 
       OBJECTS OF THE INVENTION 
       [0020]    An object of the present invention is to provide thin, flexible force or pressure sensors which are conformable to objects having complex, compoundly curved shapes such as human body parts, to facilitate measuring and mapping forces or pressures exerted on such objects, and which have a wide dynamic range. 
         [0021]    Another object of the invention is to provide thin, flexible pressure or force sensors which consist of transducers that vary in capacitance and/or electrical conductance in a predetermined way as a function of external normal forces or pressures exerted on the sensors. 
         [0022]    Another object of the invention is to provide an apparatus for measuring forces or pressures which includes in combination a sensor which varies both capacitance and conductance as a function of applied force or pressure, and circuitry for measuring the impedance of the sensor at two different discrete frequencies to obtain separate measurements of capacitive and conductive components of the sensor impedance. 
         [0023]    Various other objects and advantages of the present invention, and its most novel features, will become apparent to those skilled in the art by perusing the accompanying specification, drawings and claims. 
         [0024]    It is to be understood that although the invention disclosed herein is fully capable of achieving the objects and providing the advantages described, the characteristics of the invention described herein are merely illustrative of the preferred embodiments. Accordingly, we do not intend that the scope of my exclusive rights and privileges in the invention be limited to details of the embodiments described. We do intend that equivalents, adaptations and modifications of the invention reasonably inferable from the description contained herein be included within the scope of the invention as defined by the appended claims. 
       SUMMARY OF THE INVENTION 
       [0025]    Briefly stated, the present invention comprehends small thin, flexible force or pressure sensing sensors or transducers which are useable to measure normal forces or pressures exerted on individual areas of an object such as a human body supported by a bed or chair. Novel force or pressure sensors according to the present invention have a novel design and construction in which the electrical capacitance of the sensor varies in a repeatable fashion as function of normal force or pressure applied to the sensor, a property which may be referred to as piezocapacitance. This property enables the sensor to measure force or pressure exerted on the sensor by applying an alternating voltage or current to terminals of the sensor and measuring the output current or voltage of the sensor, which varies with force or pressure according to a transfer function that has been previously obtained for the sensor by a calibration procedure in which the impedance of the sensor is measured and recorded for a sequence of known calibrating forces or pressures applied to the sensor. 
         [0026]    Individual sensors, according to the present invention are readily configurable into a planar array of individual sensors, which facilitates obtaining a pressure or force map that may be used to quantify distribution of pressures or forces exerted on a human body by a supporting bed or chair. 
         [0027]    Preferred embodiments of force or pressure sensing transducers or sensors according to the present invention have a novel hybrid construction which includes a piezoresistive characteristic, thus resulting in a sensor in which both the d.c conductance as well as the electrical capacitance vary as a function of applied normal force or pressures. The combined variation of conductance and capacitance affords increased versatility to the hybrid sensors, including wider dynamic ranges. 
         [0028]    A basic embodiment of a piezocapacitive pressure sensor according to the present invention has a flat laminated structure which includes a base electrode consisting of a thin, flexible electrically conductive fabric or film sheet, a thin, flexible dielectric layer conformally overlying the base electrode lamination, and a thin, flexible electrically conductive fabric or film sheet upper, outer or cover electrode lamination which overlies the upper surface of the dielectric layer. 
         [0029]    The upper and lower electrically conductive sheets of the piezocapacitance sensor each consist of a thin, flexible sheet of conductive fabric such as a fabric woven from silver plated nylon threads. The dielectric layer of the sensor consists of a thin sheet, e.g., 0.010 inch thick, of an elastically deformable, open-cell polyurethane foam. In preferred embodiments of flexible piezocapacitive sensors according to the present invention, active elements of the sensor including upper and lower conductive sheets with a dielectric layer sandwiched between them are protected from external environmental influences such as humidity by being encapsulated in a flat envelope. The encapsulating envelope consists of thin upper and lower rectangular-shaped cover sheets made of a liquid and air impervious material such as polyurethane film, the peripheral edges of which are sealed together by suitable means such as adhesive or thermal bonding. Electrical connections are made to the upper and lower electrode laminations by means of rectangular tabs which are continuous with the upper and lower conductive sheets, and which extend outwards of the peripheral seals between the upper and lower cover sheets. 
         [0030]    In preferred embodiments of piezocapacitive force sensors according to the present invention, the dielectric foam core contains a regular array of multiple, laterally spaced apart circular perforations which have total area of about 50 percent of the area of the core, and the core is saturated with a liquid dielectric such as glycerin. 
         [0031]    Preferred embodiments of hybrid sensors according to the present invention include a thin, flat laminated piezoresistive section which is located below or above the piezocapacitive section. The piezoresistive section is similar in construction to the piezocapacitive section, with the exception that the foam layer of the piezoresistive section is impregnated with a piezoresistive substance such as carbon black. 
         [0032]    In a preferred, “leaky dielectric” variation of a hybrid force sensor according to the present invention, a single active center layer is provided which consists of a foam pad saturated with a dielectric liquid such as glycerin which holds in suspension a piezoresistive substance such as carbon black. 
         [0033]    According to the invention, the capacitance and conductance of the sensors are both proportional to external normal forces or pressures exerted on the sensors. Therefore, the magnitude of external forces or pressures exerted on the sensors can be accurately determined by measuring the conductance of a sensor using an applied d.c. voltage or a low frequency alternating current test signal having a frequency of, for example, 1 Hz to 30 Hz, while the capacitance of a sensor can be measured by applying a higher frequency alternating current test voltage or current of, for example, 30 KHz. Moreover, combinations of d.c. or lower frequency test voltages or currents may be applied to a sensor simultaneously or sequentially with higher frequency test voltages or currents to determine force or pressure exerted on the sensor. 
         [0034]    Optionally, a fixed value of resistance may be actually or computationally inserted in series with a sensor according to the present invention. Adding such a series resistance has been found to be effective in reducing hysterisis and increasing linearly of the sensor response. 
         [0035]    Also, it has been found that linearity can be increased and hysterisis reduced by multiplying resistive and capacitive transfer functions of a sensor, with or without a series resistance. 
         [0036]    The present inventors have also found that providing a hybrid sensor which varies both in capacitance and conductance in response to external forces or pressures exerted on the sensor affords significant advantages over sensors which vary only in capacitance or conductance. Specifically, it has been found by the present inventors that in sensors according to the present invention, response time to pressure impulses and linear dynamic range regions, among other parameters, vary differently for the conductive and capacitive sections of the hybrid sensors. These variations enable adaptive optimization of sensor accuracy, repeatability, and response time by judicious choices of combinations of the frequencies of voltages or currents used to sample the sensors. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0037]      FIG. 1  is an exploded perspective view of a basic embodiment of a, piezocapacitive force sensor according to the present invention. 
           [0038]      FIG. 2  is a vertical sectional view of the sensor of  FIG. 1 . 
           [0039]      FIG. 3  is an exploded perspective view of a modification of the basic embodiment of a piezocapacitive sensor of  FIGS. 1 and 2 , in which a central foam dielectric pad thereof is perforated. 
           [0040]      FIG. 4  is a vertical sectional view of the sensor of  FIG. 3 . 
           [0041]      FIG. 5  is an exploded perspective view of another modification of the sensor of  FIGS. 1 and 2 , consisting of a basic embodiment of a hybrid piezocapacitive, piezoresistive force sensor according to the present invention. 
           [0042]      FIG. 6  is a vertical sectional view of the hybrid sensor of  FIG. 5 . 
           [0043]      FIG. 7  is an exploded perspective view of a leaky dielectric embodiment of a hybrid piezocapactive-piezoresistive sensor according to the present invention, which has a single layer foam dielectric pad that has both piezocapacitive and piezoresistive properties 
           [0044]      FIG. 8  is a vertical sectional view of the sensor of  FIG. 7   
           [0045]      FIG. 9  is a schematic diagram of an apparatus according to the present invention useable both for determining transfer functions of the sensors shown in  FIGS. 1-8 , and for measuring forces exerted on the sensors. 
           [0046]      FIG. 10A  is a graph showing capacitance versus applied pressure for the basic embodiment of the piezocapacitive sensor shown in  FIGS. 1 and 2 . 
           [0047]      FIG. 10B  is a graph showing capacitance of the basic embodiment of the piezocapacitive sensor shown in  FIGS. 1 and 2  plotted as a function of increasing and decreasing normal force/pressure applied to the sensor, using the test circuitry shown in  FIG. 9 . 
           [0048]      FIG. 11A  is a graph showing capacitance versus normal force/pressure for the second embodiment of the sensor shown in  FIGS. 3 and 4 . 
           [0049]      FIG. 11B  is a graph showing capacitance versus increasing and decreasing pressures for the sensor of  FIGS. 3 and 4 , using the test circuitry shown in  FIG. 9 . 
           [0050]      FIG. 12  is a graph showing capacitance versus normal force/pressure for a first variation of the sensor of  FIGS. 3 and 4 , filled with glycerin. 
           [0051]      FIG. 13  is a graph showing capacitance versus normal force/pressure for a second variation of the sensor of  FIGS. 3 and 4 , filled with glycerin and iodine. 
           [0052]      FIG. 14  is a graph showing capacitance versus normal force/pressure for the hybrid sensor of  FIGS. 5 and 6 . 
           [0053]      FIG. 15  is a graph showing conductance versus applied normal force/pressure for the hybrid sensor of  FIGS. 5 and 6 . 
           [0054]      FIG. 16  is a graph showing capacitance versus normal force/pressure for the leaky dielectric sensor of  FIGS. 7 and 8 . 
           [0055]      FIG. 17  is a graph showing conductance versus normal force/pressure for the leaky dielectric sensor of  FIGS. 7 and 8 . 
           [0056]      FIG. 18  is a graph showing both conductance and capacitance plotted as a function of applied normal pressure for the leaky dielectric sensor of  FIGS. 7 and 8 . 
           [0057]      FIG. 19  is a variation of  FIG. 18 , in which the product of conductance and capacitance for the leaky dielectric sensor of  FIGS. 7 and 8  is plotted. 
           [0058]      FIG. 20  is a graph showing a plot of capacitance versus applied normal force/pressure for another modified configuration of the hybrid sensor of  FIGS. 5 and 6 , in which the piezoresistive and piezocapacitive layers are connected in parallel to configure the sensor as a two-terminal device, measured at 30 KHz, and a plot showing conductance versus pressure for the hybrid sensor of  FIGS. 5 and 6  configured as a two-terminal device, measured at 3 Hz. 
           [0059]      FIG. 21  is a graph similar to that of  FIG. 20 , but with the sensors of  FIGS. 5 and 6  modified by insertion of a 10,000 ohm resistor in series with the piezoresistive layer of the sensor. 
           [0060]      FIG. 22  is an exploded view of a simplified modification of the leaky dielectric sensor of  FIG. 7 . 
           [0061]      FIG. 23  is a vertical sectional view of the simplified leaky dielectric sensor of  FIG. 22 . 
           [0062]      FIG. 24  is a graph showing capacitance versus pressure for the sensor of  FIGS. 22 and 23 , measured at 30 KHz. 
           [0063]      FIG. 25  is an expanded scale version of  FIG. 24  showing capacitance versus pressure on sensor  450  for a smaller range of pressures. 
           [0064]      FIG. 26  is a plot of conductance versus increasing and decreasing pressure on the simplified leaky sensor  450 . 
           [0065]      FIG. 27  is a plot of the product of conductance times capacitance versus increasing and decreasing pressures on the simplified leaky sensor  450 . 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Example 1 
       [0066]      FIGS. 1 and 2  illustrate a basic embodiment of a piezocapacitive force sensor according to the present invention.  FIGS. 3 and 4  illustrate a first modification of the embodiment of  FIGS. 1 and 2 , which has a perforated foam dielectric layer.  FIGS. 5 and 6  illustrate a basic embodiment of a hybrid piezocapacitive-piezoresistive force sensor according to the present invention.  FIGS. 7 and 8  illustrate a variation of the hybrid sensor of  FIGS. 5 and 6 , which has a single layer which is both piezocapacitive and piezoresistive. 
         [0067]    Referring first to  FIGS. 1 and 2 , it may be seen that a basic embodiment  50  of a piezocapacitive force/pressure sensor according to the present invention includes a first, base, lower or inner flexible conductive sheet  51  which functions as the first conductive plate of a capacitor. Base conductive sheet  51  s preferably made of a thin, flexible, elasticity stretchable fabric which is electrically conductive. In an example embodiment of sensor  50 , base conductive sheet consisted of a square piece 2 inches on a side of a woven electrical conductive fabric made of silver plated nylon threads, having a thickness of 0.4 mm, a weight per unit/area of 4.3 oz. per square yard, and a surface resistance of about 0.5 ohms per square. The foregoing fabric is available from LESS EMF corporation, 809 Madison Ave., Albany, N.Y. 12208 as catalog or part number A321. 
         [0068]    As shown in  FIG. 1 , base conductor sheet  51  has a front laterally disposed edge  52 , a parallel rear laterally disposed edge  53 , and left and right parallel fore-and-aft disposed edges  54 ,  55 . 
         [0069]    Referring to  FIGS. 1 and 2 , it may be seen that base conductor sheet  51  has an integral rectangular-shaped conductive fabric connector tab  56  which is coplanar with and protrudes perpendicularly outwards from a corner part of the square conductor sheet. Thus, as shown in  FIG. 1 , base connector tab  56  has a front laterally disposed edge  57  which is a collinear extension of front edge  52  of base conductor sheet  51 , an outer fore-and-aft disposed edge  58  parallel to and offset laterally to the right of right-hand edge  55  of the base conductor sheet  51 , and a laterally inwardly extending rear edge  59  which is parallel to front edge  57 . 
         [0070]    Referring to  FIGS. 1 and 2 , it may be seen that sensor  50  includes a dielectric pad or core  60  which is supported on the upper surface  61  of base conductor sheet  51 . As shown in the figures, dielectric pad  60  preferably has approximately the same outline shape and size, e.g., a 2 inch square, as base conductor sheet  51 , so that the dielectric pad seats congruently of the base conductor sheet. In an example embodiment of sensor  50 , dielectric pad  60  consisted of 2-inch square piece of polyurethane open-cell foam having a thickness of about 0.025 inch. The dielectric pad  60  was cut from a piece of open cell polyurethane foam having a density of about 28.52 kg/cubic meter, obtained from Burnett and Company, Foam Division, 2112 Montevideo Road, Jussea, Md. 20794, stock number S8ZJJ. The dielectric pad  60  had a dielectric constant or relative permittivity of about 4. 
         [0071]    Referring to  FIG. 1 , it may be seen that piezocapacitive sensor  50  has an upper or outer flexible conductive sheet  71  which functions as the second or outer conductor plate of a capacitor. Outer flexible conductive sheet  71  may and preferably is substantially identical in construction to base conductive sheet  51 . However, as shown in  FIG. 1 , upper or outer flexible conductive sheet  71  is preferably flipped over and rotated 90 degrees relative to base conductive sheet, so that a connector tab  76  of the upper conductive sheet extends forward from the front edge of sensor  50 , so that it does not overly the rightwardly extending connector tab  56  of base conductive sheet  51 . 
         [0072]    As shown in  FIGS. 1 and 2 , upper or outer conductive sheet  71  has a lower flat surface  77  which contacts upper flat surface  78  of dielectric pad  60 , and dielectric pad  60  has a lower surface  79  which contacts upper surface  61  of base conductive sheet. As shown in  FIG. 2 , the sandwiched relationship between base conductive sheet  51 , dielectric pad  60 , and outer conductive sheet  71  is preferably maintained by restraining the foregoing three elements against relative movement by encapsulating them in a flat flexible envelope  80 . 
         [0073]    Thus, as shown in  FIGS. 1 and 2 , encapsulating envelope  80  includes upper and lower flexible liquid impervious polyurethane cover sheets  81 ,  82  made of 2-mil thick polyurethane film. Upper and lower encapsulating polyurethane sheets  81 ,  82  preferably have a square shape, and are slightly larger than upper conductive sheet  71 , dielectric pad  60  and base conductive sheet  51 . This size relationship enables front, rear, left and right outer peripheral edges  91 ,  92 ,  93 ,  94  of upper encapsulating cover sheet  81  to be sealingly joined by adhesive, ultrasonic bonding, or other suitable techniques to corresponding outer peripheral edges  101 ,  102 ,  103 ,  104  of lower encapsulating cover sheet  82 . 
         [0074]      FIG. 9  is a schematic diagram of a novel pressure measurement apparatus according to the present invention, showing how the sensor of  FIGS. 1 and 2  may be connected to test circuitry to measure capacitance, conductance or admittance versus external normal force or pressure exerted on the sensor from which measurements the transfer function of the sensor may be plotted. The apparatus is also useable to measure forces or pressures exerted on sensors for which the impedance-versus-force transfer function has been previously determined. 
         [0075]    As shown in  FIG. 9 , apparatus  110  includes a selectable frequency signal generator  111  which outputs a sinusoidal current that is adjustable to a selectable voltage V1, measured by a voltmeter  112 . Signal generator  111  has connected in series with output terminal  113  thereof a variable voltage d.c. power supply  114  which outputs a voltage selectable between zero and a predetermined maximum value. The output terminal  115  of d.c. power supply  114  is connected to one terminal, e.g., upper connector tab  76  of a capacitive sensor  50 . The opposite terminal, e.g. lower connector tab  56  of the sensor  50  is connected through a current sampling resistor  116  to the lower or ground output terminal  117  of signal generator  111 . 
         [0076]    Current flowing through sensor  50  in response to a d.c. voltage a.c. voltage, or combination of both a.c. and d.c. voltages applied to terminals  76 - 56  of the sensor, is measured by measuring the voltage drop V2 across resistor  116  using a voltmeter  118 . Thus the d.c. conductance of sensor  50  may be measured by applying a d.c. voltage or low-frequency A.C. signal to the sensor. The a.c. conductance or susceptance, which is proportional to capacitance, may be measured by applying a higher frequency test voltage to the terminals of sensor  50 , or, alternatively, by substituting a capacitance meter or bridge for the signal generator  111 . 
         [0077]    Table 1A lists values of capacitance measured by a capacitance meter of the sensor  50  shown in  FIGS. 1 and 2 , as a function of increasing applied pressure. 
         [0078]      FIG. 10A  is a graph showing the variation of capacitance measured by a capacitance meter of the sensor  50  shown in  FIGS. 1 and 2 , as a function of increasing applied pressure. 
         [0079]    Table 1B lists values of voltage ratios V 2 /V 1 , which are proportional to susceptance and hence capacitance, for increasing and decreasing values of normal force or pressure applied to the sensor shown in  FIGS. 1 and 2  and described above, as measured by test circuitry  110  shown in  FIG. 9 . 
         [0080]    Referring to  FIG. 9 , the total impedance seen by signal generator  111  is: 
         [0000]        Z   t =√{square root over ( R   1   2   +Z   s   2 )}
 
         [0000]      where 
         [0000]        Z   s =√{square root over ( R   s   2   +X   s   2 )}
 
         [0000]    and
 
R s  is the resistive component of sensor impedance Z s , and X s  is the capacitive reactive component of sensor impedance Z s  i.e.,
 
         [0000]        X   s =½ πfC   s  
 
         [0000]    where f is the signal generator frequency and C s  is the capacitance of the sensor. 
         [0081]    The current I s  through sampling resistor R 1  and sensor  50  is: 
         [0000]        I   s   =V   1   /Z   t , 
         [0000]    and for R 1  selected to be much smaller than Z s , 
         [0000]        I   s   =V   1   /Z   s . 
         [0082]    For the capacitance component of sensor impedance, Z s , I s =V 1 ×(B s ), where B s  is the susceptance of the capacitive component of the sensor, 
         [0000]        Bs= 2 πfC   s . 
         [0083]    For the resistive component of sensor impedance Z s , 
         [0000]        I   s   =V   1   G   s , 
         [0000]    where G s  is the d.c. conductance of the sensor. 
         [0084]    Referring to  FIG. 9 , 
         [0000]        V   2   =I   s   R   1   =V   1 2 πfC   s   R   1    
         [0000]    for the capacitance component of a sensor, and 
         [0000]    
       
      
       V 
       2 
       =I 
       s 
       R 
       1 
       =V 
       1 
       G 
       s 
       R 
       1  
      
     
         [0000]    for the resistive component. Thus, the capacitance of a sensor may be calculated from the equation: 
         [0000]        C   s =( V   2   /V   1 )(2 πfR   1 ), 
         [0000]      or 
         [0000]        Cs=k   1 ( V   2   /V   1 ); 
         [0000]    for f=30 KHz and R=1000 ohm,
 
k 1 =5.305×10 −9  farads=5.305 nanofarads, and for V 1 =9 volts, C s =k C ×V 2 =0.5895 nf/volt. For the resistance component of sensor, G s =V 2 /V 1 R 1 , R 1 =1,000 ohms, V 1 =9 volts; G s =k g (V 2 )=0.1111 millimhos/volt.
 
         [0085]      FIG. 10B  is a graph which plots the voltage ratios of Table 1 versus external pressure, and thus is a graphical representation of the transfer function of the sensor  50  of  FIGS. 1 and 2 . 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1A 
               
             
             
               
                   
               
               
                 CAPACITANCE VS. PRESSURE OF EXAMPLE 1 (FIGS. 1 and 2) 
               
             
          
           
               
                   
                 Pressure, Psi 
                 Capacitance, nf 
               
               
                   
                   
               
             
          
           
               
                   
                 0 
                 0 
               
               
                   
                 0.66 
                 0.57 
               
               
                   
                 1.29 
                 0.58 
               
               
                   
                 2.66 
                 0.6 
               
               
                   
                 7.33 
                 0.625 
               
               
                   
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 1B 
               
             
             
               
                   
               
               
                 SUSCEPTANCE VS. PRESSURE OF EXAMPLE 1 (FIGS. 1 &amp; 2) 
               
               
                 Source voltage 9 V @ 30 KHz, V2 measured across a 1K ohm 
               
               
                 series resistor 
               
             
          
           
               
                 Load, psi 
                 V2, Volts Up 
                 V2, Volts Down 
               
               
                   
               
             
          
           
               
                 0.008 
                 0.125 
                 0.14 
               
               
                 0.018 
                 0.13 
                 0.16 
               
               
                 0.028 
                 0.14 
                 0.17 
               
               
                 0.038 
                 0.15 
                 0.19 
               
               
                 0.08 
                 0.18 
                 0.23 
               
               
                 0.28 
                 0.28 
                 0.3 
               
               
                 0.48 
                 0.32 
                 0.33 
               
               
                 0.68 
                 0.34 
                 0.345 
               
               
                 0.88 
                 0.35 
                 0.355 
               
               
                 1.2 
                 0.36 
                 0.36 
               
               
                 1.36 
                 0.365 
                 0.365 
               
               
                   
               
             
          
         
       
     
       Example 2 
     Perforated Pad 
       [0086]      FIGS. 3 and 4  illustrate a modification  120  of the sensor  50  shown in  FIGS. 1 and 2 . Modified sensor  120  is substantially similar in construction and function to sensor  50 , with the primary difference being that the central dielectric pad  130  of sensor  120  contains perforations. In an example embodiment of sensor  120 , central dielectric pad  130  had over its full area an array of circular holes  131  through the thickness dimension of the pad. Each hole had a diameter of ½ inch and was spaced apart by ¼ inch from adjacent holes. The holes  131  occupied about 50 percent of the surface area of the pads. 
         [0087]      FIG. 11A  is a plot of capacitance versus applied pressure for sensor  120  shown in  FIGS. 3 and 4 . 
         [0088]    Table 2A lists values of capacitance measured by a capacitance meter of the sensor  120  shown in  FIGS. 3 and 4  as a function of increasing applied pressure. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 2A 
               
             
             
               
                   
               
               
                 CAPACITANCE VS PRESSURE OF EXAMPLE 2 (FIGS. 3 &amp; 4) 
               
             
          
           
               
                   
                 Pressure, psi 
                 Capacitance, nf 
               
               
                   
                   
               
             
          
           
               
                   
                 0 
                 0 
               
               
                   
                 0.166 
                 0.2 
               
               
                   
                 0.833 
                 1.75 
               
               
                   
                 1.33 
                 4 
               
               
                   
                 2.1 
                 8 
               
               
                   
                   
               
             
          
         
       
     
         [0089]    Table 2B and  FIG. 11B  show the variation of voltage ratios V 2 /V 1  proportional to capacitance of sensor  120  as a function of increasing (up) and decreasing (down) external pressure exerted on the sensor, i.e., the tabulated and graphical representations of the transfer function of the sensor. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 2B 
               
             
             
               
                   
               
               
                 SUSCEPTANCE VS. PRESSURE OF EXAMPLE 2 (FIGS. 3 &amp; 4) 
               
               
                 Source Voltage 9 V @ 30 KHz, 
               
               
                 V2 measured across a 1K ohm series resistor 
               
             
          
           
               
                 Load, psi 
                 V2, Volts (Up) 
                 V2, Volts (Down) 
               
               
                   
               
             
          
           
               
                 0 
                 0.07 
                 0.064 
               
               
                 0.008 
                 \0.13 
                 0.118 
               
               
                 0.018 
                 0.15 
                 0.136 
               
               
                 0.028 
                 0.165 
                 0.15 
               
               
                 0.038 
                 0.18 
                 0.164 
               
               
                 0.06 
                 0.215 
                 0.195 
               
               
                 0.236 
                 0.375 
                 0.341 
               
               
                 0.412 
                 0.48 
                 0.48 
               
               
                 0.588 
                 0.53 
                 0.53 
               
               
                 0.764 
                 0.55 
                 0.55 
               
               
                 0.962 
                 0.58 
                 0.58 
               
               
                   
               
             
          
         
       
     
       Example 3 
     Perforated Pad Saturated with Glycerine 
       [0090]      FIG. 12A  and table 3 show the variation of capacitance versus external force or pressure for a first variation  120 A of the sensor  120  (Example 3) of  FIGS. 3 and 4 , in which the central perforated dielectric pad  130  thereof had a weight of about 1 gram and was saturated with 2 grams of glycerin. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 CAPACITANCE VS PRESSURE OF EXAMPLE 3 (FIGS. 3 &amp; 4 
               
             
          
           
               
                   
                 Pressure, psi 
                 Capacitance, nf 
               
               
                   
                   
               
             
          
           
               
                   
                 0 
                 6 
               
               
                   
                 0.166 
                 8 
               
               
                   
                 0.833 
                 14 
               
               
                   
                 1.33 
                 6.25 
               
               
                   
                 2.1 
                 18 
               
               
                   
                   
               
             
          
         
       
     
       Example 4 
     Perforated Pad Saturated with Glycerine Doped with Iodine 
       [0091]      FIG. 13A  and table 4 show the variation of capacitance versus external force or pressure for a second variation  120 B of sensor  120  (Example 4) shown in  FIGS. 3 and 4 , in which the central perforated dielectric pad  130  thereof was saturated with 1 gram of glycerine doped with 1 gram of a 2.5% solution of iodine in isopropyl alcohol. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 CAPACITANCE VS PRESSURE OF EXAMPLE 4 (FIGS. 3 &amp; 4 
               
             
          
           
               
                   
                 Pressure, psi 
                 Capacitance, nf 
               
               
                   
                   
               
             
          
           
               
                   
                 0 
                 9 
               
               
                   
                 0.166 
                 16.25 
               
               
                   
                 0.833 
                 22 
               
               
                   
                 1.33 
                 30 
               
               
                   
                 2.1 
                 44 
               
               
                   
                   
               
             
          
         
       
     
       Example 5 
     Hybrid Piezocapacitive/Piezoresistive 
       [0092]      FIGS. 5 and 6  illustrate a basic embodiment of a hybrid or composite piezocapacitive-piezoresistive force/pressure sensor  240  according the present invention, which has separate pressure sensing layers. 
         [0093]    As shown in  FIGS. 5 and 6 , hybrid or composite piezocapacitive-piezoresistive sensor  240  includes a first pressure sensing layer consisting of a piezocapacitive section  250  which is substantially identical in construction and function to the modified sensor  120  shown in  FIGS. 3 and 4 . Preferably, piezocapacitance section  250  is similar to the first variation  120 A of sensor  120  described above in which a central perforated foam dielectric pad  260  thereof is saturated with 2 grams of glycerin. 
         [0094]    Referring to  FIGS. 5 and 6 , it may be seen that hybrid sensor  240  includes a second pressure sensing layer consisting of a piezoresistive section  280  which is positioned below piezocapacitive sensor section  250 . However, the location of piezoresistive section  280  relative to piezocapacitive section  250  is not critical, and may optionally be positioned above the piezocapacitive section. 
         [0095]    As shown in  FIGS. 5 and 6 , piezoresistive section  280  of hybrid sensor  240  has a laminated construction which is similar to that of piezocapacitive section  250 . Thus, piezoresistive section  280  has a lower, or base conductive sheet  291  which consists of a thin, square sheet of conductive stretchy fabric which is substantially identical to upper conductive sheet  71  of sensor  50 , and upper conductive sheet  271  of piezocapacitive section  250  of hybrid sensor  240 . Piezoresistive section  280  includes an upper conductive sheet  311  which is substantially identical to lower, base conductive sheet  251  of piezocapacitive sensor  250 . Preferably, upper conductive sheet  311  of piezoresistive section  280  and lower or base conductive sheet  251  of piezocapacitive section  250  comprise a single element  251 - 311 . 
         [0096]    Referring still to  FIGS. 5 and 6 , it may be seen that piezoresistive section  290  of hybrid sensor  240  includes a piezoresistive pad or core  390  which is supported on the upper surface  301  of base conductor sheet  291 . As shown in the figures, piezoresistive pad  390  preferably has the same outline shape and size, e.g., a 2-inch square, as base conductor sheet  291 . In an example embodiment of sensor  240 , piezoresistive pad  390  consisted of a 2-inch square piece of type S8ZJJ polyurethane foam having a thickness of about 0.025 inch. The pad  390  was cut from a piece of unperforated foam which was impregnated with 2 grams of carbon lamp black having a particle size range of about 20 nm to about 40 nm. 
         [0097]    Table 5 and  FIG. 14  show the variation of voltage ratios V 2 /V 1  measured at 30 KHZ, proportional to admittance and hence capacitance, for increasing and decreasing pressure exerted on piezocapacitive section  150  of hybrid sensor  240 , Example 5. 
         [0098]    Table 6 and  FIG. 15  show the variation of conductance measured at 10 KHZ versus external pressure exerted on the piezocapacitive section  250  and piezoresistive section  280  of hybrid sensor  240 , Example 5, measured for increasing and decreasing pressures. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 CAPACITANCE VS. PRESSURE OF EXAMPLE 5 (FIGS. 5 &amp; 6) 
               
               
                 Admittance Measured @ 30 KHz 
               
             
          
           
               
                 Pressure, psi 
                 V2, Up 
                 V2, Down 
               
               
                   
               
             
          
           
               
                 0.00 
                 0.2 
                 0.25 
               
               
                 000 
                 0.3 
                 0.3 
               
               
                 0.01 
                 0.35 
                 0.45 
               
               
                 0.02 
                 0.4 
                 0.575 
               
               
                 0.03 
                 0.45 
                 0.6 
               
               
                 0.04 
                 0.525 
                 0.625 
               
               
                 0.06 
                 0.575 
                 0.65 
               
               
                 0.07 
                 0.6 
                 0.675 
               
               
                 0.08 
                 0.65 
                 0.7 
               
               
                 0.12 
                 0.7 
                 0.8 
               
               
                 0.31 
                 0.9 
                 1.05 
               
               
                 0.49 
                 1.05 
                 1.15 
               
               
                 0.68 
                 1.2 
                 1.2 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 CONDUCTANCE VS. PRESSURE OF EXAMPLE 5 (FIGS. 5 &amp; 6) 
               
             
          
           
               
                 Pressure, Psi 
                 V2, Up 
                 V2, Down 
               
               
                   
               
             
          
           
               
                 0.00 
                 0 
                 0 
               
               
                 0.005 
                 0.005 
                 0.025 
               
               
                 0.01 
                 0.01 
                 0.05 
               
               
                 0.02 
                 0.05 
                 0.075 
               
               
                 0.03 
                 0.075 
                 0.1 
               
               
                 0.04 
                 0.1 
                 0.125 
               
               
                 0.06 
                 0.125 
                 0.15 
               
               
                 0.07 
                 0.175 
                 0.175 
               
               
                 0.08 
                 0.2 
                 0.2 
               
               
                 0.12 
                 0.225 
                 0.25 
               
               
                 0.31 
                 0.4 
                 0.55 
               
               
                 0.49 
                 0.6 
                 0.75 
               
               
                 0.68 
                 0.8 
                 0.8 
               
               
                   
               
             
          
         
       
     
       Example 6 
     Leaky Dielectric 
       [0099]      FIGS. 7 and 8  illustrate another embodiment  350  of a hybrid force pressure sensor according to the present invention. The embodiment  350  shown in  FIGS. 7 and 8  is structurally similar to the embodiment  120  shown in  FIGS. 3 and 4  and described above. However, embodiment  350  utilizes in place of the foam dielectric pad  130  a “leaky dielectric” pad  360 . 
         [0100]    In an example embodiment  350  of a leaky dielectric piezocapacitive-piezoresistive pressure/force sensor according to the present invention, upper conductive sheet  341  and lower conductive sheet  321  were substantially identical to upper and lower conductive sheets  141 ,  121 , respectively, of the embodiment  120  of a piezocapacitive sensor shown in  FIGS. 3 and 4  and described above. The central dielectric pad  360  of sensor had a composition and construction similar to that of un-perforated open-cell dielectric pad  60  of example 1 made of polyurethane foam shown in  FIGS. 1 and 2 . However, central dielectric pad  360  was treated to give it a piezoresistive characteristic in addition to a piezocapacitive characteristic by thoroughly mixing carbon black particles, of the type described above for example 5, with glycerin, and kneading the mixture of glycerin and carbon black particles into the foam pad. 
         [0101]    Table 7 and  FIG. 16  show the variation of capacitance of leaky dielectric sensor  350  as a function of external pressure exerted on the sensor, measured at a relatively high frequency of 30 KHz and thus displaying the capacitive part of the sensor transfer function 
         [0102]    Table 8 and  FIG. 17  show the variation of conductance of leaky dielectric sensor  350  as a function of external pressure exerted on the sensor, measured at a relatively low frequency of 3 Hz and thus displaying the resistive part of the sensor transfer function. 
         [0103]    Table 9 and  FIG. 18  show the variation of both capacitance and conductance of the leaky dielectric sensor  350  as a function of external pressure exerted on the sensor. 
         [0104]    Table 10 and  FIG. 19  show the variation of the product of susceptance and conductance versus pressure transfer functions of the leaky dielectric sensor  350  as a function of external pressure exerted on the sensor. As may be seen by comparing  FIG. 19  to  FIG. 18 , the product transfer function is substantially more linear and has substantially less hysterisis than either of the individual conductance or susceptance transfer functions. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 EXAMPLE 6 (FIGS. 7 &amp; 8) SUSCEPTANCE 
               
               
                 MEASURED @ 30 KHz Source Voltage 9 V @ 30 KHz, 
               
               
                 V2 measured across a 1K ohm reference resistor 
               
             
          
           
               
                 Pressure, psi 
                 V 2 , Up 
                 V 2 , Down 
               
               
                   
               
             
          
           
               
                 0.00 
                 0.1 
                 0.1 
               
               
                 0.005 
                 0.105 
                 0.105 
               
               
                 0.01 
                 0.11 
                 0.11 
               
               
                 0.02 
                 0.12 
                 0.12 
               
               
                 0.03 
                 0.125 
                 0.125 
               
               
                 0.04 
                 0.15 
                 0.14 
               
               
                 0.06 
                 0.16 
                 0.15 
               
               
                 0.07 
                 0.165 
                 0.17 
               
               
                 0.08 
                 0.17 
                 0.175 
               
               
                 0.12 
                 0.175 
                 0.2 
               
               
                 0.31 
                 0.25 
                 0.35 
               
               
                 0.49 
                 0.325 
                 0.45 
               
               
                 0.68 
                 0.4 
                 0.525 
               
               
                 0.87 
                 0.475 
                 0.6 
               
               
                 1.05 
                 0.55 
                 0.625 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 8 
               
             
             
               
                   
               
               
                 CONDUCTANCE VS PRESSURE OF LEAKY DIELECTRIC 
               
               
                 SENSOR EXAMPLE 6 (FIGS. 7 &amp; 8) MEASURED @ 3 Hz 
               
               
                 Source Voltage 9 V @ 3 Hz, V2 Measured Across A Series 
               
               
                 1K ohm Resister 
               
             
          
           
               
                 Pressure, Psi 
                 V2, Up 
                 V2, Down 
               
               
                   
               
             
          
           
               
                 0.00 
                 0.000 
                 0.000 
               
               
                 0.005 
                 0.000 
                 0.000 
               
               
                 0.01 
                 0.053 
                 0.053 
               
               
                 0.02 
                 0.084 
                 0.105 
               
               
                 0.03 
                 0.105 
                 0.126 
               
               
                 0.04 
                 0.116 
                 0.158 
               
               
                 0.06 
                 0.158 
                 0.211 
               
               
                 0.07 
                 0.189 
                 0.211 
               
               
                 0.08 
                 0.211 
                 0.211 
               
               
                 0.12 
                 0.316 
                 0.316 
               
               
                 0.31 
                 0.526 
                 0.632 
               
               
                 0.49 
                 0.789 
                 0.947 
               
               
                 0.68 
                 0.947 
                 1.158 
               
               
                 0.87 
                 1.158 
                 1.368 
               
               
                 1.05 
                 1.368 
                 1.579 
               
               
                 1.28 
                 1.684 
                 1.684 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 9 
               
             
             
               
                   
               
               
                 SUSCEPTANCE AND CONDUCTANCE OF LEAKY DIELECTRIC 
               
               
                 SENSOR EXAMPLE 6 (FIGS. 7 &amp; 8) 
               
             
          
           
               
                   
                 Susceptance 
                   
                 Conductance 
                   
               
             
          
           
               
                 Pressure, Psi 
                 V2, Up 
                 V2, Down 
                 V2, Up 
                 V2, Down 
               
               
                   
               
             
          
           
               
                 0.00 
                 0.1 
                 0.1 
                 0.000 
                 0.000 
               
               
                 0.005 
                 0.105 
                 0.105 
                 0.000 
                 0.000 
               
               
                 0.01 
                 0.11 
                 0.11 
                 0.053 
                 0.053 
               
               
                 0.02 
                 0.12 
                 0.12 
                 0.084 
                 0.105 
               
               
                 0.03 
                 0.125 
                 0.125 
                 0.105 
                 0.126 
               
               
                 0.04 
                 0.15 
                 0.14 
                 0.116 
                 0.158 
               
               
                 0.06 
                 0.16 
                 0.15 
                 0.158 
                 0.211 
               
               
                 0.07 
                 0.165 
                 0.17 
                 0.189 
                 0.211 
               
               
                 0.08 
                 0.17 
                 0.175 
                 0.211 
                 0.211 
               
               
                 0.12 
                 0.175 
                 0.2 
                 0.316 
                 0.316 
               
               
                 0.31 
                 0.25 
                 0.35 
                 0.526 
                 0.632 
               
               
                 0.49 
                 0.325 
                 0.45 
                 0.789 
                 0.947 
               
               
                 0.68 
                 0.4 
                 0.525 
                 0.947 
                 1.158 
               
               
                 0.87 
                 0.475 
                 0.6 
                 1.158 
                 1.368 
               
               
                 1.05 
                 0.55 
                 0.625 
                 1.368 
                 1.579 
               
               
                 1.28 
                 0.63 
                 0.63 
                 1.684 
                 1.684 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 10 
               
             
             
               
                   
               
               
                 SUSCEPTANCE TIMES CONDUCTANCE VS PRESSURE 
               
               
                 OF LEAKY DIELECTRIC SENSOR EXAMPLE 6 (FIGS. 7 &amp; 8) 
               
             
          
           
               
                 Pressure, Psi 
                 V 2  (Cap) × V 2  (Con) (Down) 
                 V 2  (Cap) × V 2  (Con) (Up) 
               
               
                   
               
             
          
           
               
                 0.00 
                 0.000 
                 0.000 
               
               
                 0.005 
                 0.000 
                 0.000 
               
               
                 0.01 
                 0.006 
                 0.006 
               
               
                 0.02 
                 0.010 
                 0.010 
               
               
                 0.03 
                 0.013 
                 0.013 
               
               
                 0.04 
                 0.017 
                 0.016 
               
               
                 0.06 
                 0.025 
                 0.024 
               
               
                 0.07 
                 0.031 
                 0.032 
               
               
                 0.08 
                 0.036 
                 0.037 
               
               
                 0.12 
                 0.055 
                 0.063 
               
               
                 0.31 
                 0.132 
                 0.184 
               
               
                 0.49 
                 0.257 
                 0.355 
               
               
                 0.68 
                 0.379 
                 0.497 
               
               
                 0.87 
                 0.550 
                 0.695 
               
               
                 1.05 
                 0.753 
                 0.855 
               
               
                 1.28 
                 1.061 
                 1.061 
               
               
                   
               
             
          
         
       
     
       Example 7 
     Modification of Example 5, Hybrid Sensor with Paralleled Sections 
       [0105]    Table 11 and  FIG. 20  show the variation of capacitance and conductance of a variation  240 A of the sensor shown in  FIGS. 5 and 6 , in which the piezoresistive and piezocapacitive layers are electrically paralleled by connecting together their outer terminals  226 , 296 , as shown in hybrid configuration  2  of  FIG. 9 , to configure the sensor as a two terminal device, as a function of applied pressure for test frequencies of 30 KHz and 3 KHz. 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 11 
               
             
             
               
                   
               
               
                 SUSCEPTANCE AND CONDUCTANCE OF HYBRID 
               
               
                 PARALLEL SENSOR EXAMPLE 7 (FIGS. 5 &amp; 6) 
               
             
          
           
               
                   
                 Susceptance 
                   
                 Conductance 
                   
               
             
          
           
               
                 Pressure, psi 
                 V 2 , Up 
                 V 2 , Down 
                 V 2 , Up 
                 V 2 , Down 
               
               
                   
               
             
          
           
               
                 0.00 
                 0.2 
                 0.25 
                 0 
                 0 
               
               
                 0.005 
                 0.3 
                 0.3 
                 0.005 
                 0.025 
               
               
                 0.01 
                 0.35 
                 0.45 
                 0.01 
                 0.05 
               
               
                 0.02 
                 0.4 
                 0.575 
                 0.05 
                 0.075 
               
               
                 0.03 
                 0.45 
                 0.6 
                 0.075 
                 0.1 
               
               
                 0.04 
                 0.525 
                 0.625 
                 0.1 
                 0.125 
               
               
                 0.06 
                 0.575 
                 0.65 
                 0.125 
                 0.15 
               
               
                 0.07 
                 0.6 
                 0.675 
                 0.175 
                 0.175 
               
               
                 0.08 
                 0.65 
                 0.7 
                 0.2 
                 0.2 
               
               
                 0.12 
                 0.7 
                 0.8 
                 0.225 
                 0.25 
               
               
                 0.31 
                 0.9 
                 1.05 
                 0.4 
                 0.55 
               
               
                 0.49 
                 1.05 
                 1.15 
                 0.6 
                 0.75 
               
               
                 0.68 
                 1.2 
                 1.2 
                 0.8 
                 08 
               
               
                 0.87 
                 0 
                 0 
                 0 
                 0 
               
               
                 1.05 
                 0 
                 0 
                 0 
                 0 
               
               
                 1.28 
                 0 
                 0 
                 0 
                 0 
               
               
                   
               
             
          
         
       
     
       Example 8 
     Modification of Example 8 with Series Resistance 
       [0106]    Table 12 and  FIG. 21  show the variation of capacitance and conductance with pressure for a modification  240 B of the parallel two-terminal sensor configuration  240 A, in which a 10,000 Ohm resister is inserted in series with the sensor. As may be seen by comparing  FIG. 21  with  FIG. 20 , the voltage versus pressure transfer function with a 10,000 ohm series resistance is substantially more linear and has substantially less hypersis than the transfer function without a series resistance. Optionally a numerical value of a resistance such as 10,000 ohms may be inserted computationally in series in place of an actual resistance. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 12 
               
             
             
               
                   
               
               
                 CONDUCTANCE VS PRESSURE OF HYBRID SENSOR 
               
               
                 WITH 10K OHM RESISTER IN SERIES EXAMPLE 8 (FIGS. 5 &amp; 6) 
               
               
                 Source Voltage 9 V @ 10 Hz, V2 Measured Across A 50 Ohm 
               
               
                 Reference Resistor 
               
             
          
           
               
                 Pressure, Psi 
                 V 2 , Up 
                 V 2 , Down 
               
               
                   
               
             
          
           
               
                 0.008 
                 0.0006 
                 0.0006 
               
               
                 0.0188 
                 0.0010 
                 0.0010 
               
               
                 0.0288 
                 0.0012 
                 0.0014 
               
               
                 0.0388 
                 0.0015 
                 0.0020 
               
               
                 0.0488 
                 0.0022 
                 0.0025 
               
               
                 0.0588 
                 0.0024 
                 0.0028 
               
               
                 0.0688 
                 0.0031 
                 0.0035 
               
               
                 0.1088 
                 0.0043 
                 0.0057 
               
               
                 0.1488 
                 0.0059 
                 0.0081 
               
               
                 0.1888 
                 0.0077 
                 0.0100 
               
               
                 0.3488 
                 0.0152 
                 0.0164 
               
               
                 0.6688 
                 0.0222 
                 0.0222 
               
               
                   
               
             
          
         
       
     
       Example 9 
       [0107]      FIGS. 22 and 23  illustrate a simplified modification  450  of the leaky sensor  350  shown in  FIGS. 7 and 8  and described above, in which the outer protective envelope is eliminated. 
         [0108]    Table 13 shows the variation of capacitance and conductance of the simplified leaky sensor  450  as a function of increasing and decreasing pressures exerted on the sensor. 
         [0109]      FIG. 24  is a graph showing the variation of capacitance of the simplified leaky sensor  450  as a function of increasing and decreasing pressures exerted on the sensor. 
         [0110]      FIG. 25  is an expanded scale version of  FIG. 24  showing capacitance versus pressure on sensor  450  for a smaller range of pressures 
         [0111]      FIG. 26  is a plot of conductance versus increasing and decreasing pressures on the simplified leaky sensor  450 . 
         [0112]      FIG. 27  is a plot of the product of conductance times capacitance versus increasing and decreasing pressures on the simplified leaky sensor  450 . 
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 13 
               
             
             
               
                   
               
               
                 CONDUCTANCE AND SUSCEPTANCE OF SIMPLIFIED 
               
               
                 LEAKY DIELECTRIC SENSOR EXAMPLE 9 (FIGS. 22 &amp; 23) 
               
             
          
           
               
                   
                 G × B 
               
             
          
           
               
                 Pressure, 
                 Conductance (G) 
                 Susceptance (B) 
                 V 2  (s) × V 2  © 
                 V 2  (s) × V 2  © 
               
             
          
           
               
                 Psi 
                 V 2,  Up 
                 V 2,  Down 
                 V 2,  Up 
                 V 2,  Down 
                 Up 
                 Down 
               
               
                   
               
             
          
           
               
                 0.00 
                 0.1 
                 0.1 
                 0.1111 
                 0.1111 
                 0.01111 
                 0.01111 
               
               
                 0.005 
                 0.105 
                 0.105 
                 0.1167 
                 0.1167 
                 0.012254 
                 0.012254 
               
               
                 0.01 
                 0.11 
                 0.11 
                 0.1222 
                 0.1222 
                 0.013442 
                 0.013442 
               
               
                 0.02 
                 0.12 
                 0.12 
                 0.1333 
                 0.1333 
                 0.015996 
                 0.015996 
               
               
                 0.03 
                 0.125 
                 0.125 
                 0.1389 
                 0.1389 
                 0.017363 
                 0.017363 
               
               
                 0.04 
                 0.15 
                 0.14 
                 0.1667 
                 0.1556 
                 0.025005 
                 0.021784 
               
               
                 0.06 
                 0.16 
                 0.15 
                 0.1778 
                 0.1667 
                 0.028448 
                 0.025005 
               
               
                 0.07 
                 0.165 
                 0.17 
                 0.1833 
                 0.1889 
                 0.030245 
                 0.032113 
               
               
                 0.08 
                 0.17 
                 0.175 
                 0.1889 
                 0.1944 
                 0.032113 
                 0.03402 
               
               
                 0.12 
                 0.175 
                 0.2 
                 0.1944 
                 0.2222 
                 0.03402 
                 0.04444 
               
               
                 0.31 
                 0.25 
                 0.35 
                 0.2778 
                 0.3889 
                 0.06945 
                 0.136115 
               
               
                 0.49 
                 0.325 
                 0.45 
                 0.3611 
                 0.5000 
                 0.117358 
                 0.225 
               
               
                 0.68 
                 0.4 
                 0.525 
                 0.4444 
                 0.5833 
                 0.17776 
                 0.306233 
               
               
                 0.87 
                 0.475 
                 0.6 
                 0.5278 
                 0.6667 
                 0.250705 
                 0.40002 
               
               
                 1.05 
                 0.55 
                 0.625 
                 0.6111 
                 0.6944 
                 0.336105 
                 0.434 
               
               
                 1.28 
                 0.63 
                 0.63 
                 0.7000 
                 0.7000 
                 0.441 
                 0.441