Abstract:
A microwave measurement system is utilized for the determination of displacement of a piston in a fluid filled cylindrical structure. The piston plus cylindrical encasement of the hydraulic system is modeled as a uniform cylindrical waveguide terminated in a metal plate. A novel shaped probe antenna to measure the slope of the relative phase of the reflected equivalent voltage wave with respect to frequency. The idea to measure the slope of the relative phase is novel and requires a new antenna structure. Instead of using the phase slope with respect to frequency, the total phase shift in a given frequency range is used to determine the location of the piston in the cylindrical chamber. Simulation and measurement will be used to determine the impedance of the antenna as well as the electromagnetic field at different locations inside the cylinder. In addition, the antenna will be analyzed to optimize its design, which ought to result in minimizing the reflections.

Description:
RELATED APPLICATION  
       [0001]     This application is a continuation application of allowed U.S. application Ser. No. 10/794,426, filed on Mar. 5, 2004, which in turn claims the benefit of priority from U.S. Provisional Patent Application No. 60/453,082, filed on Mar. 7, 2003, the entirety of which are incorporated herein by reference. 
     
    
     BACKGROUND  
       [0002]     Hydraulic systems are typically used to provide strong forces found in heavy-duty machinery. Hydraulic systems are found in heavy construction equipment, such as, cranes, bulldozers, excavators, dump trucks, forklifts, graders, as well as in large agricultural machinery, such as, tractors, combines, etc. The hydraulic/pneumatic systems currently used suffer from a lack of precision in control. Electric motors are often substituted for hydraulic/pneumatic systems in light duty machinery to accomplish precision control. Examples of precision control using electric motors include robots that are used in automobile manufacturing and in circuit board assembly industries. Such robots have sub-millimeter precision and are useful for light-duty applications. Heavy machinery applications typically mandate the use of hydraulic systems; however, exact control usually cannot be achieved.  
         [0003]     Leakage of hydraulic/pneumatic fluid from one side of a piston to the other side results in undesirable movement in machinery, for example, in attempting to steady the position of a fire engine ladder or of a crane during installation of steel beams. A feedback control system in conjunction with an apparatus that senses a piston position could correct the slippage of hydraulic/pneumatic pistons.  
       SUMMARY  
       [0004]     A technique that can provide accurate location of a piston is developed. It uses microwave propagation in hydraulic or pneumatic cylinders. Such a method and apparatus could be used as a sensing system to provide highly accurate position feedback information for hydraulic/pneumatic control system.  
         [0005]     A computer controlled system using an accurate sensing device (sensor) in hydraulic/pneumatic cylinders is currently not available but is needed to automate heavy machinery. Instead of the movement of several different control valves, an operator will benefit from a more convenient man machine interface, such as a mouse, touch screen, touch pad, joystick or a keypad for numerical entry. Simultaneous activation of various valves and instantaneous and precise measurements of piston positions with robotic speed significantly reduces the time operators regularly spend on routine operations. For instance, a forklift can be programmed for the appropriate height corresponding to a shipping dock if computer control is implemented.  
     
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0006]      FIG. 1  shows a Double-Acting Cylinder With Hinge Mount.  
         [0007]      FIG. 2 —shows a Transmission Line with a Short Termination.  
         [0008]      FIG. 3  shows Phase Angle of Reflection Coefficient ∠Γ versus Frequency for a shorted Transmission line  
         [0009]      FIG. 4  shows the Slope of Phase Angle vs. Frequency at different Piston depths  
         [0010]      FIG. 5  shows a Typical System Configuration of the invention showing respectively two views from two different sides.  
         [0011]      FIG. 6  shows a Typical System Diagram For measuring |Γ| and φ with multiple down conversion.  
         [0012]      FIG. 7  shows a Typical System Diagram For Measuring |Γ| and φ′.  
         [0013]      FIG. 8  shows a Typical System Diagram Using Amplitude Modulation Technique  
         [0014]      FIG. 9  shows a Typical Amplitude And Phase of Reflection Coefficient in hydraulic cylinder  
         [0015]      FIG. 10  shows a Field configurations, first is TE Z  and/or TM Z  modes in a circular waveguide  
         [0016]      FIG. 11  shows a Field configurations, additional 15 TE Z  and/or TM Z  modes in a circular waveguide  
         [0017]      FIG. 12   a  shows a Solid Antenna For TM 01  Mode  
         [0018]      FIG. 12   b  shows a Wire Mesh Antenna For TM 01  Mode  
         [0019]      FIG. 13   a  shows a Antenna For TM 02  Mode  
         [0020]      FIG. 13   b  shows the Antenna For TM 03  Mode  
         [0021]      FIG. 14  shows the Field Configurations for TE Z  modes in a coaxial waveguide  FIG. 15   a  shows the Field configurations for TM Z  modes in a coaxial waveguide  FIG. 15   b  shows the Field configurations for TM Z  modes in a circular wave-guide  FIG. 16  shows a End-Fed Antenna  FIG. 17  shows a Side Fed Antenna  FIG. 18  shows an End Fed Antenna Implementation For TM 11 , Mode  FIG. 19  shows a Cylinder with Temperature and Pressure Sensors  FIG. 20  shows a Cylinder with sensor for measuring relative dielectric constant ε r  and ε r ′ (loss tangent)  FIG. 21  shows a Side-Fed Antenna  FIG. 22  shows a Typical System Diagram One-Port Network Analyzer  FIG. 23  shows a Typical cylinder head with an antenna installed in it.  FIG. 24  shows a Typical antenna structure for antenna installed in the end cap which contains the piston arm.  
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0000]     I. Theory of Operation  
         [0022]     A detailed description of the theoretical concepts for the analysis and applications of hydraulic systems and their components such as hydraulic pistons, cylinders, pumps and control valves is discussed in ref [1].  FIG. 1  depicts a typical double-acting cylinder with a hinge. As  FIG. 1  depicts, one side-is a hollow cylinder (blind end) filled with hydraulic fluid (oil) or pneumatic fluid (air). The other side contains a piston arm (rod). The space between the piston arm and the cylinder wall is filled with the same hydraulic fluid. In order to move the arm(s), the hydraulic fluid enters one side and the fluid exits from the other side. The hollow side can be viewed as a uniform cylindrical waveguide with circular cross section.  
         [0023]     To estimate the piston&#39;s position, waveguide and transmission line theories are utilized. The cylinder functions as a waveguide and the piston functions as an electrical short. The position of the piston in the hydraulic/pneumatic cylinder is determined using the phase of the voltage reflection coefficient versus frequency. Usually, the slope of the voltage reflection coefficient is used. Instead the rate of change of the phase with respect to frequency, the total phase shift in a given frequency range is used.  
         [0024]     In a uniform cylindrical waveguide with circular cross section, the guide wavelength depends on the dimensions of the waveguide and the composition of the material that fills the waveguide; this is given by the following equation  
               λ     z   ,   mn       =     λ       1   -       (       f     c   ,   mn       /   f     )     2                   (   1   )             
 
 where 
        λ z,mn =wavelength in the longitudinal or guide direction of the mn-th waveguide mode of propagation (assumed here to be the z-direction)     m,n=indices identifying the various waveguide modes  
       λ   =         c   f     ⁢     1         ɛ   r     ⁢     μ   r             =     intrinsic   ⁢           ⁢   wavelength   ⁢           ⁢   of   ⁢           ⁢   the   ⁢           ⁢   medium   ⁢           ⁢   filling   ⁢           ⁢   the   ⁢           ⁢   waveguide           
    f c,mn =cutoff frequency of the mn-th waveguide mode which depends on the dimensions of the waveguide and the electrical parameters μ and ε of the medium filling the waveguide.     f=frequency of the wave     μ=permeability of the material that fills the waveguide     ε=permittivity of the material that fills the waveguide     For convenience, (1) is re-written as  
               λ     z   ,   mn       =     c     f   ⁢         ɛ   r     ⁢     μ   r         ⁢       1   -       (       f     c   ,   mn       f     )     2                     (   2   )             
 
 where 
    ε r =relative permittivity     μ r =relative permeability which equals unity for non-magnetic material        
 
         [0034]      FIG. 2  depicts a standard lossless transmission line. The total phase shift of the voltage reflection coefficient the shorted transmission line of length dis given by  
               ∠Γ   =         ϕ   r     ⁡     (     d   ,   f     )       =       π2β   z     ⁢   d         ⁢     
     ⁢   where           (   3   )                 β     z   ,   mn       =       2   ⁢   π       λ     z   ,   mn                 (     3   ⁢   a     )                      β Z  is the guide (z-direction)phase constant of the waveguide mode, which by Substituting (3a) into (3) yield  
                 ϕ   r     ⁡     (     d   ,   f     )       =       π   -       4   ⁢   π   ⁢           ⁢   d       λ     z   ,   mn           =     π   -       4   ⁢   π   ⁢           ⁢   fd       v     pz   ,   mn                     (   4   )             
 
 where ν pz,mn =Phase velocity in the guide for the mn-th waveguide mode of propagation (assumed here to be the z-direction) or  
             d   =           λ     z   ,   mn         4   ⁢   π       ⁡     [     π   -       ϕ   r     ⁡     (     d   ,   f     )         ]       =         v     p   ,   m         4   ⁢   π   ⁢           ⁢   f       ⁡     [     π   -       ϕ   r     ⁡     (     d   ,   f     )         ]                 (   5   )             
         
         [0036]     In order to obtain the length of a shorted transmission line d using (5), the measured phase shift {circumflex over (φ)} r (d,f) in general is insufficient since the instrumentation can only measure phase shifts in the range of [−π,+π]and for phase shifts that are more than +π single frequency phase shift measurement has an ambiguity of +2 kπ for k=. . .−3,−2,−1,0,+1,+2,+3, . . . . In order to resolve the ambiguity resulting from the limitation of range of [−π,+π] in the available measurement techniques, one could alternatively measure the slope of the phase shift with respect to frequency i.e.,  
         ∂         ϕ   ^     r     ⁡     (     d   ,   f     )           ∂   f         
 
 which equals  
           ∂       ϕ   r     ⁡     (     d   ,   f     )           ∂   f       ⁢               
 
 alternatively, measure a sweep of phase shifts with respect to frequency. 
 
         [0037]      FIG. 3  is a plot of frequency sweep of the phase angle of the voltage reflection coefficient φ r (d,f) for a shorted transmission line.  
         [0038]     Another approach for the determination of the length d of the shorted transmission line is accomplished by using the phase slope of the reflection coefficient with respect to frequency. By taking partial derivative with respect to frequency on both sides of (4) we obtain  
                 ∂       ϕ   r     ⁡     (     d   ,   f     )           ∂   f       =       -   4     ⁢   π   ⁢           ⁢   d   ⁢       ∂     (     f     v     p   ,   mn         )         ∂   f                 (   6   )             
 
         [0039]     In a hollow waveguides filled with dielectric material, the phase velocity for the mn-th waveguide mode of propagation (assumed here to be the z-direction) is given by 1     1 A detailed description of the theoretical concepts for the analysis of the fields in cylindrical waveguides may be found in ref [2].  
 
ν pz,mn =λ z,mn   ·f   (7) 
 
 where 
        ν pz,mn =phase velocity in the waveguide associated with modes m and n        
 
         [0041]     Using (2) in (7) yields  
                 v     pz   ,   mn       ⁡     (   f   )       =     c           ɛ   r     ⁢     μ   r         ⁢       1   -       (       f     c   ,   mn       f     )     2                     (   8   )             
 
 where the cutoff frequency f c  for circular waveguide is given by  
               f     c   ,   mn       =       χ   mn   ′       2   ⁢   π   ⁢           ⁢   a   ⁢     μɛ                 (   9   )                 f     c   ,   mn       =       χ   mn       2   ⁢   π   ⁢           ⁢   a   ⁢     μɛ                 (   10   )             
        with     χ′ mn =n-th zero (n=1, 2, 3, . . . ) of the derivative of the Bessel function J m  of the first kind of order (m=0, 1, 2, 3, . . . ) which is used for TE modes. Values corresponding to various indices of χ′ mn  are provided in page 472 of reference [2].     χ mn =the n-th zero (n=1, 2, 3, . . . ) of the Bessel function J m  of the first kind of order (m=0, 1, 2, 3, . . . ) which is used for TM modes. Values corresponding to various indices of χ mn  are provided on page 478 of the reference [2].        
 
         [0045]     Substituting (8) into (6) one can obtain  
                         ∂     ϕ   r       ⁢           ⁢     (     d   ,   f     )         ∂   f       =     ϕ   r   ′                 =       -       4   ⁢           ⁢   π   ⁢           ⁢   d   ⁢           ⁢         ɛ   r     ⁢           ⁢     μ   r           c       ⁢           ⁢       ∂     (     f   ⁢           ⁢       1   -       (       f   c     f     )     2           )         ∂   f                     =       -         4   ⁢           ⁢   π   ⁢           ⁢   d   ⁢           ⁢         ɛ   r     ⁢           ⁢     μ   r           c     ⁢               ⁢     (               1   -       (       f   c     f     )     2         +                 f   c   2         f   2     ⁢           ⁢       1   -       (       f   c     f     )     2                   )                     (   11   )             From         (   11   )               d   =       -         ϕ   r   ′     ·   c       4   ⁢           ⁢   π         ·       1   μɛ       ·     1         1   -       (       f   c     f     )     2         ⁢           +       f   c   2         f   2     ⁢           ⁢       1   -       (       f   c     f     )     2                           (   12   )               d   =           t   gd     ⁢   c     2     ·       1   μɛ       ·     1         1   -       (       f   c     f     )     2         +       f   c   2         f   2     ⁢       1   -       (       f   c     f     )     2                           (   13   )             
 
 where t gd  is the group delay given by  
                 t   gd     ≡     -       ∂     ϕ   r         ∂   ω           =     -       ∂     ϕ   r         2   ⁢   π   ⁢     ∂   f                   (   14   )             
 
         [0046]     In an alternative methodology, a phase sweep in the frequency range of [f,f 2 ] can be used. Using (4)  
                     ϕ   r     ⁡     (     d   ,     f   2       )       -       ϕ   r     ⁡     (     d   ,     f   1       )         =         4   ⁢   π   ⁢           ⁢     f   1     ⁢   d         v     pz   ,   mn       ⁡     (     f   1     )         -       4   ⁢   π   ⁢           ⁢     f   2     ⁢   d         v     pz   ,   mn       ⁡     (     f   2     )             ⁢     
     ⁢   or           (   15   )               d   =           ϕ   r     ⁡     (     d   ,     f   2       )       -       ϕ   r     ⁡     (     d   ,     f   1       )               4   ⁢   π   ⁢           ⁢     f   1           v     pz   ,   mn       ⁡     (     f   1     )         -       4   ⁢   π   ⁢           ⁢     f   2           v     pz   ,   mn       ⁡     (     f   2     )                     (   16   )             
 
         [0047]      FIG. 4  depicts typical curves for the slope of the phase angle of the voltage reflection coefficient φ′ r  versus frequency f. Once a value for the slope of the phase angle φ′ r  or time delay t gd  is determined, the piston distance d can be determined from (14) or (15) or utilizing curves such as those in  FIG. 4  or by a table-lookup.  
         [0000]     Implementation  FIGS. 10, 11 , and  15   b  depict the field lines of lower order modes in the cross section of a hollow cylindrical waveguide; these correspond to the hollow side of hydraulic/pneumatic cylinder.  
         [0048]      FIGS. 14, 15   a  depict field lines of the lower order modes of a coaxial waveguide; these correspond to the side of cylinder hydraulic/pneumatic containing the piston arm. Either side can be used as the waveguide region. However, due to presence of less available space in chamber which contains the piston arm the hollow side is usually preferable for placing an antenna.  
         [0049]     As shown in  FIG. 5  the antenna  150  is placed at the blind end of metallic cylindrical chamber. According to this embodiment the feed network  152  connects via radio frequency connector  166  and cable  154  and radio frequency connector  162  through coaxial section  162  to the antenna  150 . According to this figure the cable  154  passes through the space between the hinges  158  and  160  of the blind end cap and connects to radio frequency connector  162 . As the piston  165  and the piston arm  156  moves the distance d which is the distance between the antenna  15 O and piston  160  changes. The feed network  152  is typically a one port network analyzer.  FIGS. 6, 7 ,  8  and  22  are typical implementation of such one port network analyzer systems. The network analyzer determines the electrical length of the cylinder between the antenna  150  and piston  165 . The electrical length of the cylinder, i.e., the electrical distance from a reference point at the antenna  150  to the piston  165  is determined by using the measured phase versus frequency information as described above. The electrical lengths of the connecting cable  154  and radio frequency connectors  158  and  164  are known and are subtracted from the actual measurements. The cutoff frequency f c  is calculated by (9) or (10) by inputting values for the inner radius a of the cylinder and the relative permittivity ε, and permeability μ r  of the fluid filling the cylinder. The piston depth d is calculated from any of equations (12), (13) or (16).  
         [0050]     Alternatively, the antenna can be installed on the arm end utilizing coaxial waveguide modes. In that case the field lines have to match the field lines of  FIGS. 14 and 15 . For example for E 11  mode as in  FIG. 15   a  an antenna implementation is composed of two rods located at the nodes of field lines.  FIG. 23 .  
         [0051]     The antenna is connected to circuitry that measures the voltage reflection coefficient Γ (both in magnitude and phase). The phase slope with respect to frequency, is calculated and is proportional to the group delay. The phase non-linearity causes uncertainty in the measurements. The non-linearity data (shown in  FIG. 4 ) is obtained when the piston is at a known distance d, (e.g., when the arm is extended all the way out). At these same points, the phase slope measurements φ′ r (d,f) are also obtained and stored in computer memory by the software.  
         [0052]      FIGS. 6, 7 ,  8  and  22  depict the block diagrams for various implementations of one port network measurements. Both the phase angle and the magnitude of voltage reflection coefficient are measured. The magnitude of the reflection coefficient (return loss) |Γ| predicts the loss tangent ∈″ of the hydraulic fluid. By incorporating the loss tangent in the formulation i.e. substituting ∈ r =∈′−j∈″ the above equations more measurement accuracy is obtained.  
         [0053]      FIGS. 6, 7 ,  8  and  22  depict four possible methods (amongst a variety of possible techniques) for the measurement of the magnitude, phase angle and its derivative with respect to frequency, i.e., the phase slope φ′ r (d,f) or the group delay t gd  of the voltage reflection coefficient for different piston depths at different frequencies. In  FIG. 8  the phase slope or equivalently the group delay is measured directly by means of amplitude modulation techniques. The high frequency carrier signal that is amplitude modulated by a low frequency “base-band” signal and the delay in the base-band incurred as a result of passing through the cylinder under the test is measured.  
         [0054]     As in  FIGS. 6, 7 ,  8  and  22  indicated, the signal from the source circuitry  210 ,  210   a  [such as a phase-locked loop (PLL) or direct digital synthesis (DDS) device or combination of both] is coupled to a port of a three port directional device  209  such as a bridge e.g., a directional coupler or a circulator. The other port is connected to the antenna mounted in the cylinder. The signal is coupled into the cylinder and reflected by the piston. The reflected signal is coupled back to the device and is coupled to its third port. By utilizing such directional three-port devices  209 , the reflected wave from the cylinder-piston is separated from the incident wave. The phase of the reflected signal is compared to the phase of the incident signal either at the radio frequency or a lower frequency using a phase comparator  214  in order to obtain the phase angle of the voltage reflection coefficient, φ r (d,f). The ratio of the amplitude of the reflected signal to the amplitude of the incident reference (signal source) yields the magnitude of voltage. When the measurements are repeated for different frequencies, the piston location is determined using (12), (13) or (16). The frequency selection is controlled by micro-controller  213 . In another system configuration such as  FIG. 7  the micro-controller  215  handles the calculation of phase slope from the measured phase in addition to controlling the frequency of the source. According to another embodiment as described in  FIG. 8  the phase slope or equivalently the group delay can be calculated utilizing amplitude modulation. A low frequency signal source  218  provides the baseband signal to a carrier frequency generated by microwave signal source  210  using amplitude modulator  219 . The modulated signal is then split into two separate signals by power splitter  211 . One branch of the split signal feeds the AM detector  216   a  and detects the baseband signal which in turn feeds on input of phase comparator  214 . The other branch of the split signal from power splitter  211  feeds the first port of directional device  209 . The signal from the second port of the directional device  209  via connectors and cable couples a signal to the antenna in the cylinder. The reflected signal from the couples back from the cylinder to the second port of directional device  209  and in turn the signal is coupled out from the third port of directional device  209  to AM detector  216   b  which feed the input port of the phase comparator  214 . The phase comparator then provides the phase difference and or the group delay. The AM detector  216  feeds a secondary AM detector  217  in order to obtain the magnitude of the reflection coefficient. In another implementation according to  FIG. 22 , microprocessor  226  controls the frequency of signal source  210  which feeds the power splitter  211 . One port of the power splitter  211  feeds port one of a directional device  229  and then the signal from its second port is coupled to cylinder and then reflected back by the piston in turn coupled back to the second port of directional device  229  and then coupled out from the third port of directional device  229  feeding an attenuator  228  and in turn feeding the RF ports of two frequency mixers which operate as phase detectors. The other port of power splitter  211  feeds a quadrature device which provides a 90° phase shift between its outputs feeding the LO ports of the of two frequency mixers. The IF ports of the of two frequency mixers provides the I and Q channels of the reflection coefficient Γ in turn are digitized via analog to digital converters  215   a ,b  which in turn feeding a digital signal processor or micro-processor  226 . The micro-processor calculates the phase difference and subsequently calculates the distance according to one of the formulations mentioned above and outputs the measured distance d.  
         [0000]     Antenna Implementation  
         [0055]     Typically antenna design is implemented by use of a rod serving as the center conductor of a quarter wave coaxial transformer matching the input impedance (typically 50 Ω) to the wave impedance of the waveguide. Since the wave impedance of the hollow portion of the waveguide is known, the wave impedance of the coaxial portion is determined.  
         [0056]     Non-Idealistic Behavior of System Components Ideal transmission lines exhibit a constant delay versus frequency and thereby results in a linear phase versus frequency characteristic. However, waveguides deviate from ideal transmission lines and have dispersive characteristics with respect to frequency as is evident by the phase velocities being frequency dependent; (5). Other effects such as mismatches in various components of the system, e.g., the antenna, connectors and parasitic capacitances, result in additional phase non-linearities. The piston is not a perfect short due to the fact that it has recessed rings acting as capacitors. The lossy nature of the hydraulic fluid causes additional dispersion. In addition, the non-linear effects due to the presence of antenna evanescent modes are more significant when the piston is close to the antenna. Due to the non-zero loss tangent of the hydraulic fluid and the finite conductivity of the metallic portions of the system, the magnitude of the reflection coefficient is less than unity. Hence, the phase versus frequency characteristics are not linear.  FIG. 9  depicts typical phase and amplitude versus frequency characteristics of the voltage reflection coefficient for a typical hydraulic cylinder.  
         [0000]     Antenna Mode of Operation  
         [0057]      FIGS. 10 and 11  depict the cross-sectional field configuration of the first 30 TE Z  and/or TM Z  modes of a uniform cylindrical waveguide incorporated in here from reference [2]. A preferred implementation of the apparatus for hydraulic cylinder depth measurement occurs when placing the antenna in the hollow side of the cylinder and utilizing the TM 01  mode of a circular waveguide. This modal selection is due to the similarity of the field lines of the TM 01  mode in a hollow cylindrical waveguide to the field lines of a coaxial transmission lines. The electric field lines are radial and the magnetic field lines are composed of concentric circles; there are no nulls in the field distributions along the radius. FIGS.  12 - a  and  12 - b  depict the novel geometrical construction of the antenna choice to produce the needed TM 01  modes. In FIG. 12 - a,  the antenna is implemented using solid metal. The far right portion of the antenna is tapered. The tapered shape provides a radial component of the electric field only at the center to be zero as the field configuration for TM 01  mode ( FIG. 10 ). This is done in order to minimize excitation of waveguide evanescent modes which their presence at the close proximity of the antenna would interfere when the piston gets close to the antenna. In  FIG. 12 - b,  the rigid wires forming a mesh structure are utilized for the construction of the antenna. This type of antenna produces more evanescent mode fields since it does not have the tapered tip. Other modes of operation can be implemented by antennas made of multiple conductors.  
         [0058]      FIG. 13   a  depicts the views of the cross sections of the side and the front of an antenna for generating TM 02  mode which corresponds to the field configuration for the TM 02  as depicted in  FIG. 10 . The inner conductor  234  is separated from the outer conductor  230  via insulator  231 . The conductors  230  and  231  are fed with a feed network.  
         [0059]      FIG. 13   b  depicts the views of the cross sections of the side and the front of an antenna for generating TM 03  mode which corresponds to the field configuration for the TM 03  as depicted in  FIG. 11  The inner conductor  230  is separated from the intermediate conductor  236  via insulator  239  and the outer conductor  237  is separated from intermediate conductor  236  via the insulator  238 . The conductors  235  and  236  and  237  are fed with a feed network.  
         [0060]      FIG. 14  shows the Field Configurations for TE Z  modes in a coaxial waveguide brought here from ref [3].  FIG. 15   a  shows the Field configurations for TM Z  modes in a coaxial waveguide brought here from ref [3].  FIG. 15   b  shows the Field configurations for TM Z  modes in a circular wave-guide brought here from ref [3] 
         [0061]      FIG. 16  shows a End-Fed Antenna. This type of implementation is appropriate for the type of cylinders which have two flanges on the end cap and the connector  206  is attached to the cylinder  111  and feeds the antenna  204  from the space between the hinges. The antenna  204  is separated from the cylinder  11  via insulator  208 .  
         [0062]      FIG. 17  shows a Side Fed Antenna. This type of implementation is appropriate for the type of cylinders which have one flange on the end cap  112  which is at the center of the end cap and the preferable approach is to attach and the connector  206  to the cylinder  111  and from the side which feeds the antenna  204  from the space away from the hinge. The antenna  204  is separated from the cylinder  11  via insulator  208   
         [0063]      FIG. 18  shows an End Fed Antenna Implementation For TM 11  Mode of two separate antennas  204  which consists  
         [0064]      FIG. 19  shows a Cylinder  111  with Temperature sensor  220  and Pressure sensor  221  Sensors installed on the cylinder. The temperature and pressure change the electrical properties of the hydraulic /pneumatic fluid  102 . The data for relative permitivitty ∈ r =∈′−j∈″ versus pressure and temperature is the table and as necessary is looked up by the computer/digital processor in order to maintain the accuracy of the measurements as pressure and temperature changes due to factors such as friction load and the surrounding environments.  
         [0065]     Alternatively, as in  FIG. 20  the cylinder  101  is equipped with sensor for measuring relative dielectric constant ∈ r =∈′−j∈″ of the fluid  102  directly. This type of sensor could be implemented by using a capacitor in which the fluid penetrates between its plates.  
         [0066]      FIG. 21  depicts another Side-Fed Antenna configuration in which the radiating portion of the antenna  223  is mounted on an insulator  208  a coaxial line feeds the signal from connector  206  to the antenna  223  via flexible contact  208 . One possible method of securing the insulator  208  to the cylinder  101  is by cutting annular notches in the cylinder  101  and insulator  208 . A spring washer  114  is inserted in the annular notch of the insulator  208 . Spring  115  is placed on the bottom of cylinder  101 . The washer  114  is squeezed and the insulator is inserted in the cylinder and as the washer  114  reaches the notch in the cylinder  101  it expands and secures the insulator  208  in place.  
         [0067]      FIG. 23  depicts an actual antenna with tapered end installed in an end cap.  
         [0068]      FIG. 24  depicts a typical structure of antenna installed in the end cap  251  when a piston arm  254  is present. The signal is provided to the two radiators  252  and  253  by means of a feed network  256 . The radiators  253  and  254  are separated from the end cap  251  by insulators  258 . The feed network  256  functions as a two way power splitter and its outputs is connected to the antennas via cables  260  and  261  and connectors  262  and  263  flexible connecting rods  264  and  265 . This arrangement produces TM 11  mode which is referred to E 11  in reference [3] as its field configuration are depicted in  FIG. 15   a.  As seen in  FIG. 15   a  the field configuration for El, has two nodes corresponding to the tips of radiators  253  and  254 . The antenna system as described in  FIG. 24  produces field configuration E 11  as in  FIG. 15   a.  However, in order to obtain higher order modes more number radiators is necessary for example by using four radiators produces four nodes corresponding to E 21  mode, i.e., as field configuration E 2  as in  FIG. 15   a.  the advantage of higher order modes is the radiator rods are shorter and would not take as much space. Cylinders with double end rod construction require such antenna due to the fact that both ends contain a piston arm. However, in any event such antenna system can be utilized in a in a single end rod cylinders in the rod side.  
       Calibration  
       [0069]     In order to improve the measurement accuracy a calibration procedure for reducing the unwanted characteristics of the antenna as well as the other components of the system is performed. The one port network analyzer also goes through a calibration procedure with short, open and termination as done in lab equipment In on method the data collected data versus actual measurements are saved in a table and is used as table took up for interpolation. In another method the effects measurements of the antenna characteristics and the other RF components are calibrated out of the measurements. Reference 
    [1] Charles S. Hedges,  Industrial Fluid Power Volume  1,  Third Edition  (1984).     [2] C. A. Balanis,  Advanced Engineering Electromagnetics,  pp. 470-491 (1989)     [3] Nathan Marcuvitz,  Waveguide Handbook  ( 1986)