Abstract:
Soil moisture sensor systems and methods are disclosed. An exemplary soil moisture sensor system comprises a sensor configured to receive soil between parallel plates. A capacitive measurement circuit is operatively associated with the parallel sensor. A processor receives input from the capacitive measurement circuit. The processor determines moisture content of the soil between the parallel plates of the sensor based on the flowing relationship:  
       C   =       LH   d     ⁢     ɛ   0     ⁢     ɛ   r           
where L is the length of the sensor, H is the height of the sensor, and d is the separation between the parallel plates of the sensor.

Description:
PRIORITY APPLICATION  
       [0001]     This application claims priority to co-owned U.S. Provisional Patent Application Ser. No. 60/751,330 for “Soil Moisture Sensor” of John McDermid (Attorney Docket No. CVN.021.PRV), filed Dec. 16, 2005, hereby incorporated herein for all that it discloses. 
     
    
     TECHNICAL FIELD  
       [0002]     The described subject matter relates to sensors in general, and more particularly to soil moisture sensor systems and methods.  
       BACKGROUND  
       [0003]     Water conservation is increasingly important. Water supplies are essentially constant and more people are using the same water every year. In the United States, a substantial portion of the water supply is used to maintain landscape (trees, grass, etc.). Irrigation studies show that much of the water applied to the landscape by prevalent irrigation methods is wasted. Excess water ends tip as surface run-off or seepage into the ground.  
         [0004]     Water lost as such is rarely captured and reused. Instead, surface run-off typically requires erosion control measures and often impacts mosquito abatement efforts. Seepage into the ground may pollute ground water with fertilizer and pesticides  
         [0005]     Reducing water loss for a landscape is a complex process. Soil types hold varying amounts of water and not all of the water held by the soil is available to the landscape. Landscape has varying water needs depending on whether the landscape is full sun, partial sun, or shady locations. Air temperature and humidity also play roles in determining how much water the landscape needs. The ground slope may affect the amount of water to apply to the landscape.  
         [0006]     Soil moisture sensors have been used in the past. However, these sensors have been too expensive and/or inaccurate due to the variations in soil properties (e.g., composition, chemistry, compaction and temperature).  
         [0007]     Although a Soil Moisture Neutron Probe (SMNP) has been shown to be fairly accurate, the public typically will not accept the use of neutron sources in their yards. Documentation and disposal issues are also a concern. Relative permittivity measurements using either a TDR method or a capacitive method have also been shown to be an effective indicator of volumetric water content. However, both methods have drawbacks.  
       SUMMARY  
       [0008]     An exemplary soil moisture sensor system comprises a sensor configured to receive soil between parallel plates. A capacitive measurement circuit is operatively associated with the parallel sensor. A processor receives input from the capacitive measurement circuit. The processor determines moisture content of the soil between the parallel plates of the sensor based on the following relationship:  
       C   =       LH   d     ⁢     ɛ   0     ⁢     ɛ   r           
 
         [0009]     where L is the length of the sensor, H is the height of the sensor, and d is the separation between the parallel plates of the sensor.  
         [0010]     An exemplary method of determining soil moisture content comprises: receiving soil between at least two plates, measuring capacitance of the soil using a sensor circuit, and determining moisture content of the soil using the measured capacitance of the soil and length, height, and separation between the at least two plates. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]      FIG. 1  is an exemplary capacitive measurement circuit that may be implemented for the soil moisture sensor.  
         [0012]      FIG. 2  shows exemplary DAC Output for the soil moisture sensor.  
         [0013]      FIG. 3  is a ZOH view of the exemplary DACS Output shown in  FIG. 3 .  
         [0014]      FIG. 4  are exemplary measurement points for the soil moisture sensor.  
         [0015]      FIG. 5  is all expanded view of the exemplary measurement points shown in  FIG. 4 .  
         [0016]      FIG. 6  is an exemplary moisture sensor as it may be implemented using substantially parallel plates.  
         [0017]      FIG. 7  shows exemplary capacitance as a function of relative permittivity.  
         [0018]      FIG. 8  shows an exemplary correction factor that may be implemented 
     
    
     DETAILED DESCRIPTION  
       [0019]     Irrigation control conserves the water supply and reduces or altogether eliminates the cost of mitigating additional burdens from run-off and or seepage. Exemplary embodiments described and claimed herein provide a soil moisture sensor which may implement improved, or even optimal irritation control.  
         [0020]     Among other exemplary advantages, the soil moisture sensor:  
         [0021]     Enables measurements to be taken at low frequencies where dielectric relaxation is minimal and less expensive circuits may be employed.  
         [0022]     Enables capacitive measurements to be taken where the effects of ionic conduction may be reduced or altogether eliminated.  
         [0023]     Uses fewer, smaller parts.  
         [0024]     Reduces manufacture costs relative to other commercially available sensors.  
         [0025]     Provides accurate, laboratory-quality measurements.  
         [0026]     In an exemplary embodiment, a sinusoidal voltage V 1  is applied to a capacitor through a resistor, R 1 , as shown by the circuit  100  in  FIG. 1 .  
         [0027]     The value C 2 , which is indicative of the permittivity, is the value measured by the soil moisture sensor. The value R 2  represents the ionic conductivity of the medium. The voltage V out  is a complex number having real and imaginary parts, as expressed by the following equation: 
 
 V   out   =v   r   +tv   t 
 
 where t=√{square root over (−1)}
 
         [0028]     The capacitance may be determined from just the real and imaginary voltage measurements, the value of resistor R 1 , and the radian frequency, as shown in more detail below in the section titled “exemplary calculations.” The capacitance may then be expressed by the following equation:  
                               C   2     =     -         V   in     ⁢     v   i           ω   ⁡     (       v   r   2     +     v     i   ⁢             2       )       ⁢     R   1                     
 
         [0029]     Note that the capacitance value is independent of the value of ionic conductivity.  
         [0030]     The circuit may be stimulated with a digital to analog converter (DAC) whose output is stepped through the values of a sin wave as shown by the plot  200  in  FIG. 2 . In this example, the DAC begins at zero and steps through seven complete cycles of the sin wave. The frequency of the sin wave is 10 KHz and the peak amplitude is 1 volt. The DAC output is a zero order hold (ZOH) output as shown by the plot  300  in  FIG. 3 .  
         [0031]     Measurement starts with a sequence of A/D readings that are synchronized with the DAC. Sampling begins after some number of full cycles have been applied (two in this example). This delay allows any transient to settle to final value before the measurement begins.  
         [0032]     Measurement continues through all the remaining complete cycles of of the sin wave as shown by the plot  400  in  FIG. 4 . Each diamond marker indicates where a sample is taken.  
         [0033]     An expanded view of the samples is shown by the plot  500  in  FIG. 5 . Each measurement (diamond marker) is taken just prior to changing the DAC, allowing maximum settling time for the transient introduced by each step the DAC. Once the measurements have been collected, a digital Fourier transform provides the real and imaginary values. The digital Fourier transform is determined from the following equation, where N is the number of measurements taken:  
               ⁢             v   r     =         2     N     ⁢       ∑     i   =   0       N   -   1       ⁢           ⁢       V   i     ⁢     sin   ⁡     (       2   ⁢   π   ⁢           ⁢   ki     N     )                                 ⁢       v   i     =         2     N     ⁢       ∑     i   =   0       N   -   1       ⁢           ⁢       V   i     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢   ki     N     )                           
 
         [0034]     A digital Fourier transform is computed for a discrete number of frequencies. The soil moisture sensor only needs the Fourier transform at the stimulation frequency. A particular frequency is determined by the integer k, the total number of samples N, the time between samples Δt. The integer k is chosen to correspond exactly with the stimulation frequency. That relationship is expressed by the following equation:  
       F   =     k     N   ⁢           ⁢   Δt           
 
         [0035]     The number of samples and the time between samples may be adjusted until this relationship is satisfied.  
         [0036]     It is noted that the capacitor geometry does not influence the measurement sensor other than the geometry should be known and remain constant. However, proper drainage of the soil should be maintained within the capacitor. In addition, the area between the plates should be easy to fill with soil. The form should also place the sensor in or near the root zone. A parallel plate capacitor, such as the exemplary soil moisture sensor  600  shown in  FIG. 6 , is a good choice to provide these characteristics.  
         [0037]     For a parallel plate capacitor, the capacitance is expressed by the following equation, where L is the length of the sensor; H is the height of the sensor, and d is the separation between plates:  
       C   =       LH   d     ⁢     ɛ   0     ⁢     ɛ   r           
 
         [0038]     The value returned by the sensor may then be expressed by the following equation:  
         ɛ   r     =       d       ɛ   0     ⁢   LH       ⁢     (         V   in     ⁢     v   i           ω   ⁡     (       v   r   2     +     v   i   2       )       ⁢     R   1         )           
 
         [0039]     The 1.5 inch height of the soil moisture sensor helps keep the sensor at the root zone. The length and separation are sufficient to provide measurable capacitance. Of course other embodiments are also contemplated, as will be readily appreciated by those having ordinary skill in the art after becoming familiar with the teachings herein.  
         [0040]     The capacitance of the plates is shown by the plot  700  in  FIG. 7 . There is about 12 pF of capacitance between the plates in air and nearly 950 pF if the plates are immersed in water. This capacitance is within the measurement capabilities of a low cost processor that may be implemented for the soil moisture sensor, such as, but not limited to the Silicon Labs C8051F060X processor.  
         [0041]     There are two calibrations for the soil moisture sensor. First, the permittivity of water is a function of temperature. That dependence is expressed by the following equation, where Tc is the temperature in degrees Centigrade. 
 
 s   r =78.54(1−4.579×10 −3 ( T   c −25)+1.19×10 −5 ( T   c −25) 2 −2.8×10 −8 ( T   c −25) 3 )
 
         [0042]     A correction factor may be derived to correct the actual permittivity to the permittivity at 25° C. (77° F.). An exemplary correction factor is shown by the plot  800  in  FIG. 8 . The corrected permittivity may be calculated by dividing the measured permittivity by the correction factor. This factor may be applied to every measurement.  
         [0043]     The second calibration is determined from a physical model and only needs to be done only in the design cycle. While the sensor is modeled as a parallel plate capacitor, physical construction details (e.g., spacers and fasteners) may modify the form factor slightly. Once a physical model has been assembled, the permittivity in air is measured. This permittivity becomes the correction factor and is stored in the measurement processor. A connected measurement is determined by dividing the actual measurement by the measured value in air.  
         [0000]     Exemplary Calculations  
         [0044]     As discussed above with reference to  FIG. 1 , the current through R 1  may be expressed by the following equation:  
         I   s     =         V   in     -     V   out         R   1           
 
         [0045]     The complex voltage V out  is expressed by the following equation:  
               V   out     =           R   2     ⁢     1     1   ⁢   ω   ⁢           ⁢     C   2               R   2     +     1     1   ⁢   ω   ⁢           ⁢     C   2             ⁢     I   s                   =         R   2         1   ⁢   ω   ⁢           ⁢     C   2     ⁢     R   2       +   1       ⁢     I   s                   =         R   2         1   ⁢   ω   ⁢           ⁢     C   2     ⁢     R   2       +   1       ⁢     (         V   in     -     V   out         R   1       )                 
 
         [0046]     Expanding and multiplying by the denominators results in the following equation: 
 
 V   out ( tωC   2   R   2 +1) R   1   =R   2 ( V   m   −V   out )
 
         [0047]     Multiplying out the right side and collecting terms containing V out  is expressed by the following equation: 
 
 V   out ( tωC   2   R   2   R   1   +R   1   +R   2 )= R   2   V   in 
 
         [0048]     Breaking V out  into real and imaginary parts is expressed by the following equation: 
 
 V   out   =v   r   +tv   i 
 
         [0049]     Substituting real and imaginary parts for V out  is expressed by the following equation: 
 
( v   r   +tv   t )( tωC   2   R   2   R   1   +R   1   +R   2 )= R   2   V   in 
 
         [0050]     Multiplying out is expressed by the following equation: 
 
 tωC   2   R   2   R   1   v   r     30  R   1   v   t   +R   2   v   r −1 ωC   2   R   2   R   1   v   t     30  tR   1   v   t   +tR   2   v   t   =R   2   V   in 
 
         [0051]     Equating the imaginary parts on both sides of the equation results in the following equation: 
 
 tωC   2   R   2   R   1   v   r     30  tR   1   v   t   +tR   2   v   t =0
 
         [0052]     Solving for the term ωC 2 R 2 R 1  is expressed by the following equation:  
         ω   ⁢           ⁢     C   2     ⁢     R   2     ⁢     R   1       =           -     R   1       ⁢     v   i       -       R   2     ⁢     v   i           v   r           
 
         [0053]     Now solving the equation for the real parts results in the following equation: 
 
 R   1   v   r   +R   2   v   r     31  ωC   2   R   2   R   1   v   i   =R   2   V   in 
 
         [0054]     Substituting for ωC 2 R 2 R 1  from Equation 21 is shown by the following equation:  
             R   1     ⁢     v   r       +       R   2     ⁢     v   r       -       (           -     R   1       ⁢     v   t       -       R   2     ⁢     v   t           v   r       )     ⁢     v   t         =       R   2     ⁢     V   in           
 
         [0055]     Simplifying is shown by the following equation:  
             R   1     ⁢     v   r   2       +       R   2     ⁢     v   r   2       +       R   1     ⁢     v   t   2       +       R   2     ⁢     v   t   2         =       R   2     ⁢     V     i   ⁢           ⁢   n       ⁢     v   r           
 
         [0056]     Solving for R2 is shown in the following equation:  
         R   2     =       -       R   1     ⁡     (       v   r   2     +     v   t   2       )               -     V     i   ⁢           ⁢   n         ⁢     v   r       +     v   r   2     +     v   t   2             
 
         [0057]     Solving Equation 21 for C 2  results in the following equation:  
         C   2     =           -     R   1       ⁢     v   t       -       R   2     ⁢     v   t           ω   ⁢           ⁢     v   r     ⁢     R   2     ⁢     R   1             
 
         [0058]     Substituting for R 2  results in the following equation:  
         C   2     =           -     R   1       ⁢     v   t       -         -       R   1     ⁡     (       v   r   2     +     v   t   2       )               -     V     i   ⁢           ⁢   n         ⁢     v   r       +     v   r   2     +     v   t   2         ⁢     v   t           ω   ⁢           ⁢     v   r     ⁢           ⁢         -     R   1       ⁢     (       v   r   2     +     v   t   2       )             -     V     i   ⁢           ⁢   n         ⁢     v   r       +     v   r   2     +     v   t   2         ⁢     R   1             
 
         [0059]     Simplifying results in the following equation:  
               C   2     =       -     v   r       ⁢     R   1     ⁢         V     i   ⁢           ⁢   n       ⁢     v   t         ω   ⁢           ⁢       v   r     ⁡     (       v   r   2     +     v   t   2       )       ⁢     R   1   2                       =         V     i   ⁢           ⁢   n       ⁢     v   t           ω   ⁡     (       v   r   2     +     v   t   2       )       ⁢     R   1                   
 
         [0060]     In addition to the specific embodiments explicitly set forth herein, other aspects and implementations will be apparent to those skilled in the art from consideration of the specification disclosed herein. It is intended that the specification and illustrated embodiments be considered as examples only.