Abstract:
The described apparatus and methods use Time Domain Reflectometry (TDR) to determine the absolute volumetric moisture content of various media. The effects of dispersion caused by conductive and dielectric properties of the medium on the waveform are extrapolated by detecting the bulk propagation time and the slope of the distorted transition of the characteristic reflected waveform. Fast transitions are injected by a differential step function generator into a two-conductor waveguide, which is immersed in soil or other medium of interest. Unlike previous single-ended TDR systems, a differential digitizer senses the probes. Timing control between the two digitizers is critical. Use of an integrated fully differential system eliminates the need for a coaxial cable and an associated balancing transformer, or balun. This enables a two-conductor probe that is more easily inserted into soil, rather than requiring three conductors. Non-conductive probe tips may be pointed to facilitate insertion without causing measurement ambiguity.

Description:
TECHNICAL FIELD 
     The present invention relates generally to Time Domain Reflectometers, and specifically to sensors of absolute moisture based on time domain reflectometry. 
     BACKGROUND 
     Time Domain Reflectometers (TDRs) have proven to be the preferred instruments for the measurement of permittivity in various media, including soils. This popularity arises from the independence of propagation time from the electrical conductivity of the medium. Volumetric water content measurements can be calculated with high confidence from permittivity, using techniques described by Anderson in U.S. Pat. No. 6,657,443, which makes these instruments highly suitable for measuring the moisture environment in the root zone of growing crops. Many other methods of soil water content measurement are plagued by errors attributed to the electrical conductivity of the soil. 
     A further advantage of TDRs is that they can be inserted into the soil without excavation and thus can gather transpiration data without severely disturbing the delicate transpiration system comprised of the small roots and soil structures around them. This is often a critical requirement for horticultural research and for monitoring the root zone of food crops. 
     The use of Time Domain Reflectometers has been limited by their high cost. A further drawback has been the impractical deployment of TDR sets in agricultural and research fields due to their coaxial cables and power supply lines which must be strung through the crops. Both of these drawbacks have been resolved with the introduction of an integrated Time Domain Reflectometer wherein the step function generator and waveform digitizer are located immediately at the incident end of the waveguide, as disclosed in U.S. Pat. No. 6,831,468 by Anderson et al. 
     In that disclosure the waveguide is single-ended. The step function propagates along a single conductor in the presence of a reference ground plane or conductor. Although that 2-conductor waveguide provides a useful propagation path, it lacks balance and does not maximize the volume of medium subjected to the permittivity measurement. In practical systems, the reference ground plane is often divided into two rods parallel to the propagation rod and spaced equally on either side of it, thus forming a 3-rod waveguide. This improves the spatial balance of the propagating wave and facilitates the permeation of additional soil volume in the measured sample. Many traditional TDR probes are fashioned from three rods to achieve these advantages. The coaxial center conductor is wired to the center rod and the sheath is wired to the outer two rods. However, the resulting 3-rod probe is more difficult to insert into the root zone and still is not optimum for sampling volume. 
     In order to reduce the insertion force in a balanced waveguide and to improve its sampling volume some waveguide probes are built with baluns in them, a balun being a transformer used to convert between a balanced signal and a single-ended one. In other words, these devices convert the unbalanced single-ended coaxial cable into a balanced differential 2-wire transmission line. The waveguide takes the form of two rods with a balanced differential wave propagating on them. The sampled soil volume is improved by about 40% over a 3-rod waveguide having the same width, and the insertion force is reduced considerably. 
     A disadvantage exists with the 2-rod waveguide. Since the balun is reactive, being an inductive device, it acts as a high pass filter. It cannot propagate the steady state part of the step function. Many researchers depend upon the long-term response of the reflected wave to derive the electrical conductivity of the soil. When a balun is deployed as part of a measurement system, the long-term step response diminishes severely and can easily droop to zero within a few tens of microseconds. Thus, balanced waveguides equipped with baluns have not been deployed where electrical conductivity measurements require high confidence. 
     The ideal TDR waveguide system would employ all of the following: 
     1. A balanced differential wave with uniform electromagnetic (EM) field characteristics relative to the poles of the waveguide; 
     2. No more than two rods for easier insertion and higher sampling volume; and 
     3. No droop in the steady state step response, that is, no balun. 
     BRIEF SUMMARY 
     For accurate absolute soil moisture sensors, the best Time Domain Reflectometers (TDR), whether coaxial-coupled or integrated, have necessarily incorporated either a three-conductor waveguide, or a two-conductor waveguide driven by a balancing transformer (balun). The problem remains that the use of three conductors increases the insertion force required for soil moisture testing by 50% over a two-conductor system, while the use of a balun causes steady state signals to droop. 
     The shortcoming of each of those techniques is the use of a coaxial cable which is the source of the single-ended waveform problem. Integrating the step function generator and the waveform digitizer onto the waveguide allows for removal of the coaxial cable from the transmission line which eliminates the problem of a single-ended waveform. The result is a balanced, differential step function applied directly to a two-conductor transmission line, a differential waveguide. Described here are methods and apparatus for accomplishing the required ultra fast, high-resolution digitization of the differential waveform. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The particular features and advantages of the system and methods briefly described above as well as other objects will become apparent from the following description taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a block diagram of a differential Time Domain Reflectometer; 
         FIG. 2  shows time domain plots of launching and digitizing the differential waveform; 
         FIG. 3  is a time domain plots showing the detail at a point of ambiguity in the waveform; and 
         FIG. 4  depicts a two-prong probe having pointed non-conductive tips. 
     
    
    
     The following Reference Numbers may be used in conjunction with one or more of the accompanying  FIGS. 1-4  of the drawings:
       100  Integrated Time Domain Reflectometer     110  Microprocessor     120  Timing Ramp Generator     130  Timing Digital-to-Analog Converter (DAC)     135  Ultra High Speed Comparator, timing     138  Latch Strobe     140  Differential Step Generator     142  input to Differential Step Generator     144  reference input to Differential Step Generator     145  Voltage Reference     150  Successive Approximation DAC, positive     155  Successive Approximation DAC, negative     160  Ultra High Speed Latching Comparator, positive     165  Ultra High Speed Latching Comparator, negative     180  Balanced TDR Waveguide, positive     185  Balanced TDR Waveguide, negative     210  voltage ramp from Timing Ramp Generator     310  Incident Wave     320  Reflected Wave     330  Region of Ambiguity     470  Probe Tip     472  base of Probe Tip     475  Threaded Protrusion     480  Transmission Line Rod     482  Tapped Recess of Transmission Line Rod   

     DETAILED DESCRIPTION 
     An ideal Time Domain Reflectometer (TDR) waveguide system would employ a balanced differential wave having uniform electromagnetic (EM) field characteristics relative to the poles of the transmission line. It would accomplish this without the use of a balancing transformer (balun) in order to avoid droop in the steady state step response. For use in moisture sensing applications, it would also require no more than two rods in order to ease insertion into the media being measured and to provide a higher sampling volume. 
     These objectives have not been attained in a traditional coaxial-coupled Time Domain Reflectometer. The integrated TDR disclosed in U.S. Pat. No. 6,831,468 also does not meet these objectives. The implementation described there can drive a 3-conductor transmission line or it can be outfitted with a balun to drive a 2-conductor transmission line just the same as a conventional coaxial cable coupled TDR. Nonetheless, an integrated TDR is a step toward achieving the above objectives. 
     Integration of the step function generator and the waveform digitizer onto the waveguide eliminates the source of the single-ended waveform problem, namely the coaxial cable. By eliminating the intervening cable it is possible to generate a balanced, differential step function and to apply it directly to a 2-conductor, differential transmission line. Ultra High Speed Comparators with differential outputs, such as the ADCMP606 manufactured by Analog Devices, Inc., are capable of doing this. But digitizing a differential waveform with pico-second resolution is a more difficult matter. A proven method of digitizing a repetitive, differential, ultra high speed waveform is disclosed herein. 
     In  FIG. 1  a precision timing generator having pico-second resolution is controlled by a microprocessor  110  with relevant firmware. The timing generator comprises a Timing Ramp Generator  120 , a Timing DAC  130  (Digital-to-Analog Converter), and an Ultra High Speed Comparator  135 . This timing generator provides precise, programmable timing for two closely spaced events, (a) the launching of a differential step function, and (b) the sampling of that waveform at a precise, programmable time after the launch. By incrementing the programmable time offset the microprocessor  110  controls the system to acquire amplitude measurements from successive points in time until the waveform has been digitized. 
     A balanced, differential Step Function Generator  140  is constructed from an Ultra High Speed Comparator that offers differential outputs. The step function generator  140  drives the transmission line as a differential waveguide ( 180 ,  185 ). As the waveform on the upper conductor  180  of the differential waveguide increases, the waveform on the lower conductor  185  decreases at the same rate. The overall waveform is the difference between the waveforms at the upper ( 180 ) and lower ( 185 ) conductors of the differential transmission line. 
     The composite waveform is derived by digitizing the two half-waveforms at the incident end of the waveguide, and then taking the difference between them in the microprocessor ( 110 ). The waveforms are simultaneously, but independently, digitized using the positive and negative Ultra High Speed Comparators ( 160  and  165 , respectively) in conjunction with the positive and negative Successive Approximation Digital to Analog Converters (DACs  150  and  155 , respectively). 
     The process of launching and digitizing the differential waveform is described using  FIG. 2 . The microprocessor ( 110 ) activates the Timing Ramp Generator  120  to start a negative-slope voltage ramp  210 . This ramp is generated by drawing a constant current out of a capacitor that has been pre-charged to 1.4 volts. The rate of the ramp  210  is on the order of −61 mv/ns. Thus, in 20.48 ns the ramp will traverse a range of 1.25 volts. 
     One of the inputs ( 144 ) of the Step Function Generator  140  is connected to a 1.25-volt reference  145 , whereas the other input ( 142 ) is connected to the Timing Ramp Generator  120 . When the ramp reaches 1.25 volts a differential step function is applied by the Step Function Generator  140  to the waveguide ( 180 ,  185 ). 
     The Timing DAC  130  will have been pre-set to a fixed voltage output somewhat below the 1.25-volt reference level. This Timing DAC  130  is used to generate a strobe ( 138 ) signal that will latch the state of the inputs of the Voltage Sensing Comparators  160  and  165 . The output voltage of the Timing DAC  130  determines the timing of the strobe  138  relative to the launch of the waveform. For example, if the output of the Timing DAC  130  is precisely 6.1 my below the 1.25-volt reference (at 1.2439 volts), then the strobe will be generated precisely 100 psec after the launch of the step function onto the transmission line. This will cause the Voltage Sensing Comparators  160  and  165  to record the state of the waveform relative to their reference inputs at precisely 100 psec after the waveform launch. The microprocessor ( 110 ) then reads the outputs of the Voltage Sensing Comparators ( 160  and  165 ) to determine whether the positive and negative halves of the waveform were above or below the threshold settings at the comparator inputs at the 100 psec point in time. 
     By launching the waveform repetitively and changing the threshold settings of the Successive Approximation DACs ( 150  and  155 ), the waveform amplitude on the positive conductor  180  and the waveform amplitude on the negative conductor  185  can be separately determined. In the example of  FIG. 2  the amplitude is being acquired at 100 psec. The difference between the positive and negative conductor readings is the overall differential waveform amplitude. After the waveform is measured at the 100 psec point as in  FIG. 2 , the Timing DAC  130  can be decremented by 305 microvolts, that is, five percent of 6.1 mV, in order to apply the successive approximation process to capture the waveform amplitude at 105 psec. 
     It should be noted that the successive approximation process requires a waveform launch for each bit in the resolution of the Successive Approximation DACs ( 150  and  155 ). If 12-bit DACs are used then 12 waveform launches are required to digitize a given time point on the waveform. Given that a statistically sound reading is desired each point may be digitized a number of times and each point might require more than 100 waveform launches. In order to minimize the waveform acquisition time, positive and negative halves of the differential signal are digitized simultaneously. This requires the use of two Successive Approximation DACs. It should be clear that a single DAC could be used to digitize both halves of the waveform though such a sequential procedure would require twice as much time. 
     Referring to  FIG. 3 , when the step function waveform is initially applied to the TDR transmission line, the measured response tends to track the Incident Wave  310  establishing a baseline reference level. As time passes the step function reaches the open distal end of the transmission line and the Reflected Wave  320  is superimposed on top of the baseline reference level of the outbound Incident Wave  310 . It is this region of the waveforms that carries information that is useful for determining the propagation time though the medium. The propagation time then may be used to calculate a bulk dielectric constant of the medium. The characteristic slope of transition in this region is useful to determine a value for the conductivity of the medium 
     For determination of the propagation time of a waveform through a medium, alternate methods may be used. One alternate method requires taking the first and second derivatives of the waveform during the time in which the two step functions are superimposed. Due to finite rise times and losses in the medium, the two step functions no longer appear as rectangular. However, at the onset of first energy transmission in the Incident Wave  310  and at the onset of first energy reception in the Reflected Wave  320  there is a positive inflection point where the waveform turns abruptly upward from a baseline reference level. This inflection point is accompanied by a large peak in the second derivative. Noise can also create large peaks in the second derivative, but noise will not be followed by a sustained rise in the resultant waveform. That sustained rise is accompanied by a sustained positive first derivative. 
     In order to more quickly derive the propagation time, the waveform can be digitized at coarse timing resolution, for example, at intervals of 200 psec. Differences between adjacent amplitudes can be calculated to form the first derivative of the waveform. Differences between adjacent points of the first derivative are then taken to form the second derivative. The second derivative is examined to find peak values that are followed by sustained positive values in the first derivative. The points where this occurs are the points of the inflection points of the incident wave and of the reflected wave to within 200 psec accuracy. That is, a first pass series of measurements is made for the purpose of differentiating the waveform to locate a local maximum in a second derivative that is followed by a sustained positive value in a first derivative to establish an approximate time of an incident wave and an approximate time of a reflected wave. After these points are identified at 200 psec accuracy, further examination of the region of the waveform surrounding these points is made by acquisition of additional data at 5 psec resolution to determine the location and to establish the time of the inflection points with an accuracy of 5 psec. In other words, a second pass of measurements is made for the purpose of recalculating the time of the first derivative and the time of the second derivative of the waveform using minimal increments of the programmable time offset respectively from the approximate time of the incident wave and the approximate time of the reflected wave to determine a precise time of the incident wave and a precise time of the reflected wave. 
     In addition to the propagation time, another parameter of interest is the electrical conductivity of the medium. One method of determining conductivity relies upon the characteristic slope of transition which has been described in U.S. Pat. No. 6,831,468. 
     Another method depends upon the long-term, steady state, response of the reflected wave. This latter method was not an available option when using a single-ended TDR, or any system that included a coaxial cable, since the long-term step response would droop rapidly. The presently described differential system with an integrated TDR does not suffer from this shortcoming. Since droop is no longer a factor, conductivity may be derived from the steady state level of the reflected wave  320 . 
     A critical part of the waveform measurement is the timebase against which the amplitude points are referenced. The accuracy of the timebase, which is described here as based upon an analog ramp, is limited by the tolerances of the components involved. High accuracy can be obtained by comparing the measured waveform propagation time with the theoretically-derived value. The difference between the two values can be used to calculate a scale factor that is then applied to the propagation readings to correct for small errors caused by component tolerances. Those skilled in the arts will recognize that other methods of generating a programmable time offset are possible including those using ultra high speed counters driven by crystal controlled frequency synthesizers. Some of these methods do not require calibration as they are crystal controlled. The system described here provides the necessary accuracy at much lower cost. 
     A customary feature of most TDR transmission lines used with conventional coaxial cable coupled equipment is a pointed tip on the end of the probe conductors. This greatly helps with inserting the probe into the soil, but with the high resolution possible with the circuit described above the sharpened tips become a problem. 
     The problem arises when the step function waveform approaches the distal end of the transmission line. As the step function waveform encounters a changing conductor diameter due to the sharpened tips a soft reflection of the waveform is produced rather than an abrupt one. The characteristic impedance near the tip is a function of the taper in the diameter. Reflections begin where the taper begins and continue to occur until the pointed tip of the conductor is reached. The net result is a region of ambiguity  330  at the onset of the reflected wave as shown in  FIG. 3 . 
     This ambiguity has a slight impact on the accuracy of determining the propagation time. If the rod tips are blunt the ambiguity is not present, but the probe is difficult to push into the soil. A solution to this problem is to fabricate the waveguide rods as in  FIG. 4  with blunt tips and then to fasten a non-conductive, sharpened tip to the ends of the rods. This new probe tip  470  with a threaded stub can be screwed into a tapped hole in the end of the transmission line rod  480 . It can be made of plastic, ceramic or other non-conductive material with relatively low permittivity. The probe tip  470  is fabricated in the form of a cone  474  and tapered so that the base  472  of the cone  474  has the same diameter as the transmission line rod  480 , which serves as a waveguide conductor. A threaded protrusion  475  extends from the base  472  of the cone  474  so that the probe tip  470  can be screwed into a tapped recess  482  in the end of the waveguide conductor. 
     Although the presently disclosed apparatus has been described as a Time Domain Reflectometer for determination of absolute moisture content based upon permittivity of a medium such as soil, it will be recognized by those skilled in the related arts that the described apparatus and methods have applications in other fields, and that details of the above-described embodiments may be modified without departing from the underlying newly described principles. For example, the described apparatus and methods apply where the medium is bulk grain, bulk paper, baled hay, a hydrocarbon fuel, or oil, among other media. The scope of the present disclosure should, therefore, be determined only by the following claims.