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Re: Dual Frequency TDR for Coincident Measurement of W C & porosity of



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Thank you for elaborating.

>
>
>The dielectric constants for water and solid soil, Kw and Ks, are
>t-dependent.
>(Am I correct?)
>
Dielectric properties are material (matter) dependent--not time 
dependent.  The basic definition for dielectic properties comes from a 
material's ability to store energy in the presence of a dynamic electric 
field.  If the ability depends on the rate of application of the 
electric field, the dielectric property becomes representable as a 
continuous, complex function rather than a scalar.  A Bode plot showing 
amplitude and phase variations with frequency (spectrum) can be used to 
present such complex functions.  

The rise time of a TDR pulse reflects the spectrum of the transmitted 
signal.  To measure the double transit time of a fixed length of line, 
the rise time must be sufficiently rapid to enable adequate resolution 
of the time between the transmitted and reflected signals.  If the 
highest component of the transmitted signal results in the far end of 
the line appearing to be inductive rather than capacitive, ringing will 
occur when the transmitted and reflected signals combine at the 
transmitter.  The frequency of the ringing will vary with the dielectric 
properties of the line.

Because real lines are nonuniform, they present a complex reactive 
network to the signal rather than an ideal, unterminated transmission 
line.  The presence of nonuniformities create distortions and 
reflections in addition to that created by the far end of the line.

 Substantial research has been conducted to characterize water in 
various phases for both environmental and atmospheric applications. 
 Generally, the variations that occur related to your interests require 
quite precise monotonic measurement techniques to develop adequate 
resolution.  TDR signals do not lend themselves easily to this precision 
for this purpose.  High-speed TDR instrumentation similar to that used 
to characterize computer busses combined with elaborate  post-processing 
might serve.

M. G.  

>
>Thus, t' and t" can be chosen in such a way that the ratio Kw'/ Ks' is
>considerably different from Kw"/ Ks".  If this is done, then it might be
>possible to solve, for
>theta and phi, a system of two simultaneous equations of a mixing-model
>type, for instance:
>
>K'^1/2 = theta*Kw'^1/2 + (1-phi)*Ks'^1/2 + (phi-theta)*Ka'^1/2  (eq.1)
>
>K"^1/2 = theta*Kw"^1/2 + (1-phi)*Ks"^1/2 + (phi-theta)*Ka"^1/2  (eq.2)
>
>where theta stands for water content, a for air, phi for porosity.
>
>A sample of water would easily allow determination of Kw' and Kw".
>A dry sample of the soil, of known  phi, could be used to determine Ks' and
>Ks" , using equations 1 and 2.
>Once Ks' and Ks" are known for that given soil, and Kw' and Kw" are also
>known, then the system of equations 1 and 2 could now be easily solved for
>phi and theta.
>
>*HENCE, SUCH AN INSTRUMENT COULD BE USED FOR SIMULTANEOUS TDR-DETERMINATION
>OF THETA AND PHI for a given soil -- which, as far as I know, has not yet
>been described in the
>literature.*
>
>(Is the idea really new?  Has anyone read about something similar?)
>
>Other rise times, t'" and t"", could also be used to find further
>parameters, specially if a four-phase mixing model is used...
>
>I am myself very keen to test this idea.  I am considering to prepare a
>project on this and submit it to some agency for financial support.  *But*:
>I am rather inexperienced in TDR research, so I would very much
>appreciate listening to opinions on the feasibility of this idea before I
>invest more time and effort on it...
>
>I know the theory above is very much simplified.  It is just a first
>approximation.  I really want to confirm whether the central idea is
>correct...  If it is correct, then other
>mixing-models could be considered, more sophisticated than eqs. 1 and 2.
>
>I will thank you very much for any comments/suggestions/criticism/etc, on
>this idea.
>
>Best regards,
>
>Elimoel A. Elias
>e-mail: elias@imagenet.com.br
>Website:  http://elimoel.freeyellow.com/elimoel.html
>ICQ 109845414
>Tel.: +55-19-432-9458
>
>----- Original Message -----
>From: "EA Elias" <elias@imagenet.com.br>
>To: <owner-sowacs@aqua.ccwr.ac.za>
>Sent: Tuesday, October 16, 2001 11:05 AM
>Subject: TDR instrument with regulable risetime.
>
>
>Dear list members,
>
>I am seeking a TDR  instrument with regulable risetime, covering a range as
>large as possible.
>
>Has anyone in this list ever used, or heard of, something like this?
>
>I am familiar with a TDR instrument operating at a fast rise time, <200 pS.
>I have also heard of instruments with
>faster rise times, <10 pS.  I am seeking an instrument with a regulable
>risetime, covering a range as
>large as possible, perhaps from 10 to 200 pS.  But I have been unable to
>find any information about this.
>I have emailed some companies:
>Soilmoisture
>Campbell Scientific Inc.
>Tektronix
>E.S.I. Environmental Sensors Inc.
>but I have only received negative answers.
>
>I will be grateful for any information on this matter.
>
>Elimoel A. Elias
>e-mail: elias@imagenet.com.br
>Website:  http://elimoel.freeyellow.com/elimoel.html
>ICQ 109845414
>Tel.: +55-19-432-9458
>
>
>