users’ guide - digital.csicdigital.csic.es/bitstream/10261/35790/3/tdr-lab...

- Users’ Guide -

TDR-Lab Version 1.2 – Spring 2011

A TDR software program for measurements of soil volumetric water content and bulk electrical conductivity compatible with Tektronix 1502C Metallic, TDR-100

Campbell Sci. and TRASE Soilmoisture Equipment Corp. cable testers.

By:

Dr. David Moret-Fernández (EEAD-CSIC) José Vicente (UZ)

Dr. Francisco Lera (UZ-CSIC) Borja Latorre (EEAD-CSIC)

Dra. María Victoria López (EEAD-CSIC) Nuria Blanco (EEAD-CSIC)

Dr. César González-Cebollada (UZ) Ricardo Gracia (EEAD-CSIC)

María José Salvador (EEAD-CSIC) Ana Bielsa (EEAD-CSIC)

Dr. José Luís Arrúe (EEAD-CSIC)

Copyright © 2011 - FSLC, EEAD (CSIC), Avda. Montañana 1005, 50059-Zaragoza

Spain

User Guide. TDR-LAB V.1.0

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Table of Contents

Page

1. Introduction 5

2. Principles of Time Domain Reflectometry: Concepts and methods 7

2.1. Theory 7

2.2. Estimations of soil water content and bulk electrical conductivity 11

2.2.1. Graphical methods 11

2.2.2. Modelling method 13

3. Software installation 17

4. User interface 18

4.1. Running the software 18

4.2. Creating a new project and selecting the cable tester 19

4.3. The TDR-Screen 21

4.4. TDR cable tester calibration 24

4.5. Coaxial cable and TDR probe settings 24

4.6. Connecting the TDR-Lab to the cable tester and acquiring a TDR

waveform

29

4.7. Calibration of the coaxial cable and TDR probe 32

4.7.1. Calculation of the effective length of the coaxial cable and

TDR probe

32

4.7.2. Measurement of the long-time reflection coefficient of the

coaxial cable and TDR probe, in air and short-circuited

35

4.7.3. Calculation of the TDR probe cell constant 36

4.8. TDR waveform analysis 37

4.8.1. Estimation of water content 37

4.8.2. Estimation of bulk electrical conductivity 42

4.9. Automated analysis 43

4.10. Analysis results manager 45

4.11. Automated readings 46

4.12. Export / import of data files 47

3


4.13. Data waveform storage 49

4.14. Multiplexers and datalogger connections 49

REFERENCES 50

APPENDIX 52

4


1. Introduction The TDR-Lab software has been developed by the Group Física del Suelo y Laboreo de

Conservación of the Estación Experimental de Aula Dei (CSIC) in collaboration with the

Departamento de Materiales de Interés Tecnológico of the Instituto de Ciencia de Materiales

de Aragón (ICMA-CSIC) (Universidad de Zaragoza – CSIC), Zaragoza (Spain). This software

has been created with an easy Windows interface and includes the following characteristics:

· Compatibility with the Tektronix 1502C Metallic TDR, the TDR100 Campbell

Scientist and the TRASE Soilmoisture Equipment Corp. cable testers.

· TDR waveforms are expressed as a reflection coefficient as a function of time.

· The ability to use the computer’s internal clock to make timed readings.

· Self-calibration methods to increase accuracy.

· An open interface to make data visible, and make it possible to combine stored TDR

waveforms.

· Four different methods for water-content estimations (manual, derivative, tangents and

numerical methods) and two different procedures for electrical-conductivity

determinations (long-time analysis of TDR waveform and numerical method).

· Integrated project manager. All projects, measurements and analyses are stored in a

centralized database. All coaxial cables and TDR probes of the different projects are

saved in a single repository.

· Monitoring of automated waveform readings.

· Ability to change the coefficients of the third-order polynomial Topp (1980) equation.

· Option of calculating the dielectric constant from the water temperature.

· An easy procedure to calculate the probe impedance and cell constant.

This manual has been written to explain the concepts and the functionality of the TDR-Lab

application. Because it is constantly changing and because the manual is only updated at

intervals, items contained in this text may become inaccurate. If something is not contained

within this text, or is radically different, please email us your comments and questions. We

will answer any questions to the best of our ability. We hope this application proves to be of

benefit.

5


TDR-Lab team:

Dr. David Moret-Fernández Project leader

José Vicente Head programmer

Dr. Francisco Lera Electromagnetic soil modelling

Borja Latorre Programmer and Analysis Algorithm Development

Other collaborators involved in the software evaluation:

Dr. María Victoria López

Nuria Blanco

Dr. César González-Cebollada

Ricardo Gracia

María José Salvador

Ana Bielsa

Dr. José Luis Arrúe

We are also grateful to Javier Álvarez and Axel Ritter Rodríguez (Ritter-Rodriguez, 2002)

for providing us with the Trasedata source code for connecting the TDR-Lab software to the

TRASE TDR cable tester.

Acknowledgments This research was partially supported by the Ministerio de Ciencia e Inovación (Grants: PIE-200840I214; AGL2007-66320-CO2-02/AGR; AGL2009-08501) and DGA- Obra social La Caixa (Grants: GA-LC-010/2008; GA-LC-006-2008).

Grupo de Física de Suelo y Laboreo de Conservación (Soil Physics and Conservation Tillage Group)

Copyright © 2010 - FSLC, EEAD (CSIC), Avda. Montañana 1005, 50059-Zaragoza. Spain Registered:

Nº protocol: 177/11 Date: 04-02-2011

6

http://webpages.ull.es/users/aritter/software.html

http://www.eead.csic.es/index.php?id=97


2. Time Domain Reflectometry: concepts and methods Since the first soil science application in 1980, Time Domain Reflectometry (TDR) has

increased in popularity because of its versatility in providing real-time, non-destructive

estimations of soil water content (θ) and bulk electrical conductivity (σ). The main advantages

of this method over other techniques are: (a) its superior accuracy to within 1 or 2% of

volumetric water content; (b) the minimal calibration requirements for a large range of soils

(c) the avoidance of radiation exposures associated with neutron probe or gamma-attenuation

techniques; (d) excellent spatial and temporal resolution; (e) the fact that measurements are

simple to obtain, and (f) the method is capable of providing continuous soil water

measurements through automation and multiplexing (Jones et al., 2002). Limitations of the

TDR method are the relatively high equipment costs, the possibly limited applicability under

highly saline conditions due to signal attenuation, and the fact that soil-specific calibration

may be required for soils having either a large amount of bound water or high organic matter

content.

2.1. Theory

The TDR cable tester launches an electromagnetic pulse along a transmission line and

records a signal or TDR waveform, which is expressed by the voltage (V) or reflection

coefficient (ρ) as a function of time (t) (Figure 1). While the transit time of the TDR pulse

propagating one return trip along a waveguide of length L (tL) mainly depends on the TDR

probe geometry and the dielectric constant of the medium (εa), V is affected by the electrical

conductivity (σ) of the medium (Topp and Ferré, 2002).

The reflection coefficient, ρ, as a function of time, t, is typically defined as

( ) ( )iVV

VtVt−−

=0

0ρ (1)

where V(t) is the measured voltage at time t, V0 is the voltage in the cable just before the

insertion of the probe (standard impedance value of 50 Ω), and Vi is the incident voltage of the

cable tester before the pulse rise.

The transit time, tL (ns), of the TDR pulse propagating one return trip along a transmission

line (e.g., a TDR probe) of length L (m) is represented by (Topp and Ferré, 2002)

7


cLtL

*2 ε= (2)

where c is the velocity of light in free space (3 108 m s-1) and ε* the relative dielectric constant

of the medium.

Time (ns)

Ref

lect

ion

coef

ficie

nt

-1.0

-0.5

0.0

0.5

1.0

t L

Water

Figure 1. TDR waveform expressed by the reflection coefficient as a

function of time. The tL symbol indicates the transit time of the

TDR pulse propagating one return trip along a waveguide of length

L.

The relative dielectric constant, ε*, is treated as a complex form with a real part and an

imaginary part or dielectric energy loss component. The energy dissipation occurs through two

processes. The first process results from the polarization of dipolar molecules, which gives rise

to a phase lag between the imposed field and the material’s response to it. This phase lag is a

function of the angular frequency, ω, of the imposed field. Because of this lag, ε* must be

represented as a complex quantity with a real (in-phase) component, ε’(ω), and an imaginary

(out-of-phase) component, ε”(ω). The second process of energy dissipation arises from the σ.

The contribution of both polarization and conductivity to ε* is represented by (Kraus, 1984)

( ) ( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+−=

0

0* "'ωεσ

ωεωεε i (3)

8


where 1−=i , σ0 is the zero frequency electrical conductivity of the bulk sample, and ε0 is

the dielectric constant of free space. Over the TDR frequency range (≈ 1 GHz), most soils

show a negligible dielectric loss, and hence ε* ≅ ε’. In these cases, the term ‘apparent dielectric

constant’ (ε) can be used for the measured complex dielectric constant (Topp et al., 1980), and

hence ε* ≅ ε.

The soil bulk dielectric constant is mainly governed by four dielectric constituents that

compose the soil bulk: liquid water (εw ≈ 81), soil minerals (εs = 3 to 5), frozen water (εi = 4),

and air (εa = 1). The large disparity between εw and the ε of the other constituents means that

small changes in water content result in significant variations in the total soil bulk dielectric

constant. This characteristic makes the method relatively insensitive to soil composition and

texture and thus appropriate for soil water measurement.

Estimations of soil volumetric water content (θ) are typically calculated using a third-order

polynomial empirical equation (Topp et al., 1980) that relates ε and θ and fits quite well for a

large range of mineral soils

( ) ( ) ( ) ( ) 362422 10341055109221035 ε.ε.ε..θ −−−− +−+−= (4)

This function, which assumes that calibration is conducted in a fairly uniform soil without

abrupt changes in soil water content along the wave-guide, provides an adequate description

for a water content range lower than 0.5 (which covers the entire range of interest in most

mineral soils), with an estimation error of about 0.013 for θ. However, this model fails to

adequately describe the ε-θ relationship for water contents exceeding 0.5, and for both organic

soils and mineral soils high in organic matter. This is due to the fact that Topp’s calibration

was based on experimental results for mineral soils and concentrated on the range of θ < 0.5.

In these cases, specific polynomial curves (Pepin et al., 1992; Jacobsen and Shjønning, 1993)

or physically based dielectric-mixing models (Dobson et al., 1985; Roth et al., 1990; Malicki

et al., 1996) should be adopted since these take into consideration the dielectric mixing of the

constituents (air, water and solid phases) and their geometric arrangement.

The TDR waveform undergoes attenuation as the electromagnetic signal propagates in

conductive media. On the basis of the Giese and Tiemann (1975) thin-layer method, Topp et

al. (1988) found that, for ideal systems where dissipation only occurs in the sample medium,

9


the sample electrical conductivity, σ (S m−1), recorded with an uncoated twin-rod TDR probe,

can be related to the long-time attenuation of the TDR signal, where the effects of the

dielectric dissipation caused by polarization phenomena vanish. Lin et al. (2008) showed that,

the σ estimated with an uncoated probe is more accurately estimated according to

⎟⎟⎠

⎞⎜⎜⎝

⎛+−

=∞

∞

Scale,

Scale,

r

P

ρρ

ZKσ

11

(5)

where ρ∞,Scale, is the scaled steady-state reflection coefficient corresponding to the ideal

condition in which there is no instrument error o cable resistance, Zr is the output impedance

of the TDR cable tester (50 Ω); and KP (m−1) is the probe-geometry-dependent cell constant

value, which can be determined by immersing the probe in different electrolyte solutions of

known conductivity (Wraith, 2002). The ρ∞,SC to be used in the usual Giese–Tiemann equation

is calculate according to

( )( )( )( ) ( )( ) 1

112 +

+−+−+−−

=∞∞∞∞∞

∞∞∞∞

air,SC,air,air,SC,

air,SC,air,Sclae, ρρρρρρ

ρρρρρ (6)

where ρ is the steady-state reflection coefficient of the sample under measurement, ρ∞,air is the

steady-state reflection coefficient when the probe is open in air, and ρ∞,SC is the steady-state

reflection coefficient when the probe is short-circuited.

10


Time (ns)

Ref

lect

ion

coef

ficie

nt

-1.0

-0.5

0.0

0.5

1.0

ρf

Air

Water σ = 0.03 S m-1

Short-circuited

Figure 2. TDR waveforms to estimate bulk electrical conductivity (σ). The ρf

symbol denotes the long-time reflection coefficient of the TDR

waveform in water with σ = 0.03 dS m-1.

2.2. Estimations of soil water content and bulk electrical conductivity

Estimations of both θ and σ by TDR can be performed by:

• Graphical methods, where θ and σ are calculated from the graphical interpretation

of the TDR waveform.

• Modelling methods, which, using a physically based model, calculate θ and σ

from an inverse analysis of the TDR waveform.

2.2.1 Graphical methods

TDR waveform analysis for soil water content estimations

The estimation of water content using the graphical methods of TDR is based on the fact

that the reflected distance of an electromagnetic wave travelling from the TDR device

(through cables of fixed dielectric properties) to the head of the probe and back again is fairly

constant, with the exception of small variations due to temperature.

11


The most frequently used graphical method of estimating the travel time (tL) (Eq. 2) (Figure

3) is known as the tangents method (Heimovaara, 1993). The calculation of tL needs to define

the first reflection or first peak, which should be set in an initial calibration phase by the user,

and indicates the time at which the electromagnetic signal enters the rods of the TDR probe.

The travel distance, back and forth, along the probe length is determined by finding the second

reflection point, which follows the first peak. This second reflection point refers to the

intersection of the tangent from the max inflection on the wave trace after the first peak, with a

tangent from the local minimum. The local minimum refers to the minimum encountered after

the first peak, and the max inflection refers to the maximum inflection point after the first peak

(Figure 3). Alternatively, the second reflection point can also be calculated from the

intersection of the tangent from the max inflection and a tangent of the averaged slope from an

anchored point between the local minimum and the first peak. The tL is finally calculated by

subtracting the first peak from the point of the second reflection. The dielectric constant is

calculated form Eq. (2) for a known value of probe length (L), and the corresponding

conversion into the volumetric water content is finally calculated by applying the Topp et al.

(1980) equation (Eq. 4) or an equivalent.

.

Time (ns)

Ref

lect

ion

coef

ficie

nt

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

t L

WaterFirst peak

Second reflection point

Figure 3. Location of the first peak and the second reflection point

used to calculate tL using the tangents method.

The tL can also be graphically estimated using the derivative method, in which the first

peak and the second reflection point correspond to the minimum and maximum of the

12


derivative of the TDR waveform (Figure 4) (Timlin and Pachepsky, 1996). The tL and the

corresponding θ value are then calculated as described in the tangents method.

Time (ns)dρ

/dt

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Ref

lect

ion

coef

ficie

nt (ρ

)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

tL

Derivative TDR waveform

TDR waveform

Figure 4. Determination of tL using the derivative method.

Soil bulk electrical conductivity measurements

The most frequently used graphical method of estimating the soil bulk electrical

conductivity (σ) is based on the Lin et al. (2008) model (Eq. 5) (Figure 2), in which ρair and

ρsc must be previously measured by the user, and KP can be calibrated in a laboratory

experiment by immersing the TDR probe in different conductive water solutions (See Section

4.7.3., and Appendix, section App. 2.).

2.2.2. Modelling method

Basic theory

The TDR signal ρ(t) (Eq. 1) is the transient response of the cable-probe-soil set to the cable

tester excitation signal, I(t). The estimation of the soil parameters (θ and σa) from ρ(t) relies on

a numerical inversion process that searches for the values of θ and σa that minimize the root

mean square error obtained from the comparison of the measured and calculated TDR signals.

To calculate the expected TDR signal, the TDR probe and the coaxial cable that connects

the probe to the cable tester are modelled as transmission lines of length lp and lc, respectively.

Although ρ(t) is a time domain signal, transmission line modelling is easier in the frequency

13


domain, and thus Fourier analysis will be used. This approach has already been applied to

TDR characterization of soil water content (Heimovaara, 1994; Heimovaara, 2004; Huebner

and Kupfer, 2007). As the TDR signal is discrete, discrete Fourier transforms implemented in

efficient FFT algorithms are used. The frequency domain excitation signal I(ω) is obtained

from the Fourier transform of the true measured cable tester excitation as

I(ω)=FT[I(t)] (7)

The frequency domain response is then calculated as:

ρ (ω)=I(ω) H(ω) (8)

The H(ω) parameter is the frequency-domain transfer function of the soil-probe-cable set,

and is simply that of a voltage divider constituted by the output impedance of the cable tester

(nominally 50 Ω) and the frequency-dependent input impedance of the cable-probe-soil set,

Zi(ω):

( ) ( )( )ω

ωωi

i

ZZH+

=50 (9)

Then we get the time domain signal ρ(t) by using an inverse Fourier transform:

ρ (t)=IFT[ρ (ω)] (10)

Good introductions to transmission line theory can be found in electromagnetism texts. A

classical reference is by Ramo et al. (1984). In the frequency domain, transmission lines are

characterized by four distributed parameters per unit length: capacitance C (F m-1), inductance

L (H m-1), conductance G (S m-1) and resistance R (Ω m-1). Three of them are related due to

geometrical considerations for linear and homogeneous media:

εμ=LC εσ // =CG (11)

From these four distributed parameters one can obtain the characteristic impedance, Zo (Ω),

and the propagation constant γ (m-1)

( ) ( )CjGLjRjCjGLjRZ ωωβαγ

ωω

++=+=++

=0 (12)

where α is the attenuation constant (Np m-1) and β is the phase constant (rad m-1). For ideal

lossless lines, R=0 and G=0 and thus:

νωωβγ jLCjj

CLZ ====0 (13)

14


where ν is the phase velocity. Once these two parameters are known, the input impedance of a

transmission line of length L connected to a load ZL is calculated as

ll

L

Li γ

γtanhZZtanhZZZZ

0

00 +

+= (14)

In our case of study, Zi is computed in a two-step process. Firstly, we apply (8) to obtain Zp,

the input impedance of the probe inserted in the soil as a transmission line of length l=lp

ending in an open circuit load (ZL->infinity), using the probe’s characteristic Zop, and γp values

corresponding to a given θ and σa pair. Secondly, Zi is obtained using (9) again to compute the

input impedance of the coaxial cable as a transmission line of length l=lc ending in the

previously calculated load impedance ZL= Zp, now using the coaxial cable’s characteristic Zoc,

and γc values.

15


Coaxial cable model

We have used coaxial cable type RG58, with nominal 50 Ω characteristic impedance and

0.66 c propagation velocity. From these data, using Eq. (8) we obtain Lc = 250 nH m-1 and Cc

= 100 pF m-1 for the lossless ideal cable. In real coaxial cables, losses are unavoidable. In the

TDR frequency range the dominant term is due to the finite conductivity of the cable

conductors, sometimes called skin effect losses. This gives rise to a series resistance, Rc, and

to an extra external inductance, Lc2 . Both terms are frequency-dependent, as can be seen in

Nahman (1972). The actual values have been obtained from a best fit to TDR measurements of

the coaxial cable ending in open circuit, 50 Ω and short circuit:

mHLmmR cc /177/177.040 2 μω

ω =Ω+= (15)

Three-rod probes

The transmission line parameters for lossless three-rod probes in air – three identical

cylindrical rods of length lp, radius b and centre-to-centre spacing s – have been obtained from

the calculations of Ball (2002). The characteristic impedance in a vacuum, Zp0, is very well

approximated by (16), where d = b/s.

⎟⎠⎞

⎜⎝⎛= 3

0

00 2

1ln41

dZ p ε

μπ

(16)

From (5), (8) and (11) one can derive the expressions for the capacitance and inductance of

the probe in a vacuum, Cp0 and Lp0 respectively, as

( ) ( )3003

00 2/1ln

42/1ln4 dL

dC pp π

μπε== (17)

When the probe is inserted in a lossy soil with bulk conductivity σa, the distributed

conductance G is obtained by substituting ε0 with σa in the Cp0 formula. The dielectric effects,

including losses, are incorporated by again substituting in the Cp0 formula ε0 with the complex

permittivity of the soil εc= ε’– j ε’’. Το estimate εc we first compute the pure water frequency-

dependent complex permittivity εw(ω) at 16.2 ºC following Meissner and Wentz (2004). For a

soil with water content θ we obtain εa using the Topp formula (4) and finally:

( 001

00 aw

aa

aaac εε

εε)εεεε −

−−

+= (18)

16


where εa0= εa (θ=0) and εa1= εa (θ=1). The effect of the finite conductivity of the probe rods is

negligible for short lengths. If longer lengths are to be used, a procedure similar to the one

outlined for the coaxial cable losses should be followed. However, short probes need a

correction of their actual length to an apparent, longer one. This is due to the fringing of the

electromagnetic field at the open end of the probe, neglected in basic transmission line theory,

which in fact assumes infinitely long lines. We have incorporated this correction by adding an

extra length, double the one estimated by Green (1986) for two-rod probes.

17


3. Software installation To install the TDR-Lab software the following items are required

• The TDR-Lab manual

• The TDR-Lab installation program

• A PC Pentium class or equivalent, with VGA display, running under Windows XP

or higher.

• The SQL Express 2008 (SQLEXPR32_x86_ENU.exe) and Windows Installer 4.5

applications should be previously installed in the computer.

To acquire data, the following items (not required during the installation process) are needed:

• A Tektronix 1502 B/C (or 1503 B/C) Metallic TDR, Campbell Sci. TDR 100 or

TRASE Soilmoisture Equipment Cable Tester.

• A RS232 cable for the Tektronix 1502C Metallic instrument (see Appendix, section

App. 1) or the corresponding cable for the TDR-100 Campbell Sci. cable tester.

• A PC with a RS232 port or USB port with a USB-RS232 adaptor.

• A coaxial cable and a three-wire (or equivalent) probe.

Once all these items are ready

• Unzip the files that have been downloaded from our web site

• Open the extracted folder (Figure 5), launch setup.exe (double click on it or right-

click and then click open) and follow the instructions of the SETUP WIZARD

program.

• Complete the setup wizard

• A new folder named TDRLab and a shortcut TDR-Lab application is installed in the

All programs section of the Start Menu. A TDR-Lab icon is also installed at the

bottom of the computer desktop.

• Computer regional configuration should be selected as “.” and “,” to define

decimals and thousands, respectively

18

http://www.microsoft.com/downloads/en/details.aspx?displaylang=en&FamilyID=58ce885d-508b-45c8-9fd3-118edd8e6fff

http://www.microsoft.com/downloads/en/details.aspx?FamilyID=5a58b56f-60b6-4412-95b9-54d056d6f9f4&displaylang=en


Figure 5. Steps to extract the setup.exe file to install TDR-Lab.

4. User interface 4.1. Running the software

• The TDR cable tester does not need to be connected to the computer to start TDR-

Lab.

• Run TDR-Lab by clicking on the TDR-Lab.exe application, which (by default) is

located in the TDR-Lab folder of the Programs section of the Start Menu, or by

clicking on the icon displayed at the bottom of the computer desktop.

• The software takes some seconds to open the starting window named Project

manager (Figure 6).

19


Figure 6. Project manager window.

4.2. Creating a new project and selecting the TDR cable tester

The data files are organized in projects, which in turn are saved in folders that should be

created in the TDR-Lab Project manager window (Figure 6). To create a folder:

• Click on the New folder command located in the Project menu of the menu bar, or

click on the icon (Figure 6).

• Write in the Folder name and Description boxes the name and description of the

new folder, and click on the Apply button.

• The new folder will appear in the left column of the Project Manager window

(Figure 6).

To create a project, proceed as follows:

• Click on the New project command located in the Project menu of the menu bar, or

click on the

icon.

• This opens a window named New project (Figure 7).

20


Figure 7. New project window.

• Write the name of the project in the Project name box and select the TDR cable

tester listed in the TDR Model box. Four TDR model options are so far available:

the Tektronix 1502C, TDR100 Campbell Sci. and TRASE Soilmoisture Equipment

Corp. cable testers, as well as a virtual TDR cable tester that allows users to work

with simulated TDR waveforms (Figure 8).

• By clicking on the selected cable tester displayed in the TDR device box, a second

column is opened on the right-hand side of the New project window. This describes

the characteristics of the TDR cable tester and the communication settings (Figure

8). These data, which should not be manually changed, are automatically calculated

by TDR-Lab in the calibration process of the cable tester (see section 4.3).

• Click on the Create project button and the name of the new project will appear in

the right column of the Project manager window (Figure 6).

21


Figure 8. Window defining the communication characteristics between the

computer and the cable tester.

Projects and folders can be deleted by clicking on the and icons, respectively,

displayed in the menu bar of the Project manager window (Figure 9).

Figure 9. Window showing the steps to remove a project.

22


4.3. The TDR-Screen

The update, analysis and storage of the TDR waveforms are executed in a specific window,

which has a diagram column on the left (Diagram Column) and a TDR-Screen on the right

(Figure 10). This window is automatically opened by clicking on a project in the Project

manager window (Figure 6).

The Diagram Column displays the TDR probes, which should be previously configured, and

the saved TDR waveforms (see section 4.6; Figure 16).

The TDR-Screen contains three different pages:

• The Analysis page, which displays the settings of the TDR probe, the settings of the

recorded TDR waveforms (see section 4.5), and the applications for analysing the

TDR waveforms (see section 4.8) (Figure 10a). These settings can be directly

modified on the TDR-Screen or by means of the window that defines the

characteristics of the TDR probes (see section 4.5). Any changes in the Analysis

page settings need the TDR-Screen to be updated by clicking on the Refresh button

(Figure 10a).

• The Results page, which shows the last analysis of the recorded TDR waveform and

the provisional results when the numerical model is running (Figure 10b).

• The Display page, which includes the icons for changing the appearance of the

TDR-Screen and an option to display or hide, if previously selected, the long-time

TDR waveform (see section 4.8.3; Figure 25) for estimations of the bulk electrical

conductivity (Figure 10c).

The results obtained from the TDR waveform analysis are also displayed in an output

analysis box located at the top of the TDR-Screen (Figure 10).

The icon located at the top-left of the window allows the user to hide or display the

TDR-Screen (Figure 10). The TDR-Screen can also be hidden or displayed by clicking on the

Display command located in the TDR menu of the TDR-Screen menu bar

23


a

b

c

Figure 10. TDR-Screen window showing the (a) analysis, (b) results and (c) display pages,

respectively.

24


4.4 TDR cable tester calibration

In the particular case of the Tektronixs 1502C cable tester, an instrument calibration should

be performed before starting any measurement. To this end:

• Open the TDR-Screen and click on the Calibrate command which is located in

the TDR menu of the menu bar (Figure 10). Alternatively, the Calibrate

command can be opened by clicking with the secondary mouse button on the

cable tester icon displayed in the Diagram Column of the TDR-Screen.

• Switch on the TDR cable tester (see section 4.6).

• Connect the 50 Ω connector to the cable tester and click on the Ok button. Wait a

few seconds while the TDR cable tester centres the TDR waveform in the

display, and press the Save button once the calibration process has finished.

• The new calibration parameters are saved in the Settings page of the New Project

window (Figure 8).

No calibration is needed for the TDR100 cable tester.

4.5. Coaxial cable and TDR probe settings

Any measurement of water content and bulk electrical conductivity requires previous

definition and configuration of the coaxial cable and TDR probe. To this end:

• Open the corresponding TDR-Screen and select the Cable and Probe subcommand

that is located in the Add command of the Sets menu in the TDR-Screen menu bar

(Figure 11).

25


Figure 11. Steps to open the window to define the characteristics of the coaxial cable and the

TDR probe.

• This opens a first window (Figure 12a), named Cable and Probe Set, for defining

the characteristics of the coaxial cable.

o Click on the icon located on the right of the Cable box, enter the name

and characteristics of the coaxial cable in the corresponding boxes, and click

on the Next button (Figure 12a). The program automatically asks if the user

wants to save the new settings.

o The VP (propagation velocity) Impedance and DC Impedance (direct current

impedance) should be defined by the coaxial cable manufacturer.

o The Infinite values box defines the long-time reflection coefficient values at

the end of the coaxial cable in air and short-circuited. In this case, values of 1

and -1 are defined by default. To measure these values go to Section 4.7.

• The next window (Cable and probe set wizard) allows users to define the type and

characteristics of the TDR probe (Figure 12b). To this end:

o Click on the icon located on the right of the Probe box, and enter the

TDR probe characteristics in the corresponding boxes:

Probe type: for the moment only three-wire probes are available.

Probe: this displays a list of the stored TDR probes.

Name: write the name of the TDR probe.

26


Length and Effective length of the TDR probe. To calculate the

effective length of the TDR probe go to Section 4.7.

Wire spacing: the wire spacing is defined as the distance between the

central and the external rods.

Wire diameter: this defines the rod diameter of the TDR probe.

Epoxy casing width: this describes the head length of the TDR probe.

Cell constant: this denotes the Kp value used to calculate the bulk

electrical conductivity (Eq. 5).

Impedance: value of the TDR probe impedance needed to run the

numerical model. The theoretical impedance can be automatically

calculated by clicking on the icon. To recalculate the TDR

impedance, the new characteristics of the TDR probe should be

previously saved by clicking on the icon (Figure 12a).

Infinite values: this defines the long-time reflection coefficient values

of the coaxial cable plus TDR probe, measured in air and short-

circuited. Values of 1 and -1 are defined by default. To measure these

values go to Section 4.7.

o Click on the Next button once all the TDR probe characteristics have been

defined. The program automatically asks if the user wants to save the new

settings.

27


a b

Figure 12. Windows for defining the characteristics of (a) the coaxial cable, and (b) TDR probe.

• The following window (Figure 13a) defines the settings of the recorded TDR

waveforms:

o Name: this defines the coaxial cable plus TDR probe set. Different names of

TDR probes can be defined for the same cable tester and coaxial cable set.

o Cursor position: this indicates the position of the TDR waveform. The TDR

waveform position can also be modified by moving the pointer located below

the TDR-Screen (Figure 10)

o First peak: this denotes the time when the TDR trace enters the TDR wires.

o Dist / Div: this indicates the scale of the TDR-Screen.

o Num. of points: this defines the points for each TDR waveform, which

depends on the TDR cable tester. While different numbers of points are

accessible for the TDR100, only 251 points are available for the Tektronix

1502C cable tester.

o Acquire second TDR waveform: this command allows the user to record and

save a second TDR waveform, which will be subsequently used to calculate

the bulk electrical conductivity (go to Section 4.8.2). To this end, a second

scale or Dist/Div should be defined. A Dist/Div value equal to 10 is defined

by default.

28


a b

Figure 13. (a) Window defining the settings of the recorded TDR waveforms, and (b) window

summarizing the characteristics of the coaxial cable, TDR probe and TDR measurement

settings.

NOTE: The Dist/Div and Cursor position settings should be constants for a defined coaxial

cable plus TDR probe system. Variations in these values, once a TDR waveform has been

saved, will lead to errors in the estimation of tL (Figure 1).

• By clicking the Next button, a final window is opened that summarizes the settings

of the coaxial cable plus TDR probe system and the configuration of the TDR

measurements (Figure 13b).

• Click on the Finish button, and the name of the configured TDR probe will appear in

the Diagram Column of the TDR-Screen window (Figure 16).

A table summarizing all the coaxial cable and TDR probes saved in the TDR-Lab can be

opened by clicking on the Repository command located in the menu bar of the Project

manager window (Figure 14a and b), or clicking on the Repository command located in the

Sets menu of the TDR-Screen menu bar.

29


a

b

Figure 14. Window showing (a) the steps to open the repository table that contains all

the coaxial cables and TDR probes, and (b) the repository table.

4.6. Connecting TDR-Lab to the cable tester and acquiring a TDR waveform

To start the communication between TDR-Lab and the cable tester, proceed as follows:

• Connect, with the corresponding cable, the cable tester to the computer.

• Check that the cable tester is on.

• Click on the Connect command that is located in the TDR menu of the TDR-Screen

menu bar (Figure 15). TDR-Lab takes some seconds to connect with the cable tester.

30


Figure 15. Steps to connect the TDR-Lab to the cable tester.

To acquire a new TDR waveform:

• In the Diagram Column, click the coaxial cable-TDR probe set to be used and then

click the Refresh button located at the bottom of the TDR-Screen (Figure 16a).

• After a few seconds a TDR waveform is displayed on the TDR-Screen (Figure 16).

• The Analysis on refresh box located at the bottom-right of the TDR-Screen (Figure

16), with four different instructions (None, Manual, Tangents and Derivative),

indicates that TDR-Lab will automatically analyse the TDR waveform (see section

4.8) when the Refresh button is clicked. If the None command is selected TDR-Lab

will record the TDR waveform without any analysis. These preliminary analyses, the

results of which are shown in the top box of the TDR-Screen, are stored by TDR-

Lab and can be recovered by means of the Analysis results manager application (see

Section 4.10).

• The recorded TDR waveform can be stored by clicking on the Save button; the

saved TDR waveform is then displayed in the Diagram Column of the TDR-Screen

(Figure 16a).

• The saved TDR waveform is defined by the data and the time at which the signal

was stored.

• The successive saved TDR waveforms are chronologically stored by TDR-Lab

(Figure 16b).

31


a

b

Figure 16. (a) A single, and (b) a series of TDR waveforms recorded and saved by TDR-Lab.

TDR-Lab also makes it possible to compare two different TDR waveforms in the same

TDR-Screen. To this end, click on a TDR waveform displayed in the Diagram Column and

move it to the TDR-Screen (Figure 17). The second TDR waveform will be displayed in the

TDR-Screen in a different colour (Figure 17).

32


Figure 17. Comparison of two TDR waveforms in the same TDR-Screen.

4.7. Calibration of coaxial cable and TDR probe

The measurement of water content and bulk electrical conductivity using TDR-Lab requires

previous calibration of the coaxial cable and the TDR probe. Three different calibration levels

have been included:

(i) Calculation of the effective length of the coaxial cable and TDR probe using graphical

and numerical methods.

(ii) Measurement of the long-time reflection coefficient of the coaxial cable and TDR probe,

in air and short-circuited.

(iii) Calculation of the TDR probe cell constant (KP) from the long-time reflection

coefficient of the coaxial cable and TDR probe set for different values of electrical

conductivity (see Appendix, section App. 2 ).

4.7.1. Calculation of the effective length of the coaxial cable and TDR probe

The effective length of the coaxial cable is calculated as follows:

• Switch on the TDR cable tester and connect it to TDR-Lab.

• Select the coaxial cable to be calibrated, and open the Cable-Probe calibration

window by clicking on the Calibrate probe command located in the Sets menu of

the TDR-Screen menu bar (Figure 18).

• Open the Cable Calibration page, click on the Calibrate length button (Figure

18), and follow the instructions provided by the software.

33


Figure 18. Window for calibrating the effective length and the long-time reflection coefficient of the

coaxial cable.

The effective length of the TDR probe can be calculated by the graphical or the numerical

method.

To calculate the effective length:

• Switch on the TDR cable tester and connect it to TDR-Lab.

• Submerge the wires of the TDR probe in distilled water, Refresh a new TDR

waveform and fix the first peak of the TDR waveform.

• Click on the Calibrate probe command located in the Sets menu of the TDR-

Screen menu bar, and open the Probe Calibration page displayed by the Cable-

Probe calibration window (Figure 19).

• Click on the Calibrate length button (Figure 19), and the software will ask if the

user wants to calibrate the effective length by the numerical method (Figure 20).

o If NO is clicked, the software will automatically calculate the effective

length of the TDR probe by the tangents method, and will save the results in

the TDR probe settings window (Figure 12b). To this end, follow the

instructions provided by TDR-Lab.

34


Figure 19. Window for calibrating the effective length and the long-time refection coefficient of the

TDR probe.

o If Yes (Sí) is clicked, TDR-Lab will automatically calculate the effective

length of the TDR probe by the numerical procedure. To this end, follow the

instructions provided by the software, and wait several minutes until TDR-

Lab has finished all the calculations.

Figure 20. Option of calibrating the effective length by the numerical method.

35


4.7.2. Measurement of the long-time reflection coefficient of the coaxial cable and TDR

probe, in air and short-circuited

Before calibrating the long-time reflection coefficient, the scale (Dis/Div) of the long-time

TDR waveform should be fixed. To this end:

• Open the Cable-Probe calibration window by clicking on the Calibrate probe

command located in the Sets menu of the TDR-Screen menu bar, and select the

Settings page (Figure 21).

• In the Dis/Div window, select the scale defined to acquire a second TDR

waveform for electrical conductivity estimations (Figure 13a).

Figure 21. Settings window for defining the Dis/Div value to calibrate the long-time reflection

coefficient, in air and short-circuited.

To determine the long-time reflection coefficient of the coaxial cable, in air and short-

circuited (Eq. 5):

• In the Diagram Column, select the TDR probe to be calibrated, and open the

Cable-Probe calibration window by clicking on the Calibrate probe command

located in the Sets menu of the TDR-Screen menu bar.

• Select the Cable Calibration page, click on the Calibrate Rho button, and follow

the instructions provided by the software (Figure 18).

36


Similarly, the long-time reflection coefficients of the coaxial cable plus TDR probe system,

in air and short-circuited (Eq. 5), are calculated as follows:

• Select the TDR probe to be calibrated, and open the Cable-Probe calibration


the TDR-Screen menu bar.

• Select the Probe Calibration page, click on the Calibrate Rho button (Figure

19), and follow the instructions provided by the software.

4.7.3. Calculation of the TDR probe cell constant

The cell constant (Kp; Eq. 5) should be calculated in an external spreadsheet (see Appendix,

section App. 2), using measured long-time reflection coefficients that have been recorded

when the probe has been immersed in different conductive water solutions (Figure 22). To

obtain the long-time reflection coefficients:

• Select the TDR probe to be calibrated, open the Cable-Probe calibration


the TDR-Screen menu bar, and open the EC/Rho Relation page (Figure 22).

• Immerse the TDR probe in a first water solution of known conductivity and click

on the New EC/Rho button (Figure 22). This opens a new window in which the

user should enter the electrical conductivity of the water solution (Figure 22).

Click on the Ok button, and wait some seconds until the TDR-Lab displays, in

the external table (Figure 22), the measured reflection coefficient.

• Repeat this process with different conductive water solutions to obtain a series of

pairs of reflection coefficient vs. electrical conductivity values. These results will

subsequently be used to calculate the cell constant of the TDR probe (see

Appendix, section App. 2).

37


Figure 22. Window for measuring the long-time reflection coefficient of the TDR probe for

different conductive water solutions.

4.8. TDR waveform analysis

Two different methods of TDR waveform analysis for estimations of the volumetric water

content (θ) and bulk electrical conductivity (σ) have been included:

• Graphical analysis, based on the graphical interpretation of the TDR waveform

• Modelling analysis, which estimates θ and σ by inverse modelling of the TDR

waveform using numerical methods.

4.8.1. Estimation of water content

Estimations of θ can be performed on newly recorded or on saved TDR waveforms.

If θ estimations are to be performed on newly recorded waveforms, proceed as follows:

• Connect the cable tester to TDR-Lab and open the TDR-Screen.

• Select a TDR probe and record a TDR waveform by clicking on the Refresh

button (Figure 23).

• Move the Cursor until the TDR waveform, between the first peak and second

reflection point, is centred in the TDR-Screen.

• Select the method of TDR waveform analysis displayed in the Analysis box

located on the left of the TDR-Screen. Four different methods of TDR waveform

analysis are available:

38


o Manual method, where the first peak and the second reflection point of the

TDR waveform are manually chosen by the user (Figure 23a). To this end,

move the vertical lines of the first peak and second reflection point to the

desired locations (Figure 22a).

o Tangents method: a semiautomatic method in which the first peak is defined

by the user and the second reflection point is automatically fixed by the

computer using the tangents method (Heimovaara, 1993) (Figure 23b). The

tangent slope of the second reflection point can be modified by clicking on

the Use slope, Tan at min. window size and Tang. at inflec. window size

commands located at the bottom-left of the TDR-Screen. These commands

are also summarized in the Analysis Settings window (Figure 23a).

o Derivative method: an automatic method in which the first peak and second

reflection points are automatically fixed by the software, by looking for the

minimum and maximum of the derivative function of the TDR waveform,

respectively (Figure 23c).

o Numerical method for homogeneous profile media: an automatic method that

interactively calculates θ and σ by inverse modelling of the TDR waveform

using numerical methods (Figure 23d). In this case, the first peak needs to

have been previously fixed in the calibration of the effective length of the

TDR probe (see section 4.7).

• Once the method of waveform analysis has been selected, click on the Execute

button.

• The results are displayed in the top box of the TDR-Screen and are saved in the

Analysis results manager application (see section 4.10).

NOTE: While the tangents method gives accurate estimations of water content for TDR

probes greater than 5 or 10 cm in length (Dalton and Van Genuchten, 1986; Zegelin et al.,

1992), the numerical method is optimal for shorter TDR probes (i.e. between 0.7 and 3 cm in

length) (Moret-Fernández et al., 2011).

39


a

b

c

d

Figure 23. TDR waveform analysis using the (a) manual, (b) tangents, (c)

derivative, and (d) numerical methods.

40


In order to optimize the calculations with the numerical method, a pre-analysis of θ has

been included in the software. To check these pre-analysis characteristics:

• Open the Analysis Settings window by clicking on the Settings button located on

the left of the TDR-Screen (Figure 23), and click on the Advanced button

(Figure 24a).

• The TDR waveform pre-analyses (manual, tangents or derivative) are defined in

the Initial values from box (Figure 24b). In this case, the tangents method is

selected by default. The initial values of θ and σ can also be modified by the

user (Figure 24b).

• By clicking on the Use longtime waveform analysis (Fig. 24b), the TDR-Lab run

the numerical method taking the σ calculated with the Lin et al. (2008) method

(Eq. 5)

a

b

Figure 24. (a) Analysis settings window; and (b) the

characteristics of the pre-analysis θ

estimations used in the numerical model.

41


The estimations of θ can also be applied to previously saved TDR waveforms. To this end:

• Open a TDR-Screen-type window that displays the saved TDR waveform by

clicking on a TDR waveform saved in the Diagram Column of the TDR-Screen

(Figure 16).

• Select the waveform analysis to be used and click on the Execute button.

• The results are displayed in the top box of the TDR-Screen and are saved in the

Analysis results manager application.

The Topp equation coefficients used to calculate θ (Eq. 4) are defined in the Coefficients

page of the Analysis Settings window (Figure 25a). These coefficient values can be changed

by clicking on the Advanced button (Figure 25a and b).

a

b

Figure 25. (a) Analysis settings window; and (b)

the coefficients for the polynomial

equations used to calculate θ according

to the Topp equation and the numerical

model, respectively.

42


4.8.2. Estimation of bulk electrical conductivity

Estimation of σ can also be performed on newly recorded or on saved TDR waveforms.

The graphical method of estimating σ analyses the reflection coefficient of the long-time

TDR waveform (Eq. 5). To this end, a secondary TDR waveform (Figure 26) should be

previously recorded by the software (see section 4.5; Figure 13a).

The bulk electrical conductivity can also be automatically calculated by running the

numerical model.

Figure 26. Long-time TDR waveform (yellow trace) for calculating the bulk electrical

conductivity.

43


4.9. Automated analysis

An option to automate the analysis of saved TDR waveforms has been included in the

software. To run this application:

• Open the Automated Analysis Settings window by clicking on the Automated

Analysis command located in the Sets menu of the TDR-Screen menu bar.

• Select the TDR cable tester, the TDR probe, the TDR waveform to be analysed and

the Auto Analysis commands (Figure 27a) and click on the Launch button (Figure

27b).

• Only the tangents, derivative and numerical waveform analyses are available.

• The results, which are displayed in the Automated Analysis Settings window, are

organized in a table according to (Figure 27b):

o Date and time of the measurement

o Date and time of the TDR waveform analysis

o Type of TDR-waveform analysis

o Results of the volumetric water content (Theta), dielectric permeability

(Epsilon) and bulk electrical conductivity (Sigma), and details of the

numerical analysis (Time-analysis, number of iterations and fitting value),

if implemented.

• Usable results can be copied and pasted in an Excel-type table.

• To organize the results, go to the Analysis results manager window (see section

4.10.)

44


a

b

Figure 27a and b. Automated Analysis Settings window.

45


4.10. Analysis results manager

The results obtained from the TDR waveform analysis can be organized in the Analysis

Results Manager window. To check and arrange the results:

• Click with the secondary mouse button on the analysed TDR probe, and select the

Analysis Results Manager command.

• This opens the Analysis Results Manager window, in which the results (Figure 28)

are organized in columns according to:

o Date and time of the TDR waveform analysis and storage.

o Type of TDR waveform analysis

o Volumetric water content (Theta), dielectric permeability (Epsilon) and

bulk electrical conductivity (Sigma), and details of the numerical analysis

(Time-analysis, number of iterations and fitting value).

• The data can be exported (see section 4.12) or directly copied and pasted into an

Excel-type table. Undesirable results can also be removed by clicking on the Delete

button.

Figure 28. Analysis Results Manager window.

46


4.11. Automated readings

An option to automate readings at different time intervals has been included in TDR-Lab.

To this end:

• Open the Automated Measures and Analysis Settings window by clicking on the

Measure scheduler command located in the Sets menu of the TDR-Screen menu

bar (Figure 29).

• Select the project and the TDR probe to be used, and define the analysis scheduler.

Four different modes of automated reading have been included (Figure 29):

o Assisted

o As soon as possible. The minimum time intervals range between 4 and 8

seconds, depending on whether a single or two TDR waveforms (for θ and σ

estimations, respectively) have been previously selected (Figure 13a).

o At constant time intervals

o At fixed times throughout the day

• Select the TDR waveform analysis to be employed (none, tangents and/or the

derivative method), and click on the Launch button.

• The recorded TDR waveforms and the results are automatically saved by the

program.

Figure 29. Window for automating the TDR waveform readings.

47


4.12. Export / import of data files

To export the TDR waveforms and results:

• In the Diagram Column of the TDR-screen, select the coaxial cable - TDR probe

to be exported.

• Click the secondary mouse button and select the Export measures command

(Figure 30a).

• Choose the folder where the data are to be saved and click on the Save button.

• All the TDR waveforms and analyses are automatically exported in a .csv

format.

a

b

Figure 30a and b. Example of exporting TDR waveforms.

48


• The .csv file created by TDR-Lab contains the following information (Figure 31):

o Name of the TDR probe.

o Settings of the TDR waveforms.

o Pairs of points of travel time and reflection coefficients for the different TDR

waveforms.

o Results and method used to calculate the water content, dielectric constant

and bulk electrical conductivity, if estimated.

Figure 31. Example of a “.csv” file exported by TDR-Lab

NOTE: To export TDR waveforms, the projects should be saved in a folder previously created

in the Project manager window (Figure 6)

The import files application is not yet operative in this version of TDR-Lab.

49


4.13. Data waveform storage

All data created by TDR-Lab are stored in the TDRDB.mdf and TDRDB_log.ldf files which

should be saved in the C:\TDR-lab\Data folder (Figure 32), which is automatically created

during the software installation.

Figure 32. TDRDB.mdf and TDRDB_log.ldf files saving all TDR data.

4.14. Multiplexers and datalogger connections

For the moment, no multiplexer or datalogger options are available. We are currently

working to include these new applications in the second version of TDR-Lab.

50


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Timlin D.J., Pachepsky, Y.A. 1996. Comparison of three methods to obtain the apparent dielectric constant from Time Domain Reflectometry wave traces. Soil Sci. Soc. Am. J. 60, 970-977.

Topp, G.C., Ferre, T.P.A. 2002. Water content, In, Methods of Soil Analysis. Part 4. (Eds. J.H. Dane and G.C. Topp), SSSA Book Series No. 5. Soil Science Society of America, Madison WI.

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Topp, G.C., Davis, J.L., Annan, A.P. 1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour. Res. 16, 574-582.

Topp, G.C., Yanuka, M., Zebchuk, W.D., Zegelin, S. 1988. Determination of electrical conductivity using time domain reflectometry: soil and water experiments in coaxial lines. Water Resour. Res. 24, 945-952.

Wraith, J.M. 2002. Time Domain Reflectometry. p. 1289-1297. In, Methods of Soil Analysis. Part 4. (Eds. J.H. Dane and G.C. Topp), SSSA Book Series No. 5. Soil Science Society of America, Madison WI.

Zegelin, SJ., White, I., Russell, G.F. 1992. A critique of the time domain reflectometry technique for determining field soil-water content. p. 187-208. In, Advances in measurement of soil physical properties: bringing theory into practice. (Eds. G.C. Topp et al.) SSSA Spec. Publ. 30. SSSA, Madison, WI.

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APPENDIX

App. 1. RR232 cable configuration for communicating TDR-Lab to the Tektronix 1502C

cable tester

The connection between the computer and the Tektronix 1502C cable tester is established

with a 9 to 25 pin connector that connects the PC serial port to the cable tester, respectively.

Details of the connector configuration are summarized in Figure 33.

Figure 33. Relationship of pins connecting the PC

serial port with the Tektronix 1502C

connector.

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App. 2. Calculation of the TDR probe cell constant from measured long-time reflection

coefficient values

The cell constant is numerically calculated in an external spreadsheet (Figure 34) by looking

for the best fit between the measured (σexp) and the modelled (σmod) bulk electrical

conductivity. The σexp parameter is the electrical conductivity measured with a conductive cell

immersed in different conductive water solutions. The σmod factor is the bulk electrical

conductivity calculated from Eq. (5) for different values of KP and the measured ρf, ρair and ρsc

values, respectively.

Figure 34. Example of table to calculate the TDR probe cell constant.

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App. 3. keyboard shortcuts

Main menu

ALT + P Project

ALT + T TDR

ALT + S Sets

ALT + F Waveforms

ALT + W Windows

TDR display

ALT + X Execute

ALT + E TDR screen settings

ALT + A Save

ALT + R Refresh

ALT + N None

ALT + M Manual analysis on refresh

ALT + N Tangents analysis on refresh

ALT + D Derivative analysis on refresh

ALT + L Results manager window

ALT + C Clear

ALT + O Stop on numerical method analysis

ALT + B Calibration

users’ guide - digital.csicdigital.csic.es/bitstream/10261/35790/3/tdr-lab...

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