What is TDR and FDR exactly?

Contributed by Bryan T. Wacker Nov 2002

What is the difference between a capacitance probe and TDR probe?

Capacitance and TDR techniques are often grouped together because they both measure the dielectric permittivity of the surrounding medium. In fact, it is not uncommon for individuals to confuse the two, suggesting that a given probe measures water content based on TDR when it is actually uses capacitance. With that in mind, we will try to clarify the difference between the two techniques.

The capacitance technique determines the dielectric permittivity of a medium by measuring the charge time of a capacitor which uses that medium as a dielectric.

We first define a relationship between the time, t, it takes to charge a capacitor from a starting voltage, V_i, to a voltage V, with an applied voltage, V_f

[1]

where R is the series resistance and C the is capacitance (Fig. 1).

 

Fig. 1. Simple capacitor circuit.

The change in voltage across the capacitor over time, is illustrated in Fig. 2. If the resistance and voltage ratio are held constant, then the charge time of the capacitor, t, is related to the capacitance according to

. [2]



Fig. 2. Charging of capacitor when switch in Fig. 1 closes.

For a parallel plate capacitor, the capacitance is a function of the dielectric permittivity (k) of the medium between the capacitor plates and can be calculated from

[3]

where A is the area of the plates and S is the separation between the plates. Because A and S are also fixed values, the charge time on the capacitor is a simple linear function (ideally) of the dielectric permittivity of the surrounding medium

. [4]

Soil probes are not parallel plate capacitors, but the linear relationship shown in Eq. [4] still holds.

Time domain reflectometry (TDR) determines the dielectric permittivity of a medium by measuring the time it takes for an electromagnetic wave to propagate along a transmission line that is surrounded by the medium. The transit time (t) for an electromagnetic pulse to travel the length of a transmission line and return is related to the dielectric permittivity of the medium, k, by the following equation

[5]

where L is the length of the transmission line and c is the speed of light in free space (3 x 10⁸ m s^-1 ). Thus, the dielectric permittivity is calculated

. [6]

The dielectric constant is therefore proportional to the square of the transit time.

For the user, the interest is more likely to be in cost and performance, rather than theory. TDR instruments tend to be quite expensive because they must produce a series of precisely-timed electrical pulses, and digitize return voltages at intervals down to around 100 picoseconds. (Measurements are typically made on a series of pulses, with the digitization delayed for a set interval on each succeeding pulse, so a complete reflectance trace is built up over perhaps 250 pulses). Because the speed of light in air is around 30 cm (1 ft.) per ns and probe lengths range from under 10 cm to perhaps 30 cm, excellent electronics are required to resolve apparent probe length with reasonable accuracy. Therefore, the obvious disadvantage of this measurement technique is the expense of the equipment and the numerical challenges of properly analyzing each trace. The advantage is that measurements are relatively insensitive to salinity (as long as the salinity does not completely attenuate the reflected signal) and temperature.

The time measurement requirements for capacitance sensors are much less demanding than for TDR. High frequencies are important (MHz range) to minimize salinity effects, but the measurements are easily made with standard circuitry. No digitization is required until the signal has been converted to DC. The sensors are therefore much less expensive, and much simpler to use. The disadvantage is that they tend to have somewhat larger sensitivity to salinity and temperature. In soils with high electrical conductivity, capacitance probes may therefore require a soil specific calibration (though these sensors typically will continue to read when soil electrical conductivity is too high for a TDR to read). While accuracy (without a soil specific calibration) may not be as high with a capacitance sensor, its resolution typically is better than TDR because of the noise in the trace analysis process.

As noted above, both the capacitance sensor and the TDR measure the dielectric constant of the medium surrounding the probe. To make this measurement, the electromagnetic field around the probe must interact with a representative sample of the soil. The field lines are most concentrated very near the probe surface, so poor probe-soil contact (air gaps) has an enormous influence on either measurement. Thus, it is possible that accuracy of measurements can be influenced more by poor probe installation than by which type of measurement is being made.

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Extract from sowacs archives may provide the answer (more to follow as I find them)

What Johan Smit has to say
 From:œ Johan Smit ("smit.js") To:œ           SOWACS@aqua.ccwr.ac.za Date:œ Tuesday, May 7, 1996  9:24 pm Subject:œ      Re: TDR vs Radar vs shockwave reflection?  My understanging of the terms are:  TDR Time domain reflrctometry. The transmitted energy can be either in the form of  1) A single rectangular or otherwise shaped pulse. This can be  repeated, eg., to provide readable displays, but any one pulse  contains all the information. The pulse length must be longer than  the time required for the last required reflection to be returned, so that the transmitted energy is constant during the time the  reflections arrive.This is the normal TDR method for short length of cable measurements. 2) A series of sine waves, the envelope of which may be shaped. The pulse time is normally short compared to the reflection time, but  still contains a number of cycles of the carrier frequency. This is the method used in radar, and sonar. The transmitted energy is  normally zero at the time the reflection arrives. 3) A variation of 2) where a very narrow pulse is transmitted. The  transmitter rings, and the medium shapes the pulse. The reflections therefore contain most of their energy at the frequency of minimum  attenuation through the medium. Shock waves fall in this category?  FDR Frequency domain reflectometry. The frequency of the transmitted energy is swept under control, and the reflections add to the  transmitted energy, in or out of phase. The transmitted energy is  thus constant, there is no pulsing. The information required is  obtained from the reflection versus frequency graph, or Voltage Standing Wave Ratio.    The principles are the same, the applied energy  varies. To get  reflections in water, you have to apply the energy at the frequency of least attenuation through water.   The measurement of capacitance, and indirectly therefore dielectric constant, by means of a free running oscillator the output frequency of which varies depending on the capacitance, to my mind cannot be  called FDR.  Greetings to all. Johan Smit