Why TDR vs. CAPACITANCE may be missing the point

Why TDR vs. CAPACITANCE may be missing the point

When considering which soil water content sensor will work best for any application, it’s easy to overlook the obvious question: what is being measured?  Time domain reflectometry (TDR) vs. capacitance is the right question for a researcher who is looking at the dielectric permittivity across a wide measurement frequency spectrum (called dielectric spectroscopy). There is important information in these data, like the ability to measure bulk density along with water content and electrical conductivity. If this is the desired measurement, currently only one technology will do: TDR. The reflectance of the electrical pulse that moves down the conducting rods contains a wide range of frequencies. When digitized, these frequencies can be separated by the fast Fourier transform and analyzed for additional information.

The objective for the majority of scientists, however, is to simply monitor soil water content instantaneously or over time, with good accuracy, which means a complex and costly TDR system may not be necessary.

The theory behind both techniques

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 actually uses capacitance. Below is a clarification of 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, Vi to a voltage Vf with an applied voltage, Vf.

Why TDR VS. Capacitance May Be Missing the Point
Equation 1

where R is the series resistance and C is the capacitance. The charging of the capacitor is illustrated in Figure 1:

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Figure 1. The charging of the capacitor

If the resistance and voltage ratio are held constant, then the charge time of the capacitor, t, is related to the capacitance according to    

 

Why TDR VS. Capacitance May Be Missing the Point 2
Equation 2

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 by

Why TDR VS. Capacitance May Be Missing the Point 3
Equation 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.

Why TDR VS. Capacitance May Be Missing the Point 4
Equation 4

Soil probes are not parallel plate capacitors, but the relationship shown in Equation 3 is valid whatever the plate geometry. 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

Why TDR VS. Capacitance May Be Missing the Point 5
Equation 5

where L is the length of the transmission line and c is the speed of light (3 x 108 m s in a vacuum). Thus, the dielectric permittivity is calculated

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Equation 6

Therefore, the propagation time of the electromagnetic wave along the TDR probe is only a function of the square of the transit time and a fixed value (c/2L). Because c and L are a constant and a fixed length, respectively, TDR measurements are theoretically less susceptible to soil and environmental conditions compared to capacitance sensors. However, the interpretation of TDR output can be a considerable source of error when high salinity diminishes the reflectance waveform or temperature changes the endpoint.

Frequency makes a difference in accuracy

An oscillating voltage must be applied to a TDR or capacitance sensor to measure the reflection or charge time in the medium. The frequency of the oscillation is important because it is widely accepted that low frequencies (<10 MHz) are highly susceptible to changes in salinity and temperature. Because there is no limit on the possible input frequencies for either technique, it is important to verify the frequency of the soil moisture device used.

METER’s ECH2O capacitance sensors use high frequencies to minimize effects of soil salinity on readings.  The frequencies used, however, are quite a bit lower than for TDR, typically 50 to 100 MHz.  The high frequency of the capacitance probes “sees” all of the water in the soil, while being high enough to escape most of the errors from soil salinity present in older capacitance probes. The circuitry in capacitance sensors can be designed to resolve extremely small changes in volumetric water content, so much so, that NASA used capacitance technology to measure water content on Mars. Capacitance sensors are lower in cost as they don’t require a lot of circuitry, allowing more measurements per dollar.

Like TDR, capacitance sensors are reasonably easy to install. The measurement prongs tend to be shorter than TDR probes so they can be less difficult to insert into a hole. Capacitance sensors tend to have lower energy requirements and may last for years in the field powered by a small battery pack in a data logger.   

Errors are due to poor installation methods

In summary, though the theory behind the measurements is somewhat different, TDR and capacitance both measure dielectric permittivity to obtain volumetric water content. From a historic perspective, both TDR and capacitance have gained widespread acceptance, although some may perceive greater value in TDR compared to capacitance because of the extreme price difference. In general, reasonable measurements of volumetric water content can be obtained using either technique, and errors in measurements are often due more to poor installation methods than limitations in the techniques themselves.

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