5
Theory of Operation
5.1 Real and Imaginary Dielectric Permittivity
The Hydra Probe is a dielectric permittivity sensor (Seyfriend, Grant, and Humes 2005)
measuring the complex dielectric permittivity. The complex dielectric permittivity (sometimes
called the dielectric constant) is the raw electrical parameter that has real and imaginary
components (the real dielectric constant and the imaginary dielectric permitivity). These two
parameters serve to fully characterize the electrical response of soil and are measured from the
response of a reflected standing electromagnetic wave at a radio frequency of 50 MHz. Both the
real and imaginary dielectric permittivities are dimensionless quantities.
The Hydra Probe is different from all other soil sensors because it measures both components of
the complex dielectric permittivity of the soil. In other words, The Stevens Hydra Probe uses the
reflected properties of a radio waves to measure soil moisture and soil electrical conductivity
simultaneously.
The complex dielectric permittivity contains both real and imaginary components where the real
component is related to the capacitance (soil moisture) and the imagery component is related to
the electrical conductivity and frequency.
Capacitance is the measure of electric charge that can be stored in a media. The dielectric
constant is related to capacitance by the following equation:
ε
o
E
= C
x
[5.1]
ε
o
is the capacitance in a vacuum,
E
is the dielectric constant, and C
x
is the measured
capacitance of the media in Farads. Every material has a dielectric constant. As the dielectric
constant increases, the capacitance of the media increases. In other words, the capacitance
increases as a factor of the dielectric constant.
In the presence of an electromagnetic wave, the dielectric constant becomes frequency
dependent. The frequency dependence of the dielectric constant is generally termed complex
dielectric permittivity because the relationship between frequency and the dielectric constant
becomes a complex modulus containing both real and imaginary components.
The real dielectric permittivity represents the molecular orientation polarizability. The
orientation polarization of a water molecule in the presence of an electromagnetic wave is much
greater than the polarization of dry soil, which is mostly due to electronic and atomic
polarization. The real dielectric permittivity of dry soil can be from 1 to 5 where the real
dielectric permittivity for pure water is 78.54 at 20 degrees C from 25 to 1000 MHz. The real
dielectric permittivity of soil is mostly attributed to the presence of water. Figure [5.1] illustrates
the different kinds of polarization molecules can under go upon receiving electromagnetic
energy. The general equation that describes complex dielectric permittivity is:
K*
ε
0
=
E
*, K* =
E
r
- j
E
i
[5.2]
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