Section 6.3 · Home exercises · 2 of 4
Home exercise 6.3.2: Measuring a permittivity with a standing wave
Measuring a permittivity with a standing wave
#A plane wave in air is normally incident on the flat face of a thick, lossless, nonmagnetic dielectric. A field probe moved along the direction of travel in front of the face finds that the maximum of is times the minimum, a minimum lies on the dielectric surface, and adjacent minima are cm apart.
Find the frequency, (with its sign), the relative permittivity of the dielectric and the fraction of the incident power reflected.
Adjacent minima are apart, which gives the frequency. gives through Eq. (6.3.20), and the minimum at the surface fixes its sign. Then invert .
cm, so cm and MHz.
. For lossless media is real, and is a minimum at only if , that is :
gives , so . Note that : for a minimum at the face of a denser medium, .
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and . In the sketch the maxima, , lie halfway between the minima, , and .
This is the classical slotted-line measurement of a material. With a lossy sample is complex and the first minimum moves away from the face. Its position then gives the phase , and still gives .