Section 6.2 · Problems · 6 of 8
Problem 6.2.6: Complex intrinsic impedance given
Complex intrinsic impedance given
#A lossy dielectric material has a characteristic (intrinsic) impedance of at a particular frequency. If, at that frequency, the plane wave propagating in this medium has the magnetic field component
find the corresponding electric field and the attenuation constant . Find also the loss tangent, the skin depth, the polarisation of the wave and the time-average power density at .
Adapted from: M. N. O. Sadiku, Elements of Electromagnetics, Example 10.2.
holds for a complex too: its magnitude scales the amplitude and its angle shifts the phase. The angle alone fixes the loss tangent, , and the ratio , Eq. (6.2.13).
The wave travels towards . In phasors , and , so
leads by and keeps the direction : the wave is linearly polarised along .
has the angle , so
has the angle , so
, while the wavelength is . At
decaying as .
at , is , along as it must be.
The phase of is a complete loss meter: for a lossless medium, for a good conductor. Here means a very lossy dielectric with , and the wave barely completes one period in space before it is gone (Figure 6.2.22).