By Orfanidis S.J.
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Additional resources for Electromagnetic waves and antennas
1) does depend only on the relative velocity. 8) 1 − β2 Setting kz = k cos θ, kx = k sin θ, with k = ω/c, and similarly in the S frame, kz = k cos θ , kx = k sin θ , with k = ω /c, Eqs. 7) Using the ﬁrst-order Taylor series expansion (1 + x)±1/2 = 1 ± x/2, one can show that Eq. 6) can be written approximately as Eq. 5). Next, we present a more precise discussion of the Doppler effect based on Lorentz transformations. Our discussion follows that of Einstein’s 1905 paper on special relativity .
A decrease by a factor of 100 = 1020/10 corresponds to A = 20 dB, effectively doubling the above depths. 58 2. 7. 45 GHz is used to defrost a frozen food having complex permittivity c = (4 − j) 0 farad/m. Determine the strength of the electric ﬁeld at a depth of 1 cm and express it in dB and as a percentage of its value at the surface. Repeat if c = (45 − 15j) 0 farad/m. 31 rad/m. 1) σ+ω d 2ω d Thus, the phase and attenuation constants are: Thus, the ﬁelds at a depth of 1 cm are 88% and 57% of their values at the surface.
The most famous of these is the Zenneck wave, which is a surface wave propagating along a lossy ground, decaying exponentially with distance above and along the ground. Another example of current interest is surface plasmons [576–614], which are surface waves propagating along the interface between a metal, such as silver, and a dielectric, such as air, with the ﬁelds decaying exponentially perpendicularly to the interface both in the air and the metal. 5. For a classiﬁcation of various types of complex waves and a review of several applications, including the Zenneck wave, see Refs.