Search for question
Question

Consider the standing wave pattern (SWP) for plane wave propagation in the Z-direction in a lossless material, given by eq. (4-12 a) in Balanis. Note that the SWP may be

expressed as: \text { SWP }=E_{0}^{+} \sqrt{1+\left(\frac{E_{0}^{-}}{E_{0}^{*}}\right]^{2}+2 \operatorname{Re} \Gamma(z)} ^^20SWP^^20=E^+_0\sqrt[]{e^{-2az}+\mleft(\frac{E_{0}^{-}}{E_{0}^{*}}\mright)^2e^{2az}+2\operatorname{Re}\Gamma_0(z)} where \Gamma(z)=\frac{E_{0}}{E_{0}}e^{2j\beta z} Next, consider the corresponding SWP for Z-directed plane wave propagation in a lossy material,given by eq.(4-33) in Balanis. Note that the SWP in this case may be written as: \Gamma(z)=\frac{E_0}{E_0}e^{2j\beta z}e^{2az}=\Gamma_0(z)e^{2az} where (i) Using a suitable computer plotting routine (Matlab or equivalent), plot the SWP in eq.(1) vs.distance z measured in wavelengths (A) in the range (-2n <=z <=2n), for the values of |To(z) |(i)= 0, 0.3, 0.6, 1.0. Express the results in terms of Eo*. Graph all 4 plots on the same paper.This will then yield 1 graph with 4 plots. (ii) Repeat the plots of case (i) for eq.(2) for |To(z)| = 0, 0.3, 0.6, 1.0 at an operating frequency of f= 250 MHz, µ: = 1, for the three cases, (a) o = 300, (b) a= 3.0, (c) G =0.03. Graph all 4 plots on the same paper for each case. This will yield 3 graphs with 4 plots each. Submit a set of 4 graphs (one for part i and three for part ii for the 3 conductivities), along with a one-to-two-page discussion of your results, including methods used, and reasons for similarities or discrepancies,and the main differences in lossy versus lossless behavior, if any,Submit also your paper calculations (if any), and samples of the computer programs used.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9

Fig: 10

Fig: 11