Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 12, Problem 12.22P
To determine
The expression of the maximum value of
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A wave is normally incident upon a surface with a layered lossless dielectric. Find the magnitude of effective reflection coefficient if medium 1 is free space, medium 2 has a relative permittiviy of 4
medium 3 has a permittivity of 9, and the thickness of medium 2 is 12/2.
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What are reflection and transmission coefficients? Derive the formula for the same. When an EM wave travels from a dielectric (medium-1) to the conductor,then what will be the value of these parameters?
Electrical Engineering
1a.) What electric and magnetic fields correspond to the TM modes of a 1D ideal metallic waveguide?
1b.) What wave equation or wave equations apply to the TM modes?
1c.) How do you describe a TM plane wave bouncing between the two infinite metallic sheets?
1d.) What wave equation are you solving for the TM modes?
Chapter 12 Solutions
Engineering Electromagnetics
Ch. 12 - Prob. 12.1PCh. 12 - Prob. 12.2PCh. 12 - A uniform plane wave m region 1 is normally...Ch. 12 - Prob. 12.4PCh. 12 - Prob. 12.5PCh. 12 - In the beam-steering prism of Example 12.8,...Ch. 12 - The semi-infinite regions z 0 and z 1m are free...Ch. 12 - Prob. 12.8PCh. 12 - Prob. 12.9PCh. 12 - Prob. 12.10P
Ch. 12 - Prob. 12.11PCh. 12 - Prob. 12.12PCh. 12 - Prob. 12.13PCh. 12 - Prob. 12.14PCh. 12 - Prob. 12.15PCh. 12 - Prob. 12.16PCh. 12 - Prob. 12.17PCh. 12 - Prob. 12.18PCh. 12 - You are given Four slabs of lossless dielectric,...Ch. 12 - Prob. 12.20PCh. 12 - Prob. 12.21PCh. 12 - Prob. 12.22PCh. 12 - Prob. 12.23PCh. 12 - Prob. 12.24PCh. 12 - Prob. 12.25PCh. 12 - Show how a single block of glass can be used to...Ch. 12 - Prob. 12.27PCh. 12 - Over a small wavelength range, the refractive...Ch. 12 - Prob. 12.29PCh. 12 - Prob. 12.30P
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- In a uniform electromagnetic wave which is at a significant distance from the source of energy if the wave is falling from medium 1(z<0,σ=0,µr = 2,ɛr =9) to a second medium where the values are (z>0,σ=0,µr = 16,ɛr =4) . Find the values of reflection and transmission coefficient in this scenarioarrow_forwardAn X band copper rectangular waveguide (22.9 mm × 10.2 mm) is filled with dielectric material having relative permittivity of 2.5 and loss tangent 0.0015. The target operating frequency is 7 GHz. (i) Determine the lowest cutoff frequency, f1. (ii) Determine the next mode cutoff frequency, f2. (iii) Find the guided wavelength at 7 GHz. (iv) Determine the dielectric loss through the waveguide. (v) Determine the conductor loss (consider σ = 5.8 × 107 S/m for copper).arrow_forwardA plane wave of which the electric field vector, E0=10V/m, f=5GHz, is parallel to x-z plane, arrives on a dielectric medium of permittivity εr,=4 with an incident angle of 45∞. Find the reflection coefficient, Γ, transmission coefficients, T, and reflection, transmission angles. Calculate the incident angles for zero reflection and full reflection. Calculate the phase velocity and wavelenght in both media.arrow_forward
- How would you classify (imperfect dielectric or good conductor) the two materials, a and b, in which uniform plane waves of the same requency are propagating given with the following electric fields, respectively:arrow_forwardQUESTION 3: i. In an optical fiber laboratory experiment the following measurements were observed, the numerical aperture of 0.20 and a cladding refractive index of 1.59. Determine: a. The acceptance angle for the fiber in water. b. The critical angle at the core-cladding interface. Comment on any assumptions made about the fiber ii. Define the normalized frequency for optical fiber and explain its use in the determination of the number of guided modes propagating within a step-index fiber. iii. A step-index fiber in the air has a numerical aperture of 0.16, a core refractive index of1.45, and a core diameter of 60 µm. Determine: a. The number of guided modes propagating in the fiber when the light at a wavelength of 0.9 μm is transmitted.arrow_forwardFind the velocity of a plane wave in a lossless medium having a relative permittivity 4 and relative permeability of 3.55.arrow_forward
- a) Discuss the conditions where you can apply or use the free-space path loss model for radio wave loss in wireless communications. b) Some claim radio waves are hazardous to human health. Discuss your opinion with the support of suitable references.arrow_forwardType your question here n an anisotropic medium, permittivity varies with electric field direction, and is a property seen in most crystals. Consider a uniform plane wave propagating in the z direction in such a medium, and which enters the material with equal field components along the x and y axes. The field phasor will take the form: ?? (?) = ?0(?? + ??? ?∆?? )? −??? Where ∆? = ?? − ?? is the difference in phase constants for waves that are linearly polarized in the x and y directions. Find distances into the material (in terms of ∆?) at which the field is (a) linearly polarized and (b) circularly polarized. (c) Assume intrinsic impedance ? that is approximately constant with field orientation and find ??and < S >.arrow_forwardIf a wave propagating in z-direction and incident on the air-glass interface at z= 0, plot the E field (amplitudes only) in the yz plane (plane of incidence) for :a. TE incidenceb. TM incidence Take -2lambda<y,z<2lambda for plotting. (Take lambda of your own choice. Amplitude = 1V/m.) If the angle of incidence is 30 degrees in the above case, what should be the E field distribution?arrow_forward
- Specify the boundary conditions on the E-field for TE modes in the rectangular waveguide from the figure. Ex=0 at y=0, b; Ey=0 at x=0, a.arrow_forwardPlot an Excel surface model of a Gaussian light intensity distribution at z = 539 mm, whereby the maximum intensity there is 0.5 W/cm^2arrow_forwardAssuming that the amplitude of the electric intensity of a plane wave propagating in a certain lossy medium is 1 (mV/m) at P1 and 0,8 (mV/m) at P2 50(m) away, finda) the total attenuation between points P1 and P2 both in nepers and in decibels.b) α in (Np/m).arrow_forward
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