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Problem 3: A uniform plane wave at frequency f is normally incident from the left on...
Consider a TEM plane wave with electric field Ei) = Â E)e-ikız normally-incident on the finite-thickness...
Consider a TEM plane wave with electric field Ei) = Â E)e-ikız normally-incident on the finite-thickness slab shown below. E 1 €2 E 1 ZEL Z=L Write the reflected electric field as E(") = EY") eikız, the field inside the slab as E(2) = î (Ae-ik3z + Beikaz), and the transmitted field as E(t) = Â Ce-iki(z-L). (a) Determine the magnetic fields H and enforce the boundary conditions at z = EL to obtain 4 equations in the 4 unknowns...
Please show all work Consider a uniform transverse electromagnetic plane wave be normally incident on an...
Please show all work
Consider a uniform transverse electromagnetic plane wave be normally incident on an interface between region 1 and region 2, at z = 0. Let the known incident wave in region 1 be (1.20) E(1)(r) = Â Ee-ikız îkı * E")(r) у ki H*)(r) E e-ikız. (1.21) ωμι wi where kı = w M€1. Let the unknown reflected wave be (1.22) E")(r) = în Ef")eikız ku r(r) Hr)(r) = -ġ whi EX")eikiz (1.23) and the unknown transmitted...
A 1-GHz plane wave with electric field Ei = x Ee-j2ßoz is incident onto a pair...
A 1-GHz plane wave with electric field Ei = x Ee-j2ßoz is incident onto a pair of lossless dielectric slabs as shown below. The reflected magnetic field in Layer 1 is given by Eo 2η。 (a) Write the expression for the incident magnetic feld în Layer l Your expression may contain η 0, but not Layer 1 Layer 2 12 Layer 3 13 Er (b) Determine the thickness d of Layer 2 (in cm) and the relative permittivity r3 of...
4. 30 points Consider at 100MHz wave with amplitude 6.0 V/,m obliquely incident from a lossless, ...
4. 30 points Consider at 100MHz wave with amplitude 6.0 V/,m obliquely incident from a lossless, non-magnetic material with fr 9 onto air. The angle of incidence θ¡ is one-half of the critical angle for total internal reflection. The electric field phasor is of the form 2 a) (5 points) Find the wavelength of the signal in the dielectric. b)(5 points) Find the critical angle for total internal reflection. c) (10 points) Find the magnetic field in the dielectric. d)...
8a: a light wave of amplitude E sub 0 = 1 traveling in the +z direction...
8a: a light wave of amplitude E sub 0 = 1 traveling in the +z direction is incident on a slab of glass, refractive index n=1.5, at perpendicular incidence. It has wavelength λ = 2π/k in vacuum. Determine the reflection coefficient, R, and transmission coefficient, T for the wave. b. Now assume that the slab has thickness a, meaning its boundaries are located at z = 0 and z = a. Assume it is infinite in all other directions. In...
Ē"(z)= 2a e 3x104) 1) A uniform plane wave is incident normally on an air-sea water...
Ē"(z)= 2a e 3x104) 1) A uniform plane wave is incident normally on an air-sea water interface at z=0. The phasor expression of the incident electric field intensity is: (V/m) The parameters of the sea-water are: E = 80€, (F/m), u = H (H/m)and o = 4(S/m). Find: a) The intrinsic impedance of medium (1) and medium (2). b) The reflection and transmission coefficients. c) The attenuation and phase constants in the second medium. d) The ratio of the sea-water...
Problem 1 (12.5 marks) A uniform plane wave is normally incident as shown in the figure...
Problem 1 (12.5 marks) A uniform plane wave is normally incident as shown in the figure below. Assume that all regions are lossless. Prove that the input intrinsic impedance can be given by 13 cos(B21) + 1 n2 sin(21) Min = 12 n2 cos(B21) + j n, sin(B,1) 92 73 incident wave -1 nin 0 ho
3. A perpendicular-polarized plane wave is incident at an angle 0, - 20P from plastic (?...
3. A perpendicular-polarized plane wave is incident at an angle 0, - 20P from plastic (? 4e, , ? Ho) to a region of free space. Find the angle of transmission Find the value of the reflection coefficient ?? . Find the value of the transmission coefficient ? Find the critical angle, defined as the angle of incidence ?, at which the a) . c) angle of transmission becomes ?.-900
2. [5 Marks] A perpendicularly polarised plane wave (i.e the E-field is in the y-direction), propagates...
2. [5 Marks] A perpendicularly polarised plane wave (i.e the E-field is in the y-direction), propagates from region 1 with ?,-8.5 and into region 2 which is a vacuum. The wave exits at an angle of 15°. Given that the incident E-field amplitude is 10??/cm, find: a) The amplitude of the reflected electric field. b) The amplitude of the transmitted electric field c) The amplitude of the reflected magnetic field. d) The amplitude of the transmitted magnetic field. Useful Equations:...
3.A uniform electromagnetic plane wave is normally incident from the air region ( medium #1 with+ η = η。= 120π ) upon the planar interface separating air from a lossy dielectric medium (medium #...
3.A uniform electromagnetic plane wave is normally incident from the air region ( medium #1 with+ η = η。= 120π ) upon the planar interface separating air from a lossy dielectric medium (medium #2 with intrinsic impedance 20π + jlOr ). The incident plane wave in air has a phasor electric field given by E(x)-le, x<0 Find: (a) the frequency f (Hertz) (b) the magnitude and the phase of the reflected phasor electric field E as a function of coordinates...
Consider a TEM plane wave with electric field Ei) = Â E)e-ikız normally-incident on the finite-thickness slab shown below. E 1 €2 E 1 ZEL Z=L Write the reflected electric field as E(") = EY") eikız, the field inside the slab as E(2) = î (Ae-ik3z + Beikaz), and the transmitted field as E(t) = Â Ce-iki(z-L). (a) Determine the magnetic fields H and enforce the boundary conditions at z = EL to obtain 4 equations in the 4 unknowns...
Please show all work
Consider a uniform transverse electromagnetic plane wave be normally incident on an interface between region 1 and region 2, at z = 0. Let the known incident wave in region 1 be (1.20) E(1)(r) = Â Ee-ikız îkı * E")(r) у ki H*)(r) E e-ikız. (1.21) ωμι wi where kı = w M€1. Let the unknown reflected wave be (1.22) E")(r) = în Ef")eikız ku r(r) Hr)(r) = -ġ whi EX")eikiz (1.23) and the unknown transmitted...
A 1-GHz plane wave with electric field Ei = x Ee-j2ßoz is incident onto a pair of lossless dielectric slabs as shown below. The reflected magnetic field in Layer 1 is given by Eo 2η。 (a) Write the expression for the incident magnetic feld în Layer l Your expression may contain η 0, but not Layer 1 Layer 2 12 Layer 3 13 Er (b) Determine the thickness d of Layer 2 (in cm) and the relative permittivity r3 of...
4. 30 points Consider at 100MHz wave with amplitude 6.0 V/,m obliquely incident from a lossless, non-magnetic material with fr 9 onto air. The angle of incidence θ¡ is one-half of the critical angle for total internal reflection. The electric field phasor is of the form 2 a) (5 points) Find the wavelength of the signal in the dielectric. b)(5 points) Find the critical angle for total internal reflection. c) (10 points) Find the magnetic field in the dielectric. d)...
Ē"(z)= 2a e 3x104) 1) A uniform plane wave is incident normally on an air-sea water interface at z=0. The phasor expression of the incident electric field intensity is: (V/m) The parameters of the sea-water are: E = 80€, (F/m), u = H (H/m)and o = 4(S/m). Find: a) The intrinsic impedance of medium (1) and medium (2). b) The reflection and transmission coefficients. c) The attenuation and phase constants in the second medium. d) The ratio of the sea-water...
Problem 1 (12.5 marks) A uniform plane wave is normally incident as shown in the figure below. Assume that all regions are lossless. Prove that the input intrinsic impedance can be given by 13 cos(B21) + 1 n2 sin(21) Min = 12 n2 cos(B21) + j n, sin(B,1) 92 73 incident wave -1 nin 0 ho
3. A perpendicular-polarized plane wave is incident at an angle 0, - 20P from plastic (? 4e, , ? Ho) to a region of free space. Find the angle of transmission Find the value of the reflection coefficient ?? . Find the value of the transmission coefficient ? Find the critical angle, defined as the angle of incidence ?, at which the a) . c) angle of transmission becomes ?.-900
2. [5 Marks] A perpendicularly polarised plane wave (i.e the E-field is in the y-direction), propagates from region 1 with ?,-8.5 and into region 2 which is a vacuum. The wave exits at an angle of 15°. Given that the incident E-field amplitude is 10??/cm, find: a) The amplitude of the reflected electric field. b) The amplitude of the transmitted electric field c) The amplitude of the reflected magnetic field. d) The amplitude of the transmitted magnetic field. Useful Equations:...
3.A uniform electromagnetic plane wave is normally incident from the air region ( medium #1 with+ η = η。= 120π ) upon the planar interface separating air from a lossy dielectric medium (medium #2 with intrinsic impedance 20π + jlOr ). The incident plane wave in air has a phasor electric field given by E(x)-le, x<0 Find: (a) the frequency f (Hertz) (b) the magnitude and the phase of the reflected phasor electric field E as a function of coordinates...
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