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Luis Reinel Nova Group 203058_4 1101758176

UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA UNAD Escuela de Ciencias Básicas, Tecnología e Ingeniería Teoría Electromagnética y Ondas 2019 10-23

Introduction

In introducing the document's usually described, and a brief explanation or summary thereof is given. A reader to read the introduction should be able to get an idea about the content of the text before reading itself. (4 to 10 lines).

Questions: (write with your own words) What are the modes of propagation of electromagnetic waves? Electromagnetic waves travel through the guides through various configurations that we call propagation nodes. One way is the way in which energy can be propagated along the waveguide, it is clear that all modes must satisfy certain boundary conditions so that they can occur.The propagation modes depend on the wavelength, polarization and guide dimensions,the longitudinal mode of a waveguide is a particular type of standing wave formed by waves confined in the cavity. Transversal modes are classified into different types: TE (Transversal electric) mode, the electric field component in the propagation direction is zero. TM (Transverse Magnetic) mode, the magnetic field component in the direction of propagation is null. TEM mode (Transversal electromagnetic), the component of both the electric and magnetic fields in the direction of propagation is zero. Hybrid mode, are those that do have component in the direction of propagation in both the electric and magnetic fields.

What does it mean to polarize an electromagnetic wave?

The polarization of the electromagnetic wave is defined as the path described by the electric field vector component in its propagation, so as to maintain orthogonality with respect to the magnetic field vector component.

Figure 1. Polarization What is the phenomenon of total reflection of an electromagnetic wave? This occurs when a wave passes from a medium with a higher refractive index to a medium with a smaller refractive index, the phenomenon of total reflection occurs. When the phenomenon of total reflection occurs if the transmission coefficient can be said to be zero, because in terms of impedance the entire incident field is reflected towards medium 1 when the impedance of medium 2 is much lower than that of the medium one; It becomes almost negligible, that is, zero.

Figure 2. phenomenon of total reflection

What is the phenomenon of total refraction of an electromagnetic wave? The refraction coefficient in TM (Magnetic Transversal) mode using Snell's law (θ −θ )

is expressed as r12_TM = (θ1 +θ2)then when the sum of the angles of incidence and 1

2

refraction It is 90 ° the coefficient of Fresnel reflection is canceled where the parallel electric field is not reflected, but is completely refracted. This condition is called total refraction. θ1 + θ2 = 90° → r12_TM = 0

Figure 3. phenomenon of total refraction

What is the purpose of Snell's Law in the study of the propagation of waves? This law is defined in a formula that allows to calculate the angle of refraction (it is the change of direction that a wave exerts the passing from one material to another) of the light when passing from one surface to another. 𝐴𝑛𝑔𝑢𝑙𝑜 𝑐𝑟𝑖𝑡𝑖𝑐𝑜 (𝜃𝑐 ) (It is the angle of incidence limit) 𝑛1 𝑠𝑒𝑛 𝜃𝑐 = 𝑛2 𝑠𝑒𝑛90° 𝑛2 𝑠𝑒𝑛𝜃𝑐 = 𝑛1

Figure 4

Application exercises: 1. An electromagnetic wave of 𝑓 = 4 𝑀𝐻𝑧 and 𝑃1+ = 200𝑚𝑊/𝑚2 , incident from the air (𝜂1 = 120𝜋 𝛺), perpendicular to an infinite wall with an intrinsic impedance 𝜂2 = 110𝛺. Calculate the reflected power 𝑃1− and the transmitted power 𝑃2+ to the wall.

2. Figure 1: Propagation of “normal wave” in infinite medium. reflection coefficient:

𝒓 = 𝒏𝟐−𝒏𝟏 = 𝒏𝟐+𝒏𝟏

𝟏𝟏𝟎−𝟏𝟐𝟎π 𝟏𝟏𝟎+𝟏𝟐𝟎π

=−𝟎, 𝟓 = 𝟎, 𝟓 < 𝟏𝟖𝟎°

reflectance 𝑹 = |𝒓|𝟐 = 𝟎, 𝟓𝟐 = 𝟐𝟓% transmittance

𝑻 = 𝟏 − 𝑹 = 𝟏 − 𝟐𝟓% = 𝟕𝟓% 𝒎𝒘

𝒎𝒘

𝒎𝒘

reflected power |𝒑− 𝟏 | = 𝑹 ∗ 𝟏𝟎𝟎 𝒎𝟐 = 𝟐𝟓% ∗ 𝟏𝟎𝟎 𝒎𝟐 = 𝟐𝟓 𝒎𝟐

𝒎𝒘

𝒎𝒘

𝒎𝒘

transmitted power |𝒑− 𝟐 | = 𝑻 ∗ 𝟏𝟎𝟎 𝒎𝟐 = 𝟕𝟓% ∗ 𝟏𝟎𝟎 𝒎𝟐 = 𝟕𝟓 𝒎𝟐

2. An electromagnetic wave of 𝑓 = 4 𝑀𝐻𝑧 and 𝑃1+ = 200𝑚𝑊/𝑚2 , coming from a wave generator located 30𝑐𝑚 from the wall, which impinges from the air (𝜂1 = 120𝜋 𝛺) perpendicularly on a wall with an intrinsic impedance 𝜂2 = 110𝛺 and 10𝑐𝑚 thick. The wall is made of a non-magnetic and non-dissipative material. On the other side of the wall is a receiver located 20cm away.

Figure 2: Propagation of “normal wave” in finite medium.

a. Calculate the coefficient of reflection and transmission seen by the generator. b. Determine in [%] and [𝑚𝑊/𝑚2 ] the power that is transmitted to the receiver. Solution 𝝁𝟎 𝒏𝟎 𝒏=√ = 𝜺𝒓 = ( )𝟐 𝜺𝟎 𝜺𝒓 𝒏 𝜺𝒓 = (

𝟏𝟐𝟎𝝅 𝟐 ) 𝟏𝟏𝟎

𝝐𝒓 = 𝟏𝟏. 𝟕𝟒

Now we calculate the phase constant of the wall 𝒘

𝜷 = 𝒘√𝝁𝟎 𝝐𝟎 𝜺𝒓=𝝐 √𝜺𝒓 𝟎

𝟐𝝅 ∗ 𝟐𝟓𝟎𝒙𝟏𝟎𝟔 𝜷= √𝟏𝟏. 𝟕𝟒 𝟑𝒙𝟏𝟎𝟖 𝜷 = 𝟏𝟕. 𝟗𝟒

𝒓𝒂𝒅 𝒎

we find the input impedance seen, from the first frontier

𝒏 𝒏

𝒏 +𝒋𝒏𝟏 𝒕𝒂𝒏(𝜷𝒙) 𝒊𝒏=𝒏𝟏 𝟐 𝒏𝟏 +𝒋𝒏𝟐 𝒕𝒂𝒏(𝜷𝒙) 𝒊𝒏=𝟏𝟏𝟎

𝟏𝟐𝟎𝝅+𝒋𝟏𝟏𝟎𝒕𝒂𝒏(𝟏𝟕.𝟗𝟒𝒙 𝟎.𝟐𝟎) 𝟏𝟎𝟎+𝒋𝟏𝟐𝟎𝝅𝒕𝒂𝒏(𝟏𝟕.𝟗𝟒𝒙 𝟎.𝟐𝟎)

𝒏𝒊𝒏=(𝟏𝟐𝟓−𝟏𝟓𝟑𝒊) calculate reflection coefficient 𝑟1=

𝒏𝒊𝒏 − 𝒏𝒂𝒊𝒓𝒆 𝟏𝟐𝟓 − 𝟏𝟓𝟑𝒊 − 𝟏𝟐𝟎𝝅 = 𝒏𝒊𝒏 + 𝒏𝒂𝒊𝒓𝒆 𝟏𝟐𝟓 − 𝟏𝟓𝟑𝒊 + 𝟏𝟐𝟎𝝅

𝑟1= − 0,37 − 0,41𝑖=0,55(−132°)

we found transmission coefficient

𝜏1= 1 + 𝑟1 = 0.37 − 0.41𝑖

we found percentage of power transmitted to the wall 𝑇1= 1 − |𝑟1 |2 =1 − 0,552=0,69

reflectance on the first face of the wall 𝑅 = 1 − 𝑇1 = 1 − 0,70 = 0,30

coefficient of reflection on the second side 𝑟2 =

𝑛𝑎𝑖𝑟 − 𝑛𝑤𝑎𝑙𝑙 𝑛𝑎𝑖𝑟 + 𝑛𝑤𝑎𝑙𝑙

𝑟2 =

120𝜋 − 110 = 0,54 120𝜋 + 110

we calculate transmittance

𝑇2= 1 − |𝑅2|2=1-0,542 = 0,70

we calculate transmittance

𝑇𝑡 = 0,70 ∗ 0,69 = 0,483 200 𝑚𝑤 ) 𝑚2

|𝑃𝑟 + | = 0,483 (

= 96.6

𝑚𝑤 𝑚2

Conclusions Conclusion 1: Conclusion 2: The conclusions should be written with their own words and should focus on the concepts explored, learned, discovered and practiced in the development of the activity, it is suggested to present a conclusion by topic, the result of learning obtained as evidence of conceptual assimilation. To obtain a good writing it is suggested to read the written several times, correcting and adjusting the text until obtaining a clear and coherent postulate. Avoid superficiality and simplicity. Bibliography Bibliography 1:

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