Lec08 Wave Equation-II PDF

EE340 Electromagnetic Theory Wave Equation-II 20-08-2024 EE340 EEE Institute of Technology Guwahati 1 Plane waves in lossy medium Attenuation constant (𝛼) If a wave propagates along 𝑎ො𝑧 and decrea...

EE340 Electromagnetic Theory Wave Equation-II 20-08-2024 EE340 EEE Institute of Technology Guwahati 1 Plane waves in lossy medium Attenuation constant (𝛼) If a wave propagates along 𝑎ො𝑧 and decreases its amplitude by a factor 𝑒 −α𝑧. Then α is called as attenuation constant. It’s unit is Neper/m or decibels per meter (dB/m). Phase constant (𝜷) 𝛽 is a measure of phase shift per length called as phase constant or wave number. 20-08-2024 EE340 EEE Institute of Technology Guwahati 2 Plane waves in lossy medium Loss tangent: tan 𝜃 is known as loss tangent, and 𝜃 is loss angle of the medium. Also, 𝜃 = 2𝜃η 𝜃η is the phase difference between E and H 20-08-2024 EE340 EEE Institute of Technology Guwahati 3 20-08-2024 EE340 EEE Institute of Technology Guwahati 4  Complex permittivity 20-08-2024 EE340 EEE Institute of Technology Guwahati 5  Plane waves in Free Space Free space properties are: 𝜎 = 0, 𝜖 = 𝜖0 , µ = µ0 So 𝜔 𝛼 = 0, β = 𝜔 𝜖µ = 𝑐 𝑐 is the speed of light in vacuum (𝑐 = 3 × 108 𝑚/𝑠). Intrinsic impedance of the free space is : 20-08-2024 EE340 EEE Institute of Technology Guwahati 6  Plane waves in Good Conductors Good conductors are having 𝜎 ≫ 𝜔𝜖 𝜎 i.e. 𝜔𝜖 ≫ 1 So 𝜔µ𝜎 𝛼= β= = 𝜋𝑓µ𝜎 2 Intrinsic impedance is : Skin depth: 20-08-2024 EE340 EEE Institute of Technology Guwahati 7  Summary 20-08-2024 EE340 EEE Institute of Technology Guwahati 8  List of few common RF materials https://www.rfcafe.com/references/electrical/dielectric-constants-strengths.htm 20-08-2024 EE340 EEE Institute of Technology Guwahati 9 Numerical Problem 20-08-2024 EE340 EEE Institute of Technology Guwahati 10  Wave Polarization Polarization is a concept developed to describe the various types of electric field variation and orientation in EM waves. Types of Polarization Linear Circular Elliptical 20-08-2024 EE340 EEE Institute of Technology Guwahati 11  Types of Polarization Linear Circular Elliptical Linear and circular polarizations are special cases of the more general case of the elliptical polarization. 20-08-2024 EE340 EEE Institute of Technology Guwahati 12  Polarization Linear Polarization: If the wave is propagating in Z- direction, then Ex and Ey field vectors will be in phase. Vertically polarized when Ex=0 Horizontally polarized when Ey=0 Polarized at any particular angle when Ex≠0 and Ey≠0, The angle depends upon the magnitude of Ex and Ey components. Circular Polarization: Circular polarization when 𝐸𝑥 = 𝐸𝑦 and the two field vectors are 90 degree out of phase. Left handed circular polarization (LHCP) when E field vector is rotating in anti-clockwise direction looking from source of EM waves. Right handed circular polarization (RHCP) when E field vector is rotating in clockwise direction looking from source of EM waves. Elliptical Polarization: Elliptic polarization when 𝐸𝑥 ≠ 𝐸𝑦 and the two field vectors are out of phase. 20-08-2024 EE340 EEE Institute of Technology Guwahati 13  Polarization Linear Polarized light Linear Polarized light (Vertically Polarized) (Horizontally Polarized) Right Circularly Polarized (when Left Circularly Polarized (when looking from source direction) looking from source direction) 20-08-2024 EE340 EEE Institute of Technology Guwahati 14  Polarization Elliptical Polarization 20-08-2024 EE340 EEE Institute of Technology Guwahati 15 20-08-2024 EE340 EEE Institute of Technology Guwahati 16 20-08-2024 EE340 EEE Institute of Technology Guwahati 17  Practice Question 20-08-2024 EE340 EEE Institute of Technology Guwahati 18