7 PLANE WAVE PROPAGATION 7 e Applied EM

7. PLANE WAVE PROPAGATION 7 e Applied EM by Ulaby and Ravaioli

Chapter 7 Overview

7. 1 Time-Harmonic Fields Time-harmonic = Sinusoidal (정현파) EM = Electromagnetic EM wave (Radio wave): 전파, 전자기파 전자파: 전기장/자기장이 파동형태로 공간으로 퍼져 나감. 전파(propagation): 발생지점에서 공간으로 파동이 퍼져 나가는 현상 Guided EM Waves Unbounded EM Waves

Maxwell’s Equations (맥스웰 방정식) For sinusoidal time variations: In a source-free region: Hence: Consequently, Maxwell’s equations beco We will use these to derive the wave equation for EM waves.

Wave Equations (파동 방정식)

7. 2 Plane-Wave Propagation in Lossless Media (무손실 매질) If the medium is nonconducting (σ = 0), the wave does not suffer any attenuation as it travels and hence the medium is said to be lossless. (파수)

Uniform Plane Wave (균일 평면파) Cont.

Summary: This is a plane wave with General Form of the Solution: with For a wave travelling along +z only: η (intrinsic impedance): 고유임피던스 Application of yields: 고유 임피던스 = 평면파에서 전기장과 자기장의 비

Time-Domain Solution

Cont.

Example 7 -1 cont.

TEM Wave

Wave decomposition

Tech Brief 13: RFID Tags

Overall System View

RFID Tag Communication

RFID Tag Frequencies

7. 3 Wave Polarization (편파) If: Plane wave propagating along +z : then

Polarization State Polarization state describes the trace of E as a function of time at a fixed z Magnitude of E Inclination Angle

Linear Polarization (선편파) or

Polarization Handedness (편파회전방향)

Cont.

Example 7 -2 cont. Wave with electric field magnitude of 3 (m. V/m) traveling in the +ydirection Cont.

Example 7 -2 cont.

Elliptical Polarization (타원편파) (가장 일반적인 표현식) Linear and circular polarizations are special cases of elliptical

Axial Ratio (축비)

Cont.

Example 7 -3 cont.

Tech Brief 7: LCD Liquid crystals are neither a pure solid nor a pure liquid, but rather a hybrid of both. One particular variety of interest is the twisted nematic liquid crystal whose rodshaped molecules have a natural tendency to assume a twisted spiral structure when the material is sandwiched between finely grooved glass substrates with orthogonal orientations.

Operation of a Single Pixel

LCD 2 -D Array

7. 4 Plane-Wave Propagation in Lossy Media (손실 매질) Cont.

Attenuation Constant (감쇠정수) and Phase Constant (위상정수)

Attenuation (감쇠) E and H fields: Cont.

Magnitude of E Skin depth

Low and High Frequency Approximations

Example 7 -4: Plane Wave in Seawater Cont.

Example 7 -4: Plane Wave in Seawater Cont.

Example 7 -4: Plane Wave in Seawater Cont.

Example 7 -4: Plane Wave in Seawater Cont.

Example 7 -4: Plane Wave in Seawater

7. 5 Current Flow in Good Conductor

Linear Conductor For a conductor with E 0 at the surface: Total current crossing y-z plane:

Attenuation in Conductor

Surface Impedance (표면저항) Thus, conductor is equivalent to a resistor in series with an inductor.

Summary: Planewave in Conductor

AC Resistance of Coaxial Cable Since in the ac case, most of the current flows through a very thin skin along the outside of the inner conductor and along the inside of the outer conductor, we can use the results of the planar conductor to figure out the resistance of the coax. The procedure leads to the following expression for the resistance per unit length:

7. 6 Electromagnetic Power Density (전력밀도) Poynting vector: E : V/m H : A/m EH : VA/m 2 Total power intercepted by A: Time-average power density:

Proof of Poynting Vector (Requires some studying)

For a plane wave with E field : the average power density carried by the wave is:

Plane Wave in Lossy Medium (손실매질에서의 평 면파) For a plane wave travelling in a lossy medium: the power density is :

Summary