RS ENE 428 Microwave Engineering Lecture 3 Polarization, Reflection and Transmission at normal incidence 1

RS Uniform plane wave (UPW) power transmission from W/m 2 2

RS Polarization UPW is characterized by its propagation direction and frequency. Its attenuation and phase are determined by medium’s parameters. Polarization determines the orientation of the electric field in a fixed spatial plane orthogonal to the direction of the propagation. 3

RS Linear polarization Consider in free space, At plane z = 0, a tip of field traces straight line segment called “linearly polarized wave” 4

RS A pair of linearly polarized wave also produces linear polarization Linear polarization At z = 0 plane At t = 0, both linearly polarized waves have their maximum values. 5

RS More generalized of two linearly polarized waves, Linear polarization occurs when two linearly polarized waves are More generalized linear polarization in phase out of phase 6

RS Superposition of two linearly polarized waves that If  x = 0  and  y = 45 , we have Elliptically polarized wave 7

RS occurs when E xo and E yo are equal and Right hand circularly polarized (RHCP) wave Left hand circularly polarized (LHCP) wave Circularly polarized wave 8

RS Phasor forms: for RHCP, for LHCP, Circularly polarized wave from Note: There are also RHEP and LHEP 9

RS Ex1 Given,determine the polarization of this wave 10

RS Ex2 The electric field of a uniform plane wave in free space is given by, determine a)f b)The magnetic field intensity 11

RS c) d) Describe the polarization of the wave 12

RS Reflection and transmission of UPW at normal incidence 13

RS Assume the medium is lossless, let the incident electric field to be or in a phasor form since then we can show that Normal incidence – the propagation direction is normal to the boundary Incident wave 14

Transmitted wave RS Assume the medium is lossless, let the transmitted electric field to be then we can show that Transmitted wave 15

RS At z = 0, we have and   1 =  2 are media the same? From boundary conditions, Reflected wave (1) 16

There must be a reflected wave RS and This wave travels in –z direction. Reflected wave (2) 17

Boundary conditions (reflected wave is included) RS from therefore at z = 0 (1) Reflection and transmission coefficients (1) 18

RS from therefore at z = 0 (2) Boundary conditions (reflected wave is included) Reflection and transmission coefficients (2) 19

Solve Eqs. (1) and (2) to get RS Reflection coefficient Transmission coefficient Reflection and transmission coefficients (3) 20

RS Types of boundaries: perfect dielectric and perfect conductor (1) From . Since  2 = 0 then  = -1 and E x10 + = -E x10 -  21

RS Types of boundaries: perfect dielectric and perfect conductor (2) This can be shown in an instantaneous form as Standing wave 22

RS Standing waves (1) When  t = m , E x1 is 0 at all positions. and when  z = m , E x1 is 0 at all time. Null positions occur at 23

RS Standing waves (2) Since and, the magnetic field is or. H y1 is maximum when E x1 = 0 Poynting vector 24

RS Power transmission for 2 perfect dielectrics (1) Then  1 and  2 are both real positive quantities and  1 =  2 = 0  Average incident power densities 25

RS Ex3 Let medium 1 have  1 = 100  and medium 2 have  2 = 300 , given E x10 + = 100 V/m. Calculate average incident, reflected, and transmitted power densities 26

RS Wave reflection from multiple interfaces (1) Wave reflection from materials that are finite in extent such as interfaces between air, glass, and coating At steady state, there will be 5 total waves 27

RS Wave reflection from multiple interfaces (2) Assume lossless media, we have then we can show that 28

RS Wave reflection from multiple interfaces (2) Assume lossless media, we have then we can show that 29

RS Wave impedance  w (1) Use Euler’s identity, we can show that 30

RS Wave impedance  w (2) Since from B.C. at z = -l we may write 31

RS Input impedance  in solve to get 32

RS Refractive index Under lossless conditions, 33