ELEG 648 Plane waves II Mark Mirotznik Ph
- Slides: 43
ELEG 648 Plane waves II Mark Mirotznik, Ph. D. Associate Professor The University of Delaware Email: mirotzni@ece. udel. edu
Uniform Plane Waves: Propagation in Any Arbitrary Direction z H f q x E y
Uniform Plane Waves: Propagation in Any Arbitrary Direction z H f q x E y
Uniform Plane Waves: Propagation in Any Arbitrary Direction z Since E and b are at right angles from each other. H f E q y x where and
Uniform Plane Waves: Propagation in Any Arbitrary Direction Summary and Observations: Frequency Domain Time Domain Observation 1. E, H and b vectors are pointing in orthogonal directions. Observation 2. E and H are in phase with each other, however, H’s magnitude is smaller by the amount of the wave impedance
Uniform Plane Waves: Propagation in 2 D y H E Can we write this a bit more compact? q x
Uniform Plane Waves: Propagation in 2 D y H Can we write this a bit more compact? E q x
Uniform Plane Waves: Propagation in 2 D y H E What about the polarization of E? q x
Uniform Plane Waves: Propagation in 2 D y H E What about the polarization of E? q x
Uniform Plane Waves: Propagation in 2 D y H E What about the polarization of E? q x
Uniform Plane Waves: Propagation in 2 D What about the polarization of E? Two cases y y Parallel Polarization Perpendicular Polarization H H E E q q x x
Uniform Plane Waves: Propagation in 2 D y H What about H? E q x
Uniform Plane Waves: Propagation in 2 D What about the polarization of H? Two cases y y Parallel Polarization Perpendicular Polarization H H E E q q x x
Reflection and Transmission Write down the electric fields in the two regions (2 unknowns, R and T)
Reflection and Transmission Next find the magnetic fields in each region
Reflection and Transmission Apply boundary conditions
Reflection and Transmission
Reflection and Transmission Write down the E field in both regions (4 unknowns, R, T, qr and qt)
Reflection and Transmission Find the H field in both regions
Reflection and Transmission Apply boundary conditions 2 equations and 4 unknowns We need two more equations. How do we get them?
Reflection and Transmission
Reflection and Transmission
Reflection and Transmission
Reflection and Transmission
Reflection and Transmission
Reflection and Transmission
Reflection Coefficient Example: Reflection from an Ocean Interface Angle of Incidence, Degrees
Reflection and Transmission from Dielectric Slabs 1. Normal Incidence Region III Region II z=0 z=d
Reflection and Transmission from Dielectric Slabs Region I: Region III: Boundary Conditions z=0 z=d
Reflection and Transmission from Dielectric Slabs Boundary Conditions z=0 z=d Four equations and four unknowns Solution for the Reflection Coefficient:
Reflection and Transmission from Dielectric Slabs Special Cases I. Half Wavelength Thickness Slab Region I z=0 Region III z=l 2/2
Reflection and Transmission from Dielectric Slabs Special Cases II. Quarter Wavelength Thickness Slab Region I z=0 Region III z=l 2/4
Reflection and Transmission from Dielectric Slabs: Example Region III Region II z=0. 25 m
Reflection and Transmission from Dielectric Slabs: Example |R| Frequency, MHz
How do we broaden the bandwidth around the zero reflection point? |R| Frequency, MHz
One Solution is Multiple Dielectric Layers
Reflection and Transmission from Dielectric Slabs 1. Oblique Incidence ( Parallel Polarization) f. II fr ft f. II fi Region II z=0 Region III z=d
Reflection and Transmission from Dielectric Slabs Region I: Region II:
Reflection and Transmission from Dielectric Slabs Region III: Boundary Conditions z=d z=0 Phase Matching Conditions
Reflection and Transmission from Dielectric Slabs Six Equations and Six Unknowns
Reflection and Transmission from Dielectric Slabs: Solution (parallel polarization) *note we have assumed all non-magnetic materials here
Reflection and Transmission from Dielectric Slabs: Solution (perpendicular polarization) *note we have assumed all non-magnetic materials here
Reflection and Transmission from Dielectric Slabs: Example fi Region III Region II z=0. 25 m
