Complex Wave Parameters Visualization of EM Waves Complex Wave Parameters for Special Cases

Transcription

1 Course Instructor Dr. Ramond C. Rumpf Office: A 337 Phone: (915) E Mail: rcrumpf@utep.edu EE 4347 Applied Electromagnetics Topic 3d Waves in Loss Dielectrics Loss Dielectrics These notes ma contain coprighted material obtained under fair use rules. Distribution of these materials is strictl prohibited Slide 1 Lecture Outline Comple Wave Parameters Visualiation of EM Waves Comple Wave Parameters for Special Cases Loss dielectrics (general case) Good dielectrics Good conductors Loss Dielectrics Slide 1

2 Comple Wave Parameters Loss Dielectrics Slide 3 The Comple Permittivit, There are two was to specif the electrical properties of a material: Comple Permittivit: Real Permittivit & Conductivit: j and We can relate the two sstems above using Mawell s equations. Comple Permittivit: H j E Real Permittivit & Conductivit: H J j E E j E j E The relation is: j j E j j Loss Dielectrics Slide 4

3 The Comple Permeabilit, Similarl, the permeabilit can also be a comple number. j Loss Dielectrics Slide 5 The Comple Wave Number, k A wave travelling the + direction can be written in terms of the wave number k as E Pe jk k k jk Substituting this into the wave solution ields E Pe j k jk Pe k e jk attenuation oscillation Loss Dielectrics Slide 6 3

4 The Comple Propagation Constant, A wave travelling the + direction can be written in terms of the comple propagation constant as E Pe j Substituting this into the wave solution ields j j E Ee Ee e attenuation oscillation Loss Dielectrics Slide 7 Attenuation Coefficient and Phase Constant A wave travelling the + direction can also be written in terms of an attenuation coefficient and a phase constant and as k jk j E E e e E E e e j j E E e e E E e e attenuation oscillation attenuation oscillation We now have the phsical meaning of the real and imaginar parts of the wave vector k and propagation constant. k j Imk Rek j Re Im Loss Dielectrics Slide 8 4

5 Phsical Meaning of and E E e 1 Attenuation described b e Equation of the Wave E j E e e takes on the meaning of the wave vector we discussed up to this point. kn Oscillation described b j e Loss Dielectrics Slide 9 Calculating and from,, and Given comple permeabilit and permittivit, k j Im Re Given real permeabilit, permittivit and conductivit, j j j j j j j j collects all loss information into a single parameter. collects all phase information into a single parameter. Both are an unintuitive mi of the fundamental parameters. Loss Dielectrics Slide 1 5

6 Absorption Coefficient, P The absorption coefficient P describes how power decas as a function of position. P Pe P We previousl defined the attenuation coefficient that described how the field amplitude decas as a function of position. E E e e j Given that P E, the attenuation coefficient and absorption coefficient P are related through P E E e P Loss Dielectrics Slide 11 Waves with Comple k Purel Real k Purel Imaginar k Comple k Uniform amplitude Oscillations move power Considered to be a propagating wave Decaing amplitude No oscillations, no flow of power Considered to be evanescent Decaing amplitude Oscillations move power Considered to be a propagating wave (not evanescent) This implies that these are the onl.5 configurations that electromagnetic fields can take on. Loss Dielectrics Slide 1 6

7 D Waves with Doubl Comple k Real k Imaginar k Comple k Real k Imaginar k Comple k Loss Dielectrics Slide 13 Comple Impedance The wave impedance is in general a comple number. R jx The amplitude/phase form is the most meaningful when substituted into the epression for the magnetic field component of a wave. ˆ kˆ k P P jk jkr r e H e affects phase affects magnitude Loss Dielectrics Slide 14 7

8 Impedance in Terms of,, and Given comple permeabilit and permittivit, Given real permeabilit, permittivit and conductivit, j 1 j tan collects all amplitude and phase information between E and H into a single parameter. It is an unintuitive mi of the fundamental parameters. Loss Dielectrics Slide 15 Comple Refractive Inde, n (3 of 3) Recall that k kn. However, we now know that k is a comple number, so refractive inde must be as well. n n j o Ordinar refractive inde, n o k kn k jkk n j o j k n j o Etinction coefficient, We can now relate the real and imaginar parts of refractive inde to the real and imaginar parts of k as well as and. n k k Loss Dielectrics Slide 16 o Re k Im k k k 8

9 Loss Tangent Sometimes material loss is given in terms of a loss tangent. tan Recall that interpreting wave properties (velocit and loss) is not intuitive using just the comple dielectric function. To do this, we preferred the comple refractive inde. It turns out that the loss tangent and the etinction coefficient are essentiall the same quantit. abs n k n P Pe kn It is called a loss tangent because it is the angle in the comple plane formed between the resistive component and the reactive component of the electromagnetic field. or Loss Dielectrics Slide 17 or Visualiation of EM Waves 9

10 Waves in Materials (1 of 3) Waves in Vacuum H is 377 smaller than E. E H E and H are in phase Im E H H k P Amplitude does not deca Loss Dielectrics Slide 19 Waves in Materials ( of 3) Waves in Dielectric H is larger now, but still smaller than E. 1 E and H are still in phase Im E H H k P Amplitude still does not deca Loss Dielectrics Slide 1

11 Waves in Materials (3 of 3) Loss Dielectric Waves in Loss Dielectric H remains larger, but still smaller than E. 1 E and H are out of phase! Im E H H k P Amplitude decas Loss Dielectrics Slide 1 More Realistic Wave (E Onl) It is important to remember that plane waves are of infinite etent in the and directions. Loss Dielectrics Slide 11

12 More Realistic Wave (E & H) It is important to remember that plane waves are of infinite etent in the and directions. Loss Dielectrics Slide 3 Comple Wave Parameters for Special Cases Loss Dielectrics Slide 4 1

13 Summar of Waves in Loss Dielectrics Condition: Fundamental Parameters: This is the general case. All materials have loss.,, r r j Attenuation Coefficient: Phase Constant: Imk Rek Impedance: 1 j tan 1 Loss Dielectrics Slide 5 Summar of Waves in Lossless Dielectrics Condition: Fundamental Parameters:,, r r Attenuation Coefficient: No attenuation Phase Constant: Impedance: H is 3 small than E. r r E and H are in phase Notes: Most commonl analed, due to eas math. Usuall a good approimation for dielectrics. Not phsicall real, ecept in vacuum. All materials have loss. Loss Dielectrics Slide 6 13

14 Summar of Waves in Good Conductors Condition: Fundamental Parameters:,, r r Attenuation Coefficient: Strong attenuation Phase Constant: Impedance: j 45 E and H are out of phase. Notes: Ver strong attenuation. Waves tend to reflect from good conductors so often do not eperience the loss. E leads H b 45. Loss Dielectrics Slide 7 14