Electromagnetic Theory

Transcription

1 lectromagnetic Theory

2 Introuction o Textbook: Davi M. Pozar, "Microwave ngineering," 3r eition, ison Wesley, 5 Rf Reference book: kjoseph hf. White, "igh h Frequency Techniques - n Introuction to RF an Microwave ngineering," Wiley, 4 Outline: core Distribution:. Introuction omework %. Transmission Line Theory Mi-term xam 4% 3. mith Chart Final xam 4% 4. -Parameters 5. Resonators 6. Couplers 7. Filters 8. Mixer 9. mplifiers

3 Introuction o Frequency (z) 3x 5 3x 6 3x 7 3x 8 3x 9 3x 3x 3x 3x 3 3x 4 ve Long wa raio M broac cast raio hort wa ave raio VF TV FM broacast raio Microwaves Far Infrar re Infrare Visible lig ght Figure. The electromagnetic spectrum The spee of light in free-space: c f c m/sec 3

4 Introuction o Figure. The electromagnetic spectrum (continue). 4

5 Introuction o tanar Prefixes Prefix tera giga mega kilo hecto k eka bbreviation T G M k h a Factor Prefix bbreviation Factor eci 9 6 centi c milli m micro 3 6 nano n pico p femto f atto a

6 Introuction pplications of Microwave ngineering The ifficulties an the opportunities of higher frequency ntenna gain electric size of the antenna More banwith at 6Mz: banwith = % 6Mz at 6Gz: banwith = % 6Mz Microwave signal travel by line of sight an not bent by the ionosphere f << f p f < f p f >> f p The effective reflection area (raar cross section) electric size of the target Various molecular, atomic, an nuclear resonances at microwave frequencies (remote sensing, meical iagnostics, heating ) 6

7 Introuction o pplications of Microwave ngineering raar systems (Military, Vehicle collision prevention) communications systems Cellular telephone atellite telephony systems GP DB WLNs UWB environmental remote sensing meical systems hort istory of Microwave ngineering 7

8 Introuction t ouct o Figure. (p. 4) Photograph an ientification courtesy of J.. Bryant, University of Michigan. 8

9 Mathematics Definitions fiel is a spatial istribution of a quantity, which may or may not be a function of time. x: gravitational fiel. Mathematical form : GMm Fx, y, z R x, y, z F : C The work one C by the fiel B : W j j q cos B q j j j j j n n B n 9

10 Mathematics Definitions s : B B B an an a n B B cos B where a n ij an, ij ij B ij Tk Take ij B ij ij the limitit : lim ij B ij ij B s

11 Mathematics Definitions Graient: the vector that represents both the magnitue an the irection of the maximum space rate of increase of a scalar. grav V a V a x V x a y V. n V y n a z V z

12 Mathematics atcsdefinitions to Divergence iv lim s. v v iv x x y y z z. B r r r B B z z rb. r Divergence theorem V v s.

13 Mathematics Definitions Mathematics Definitions Curl x y z x y z a a a. y x x z z y z y x a a a. z y x z y x a a a z y x z y x z r r a a a. r z r z r r 3

14 Maxwell s quations Differential form Integral form B M l s s C t t B M D J l D s s D s C t t J t I D D s v Q V B B s continuity equation: J t Figure.3 (p. 7) The close contour C an surface associate with Faraay s law. 4

15 Maxwell s quations phasor form: e D j t (with time epenence) ( xyzt,,, ) Re xyze (,, ) j t j BM j DJ D B complex permittivity: j e jtan jtan The constitutive relations: ( for free space) B ( for free space) j M j J D B r loss tangent: tan permeability: m j 5

16 Maxwell s quations Figure.4a/b (p. 9) rbitrary volume, surface, an line currents. (a) rbitrary electric an magnetic volume current ensities. (b) rbitrary electric an magnetic surface current ensities in the z = z plane. 6

17 Maxwell s quations Figure.4c/ (p. 9) rbitrary volume, surface, an line currents. (c) rbitrary electric an magnetic line currents. () Infinitesimal electric an magnetic ipoles parallel to the x-axis. 7

18 Bounary Conitions o Figure.5 (p. ) Fiels, currents, an surface charge at a general interface between two meia. Figure.6 (p. ) Close surface for equation (.9). Ds v V nˆ D D s similarly, nˆb nˆb 8

19 Bounary Conitions o Figure.7 (p. 3) Close contour C for quation (.33). l j Bs M s C n ˆ M s similarly, nˆ J s Dielectric interface nˆ D nˆ D nˆb nˆb nˆ nˆ nˆ nˆ PC interface nˆ D s nˆ B nˆ nˆ J s PMC interface nˆ D nˆ B n ˆ M s nˆ 9

20 Wave quation an Plane Waves Combine two curl equations j j an use vector ientity, then we have elmholtz equations k k General solutions : e jk r nˆ Figure.8 Orientation n of the,, an k vectors for a general plane wave. k nˆ n

21 Wave quation an Plane Waves Qantity Complex propagation constant Phase constant ttenuation constant Impeance kin epth Wavelength Phase velocity Lossless γ k jω k s v p Type of Meium Goo Conuctor General Lossy or γ jω j jω j Im Im / Re j s v p Re / j s v p

22 Wave quation an Plane Waves xample.( 舊版 ) plane wave with a frequency of 3Gz is propagating in an unboune material with r = 7 an r = 3. Compute the wavelength, phase velocity, an wave impeance for this wave. ol. v p v p 8 c r r r r f m. r r m/sec.

23 Wave quation an Plane Waves xample. plane wave propagating in a lossless ielectric material has an electric fiel given as x = cos(.5x t 6.6z). Determine the wavelength, phase velocity, an wave impeance for this wave, an the ielectric constant of the meium. ol..5 ra/sec, k 6.6 m.. m. k v p.45 m/sec. k c r v p 377 r ( c /.5) 3

24 Wave quation an Plane Waves xample. Compute the skin epth of alumina, copper, gol, an silver at a frequency of Gz. ol. 3 s f s,l m s,cu m. 3 7 s, u m. 3 7 s,g m

25 Wave quation an Plane Waves Plane wave traveling in z irection : If xˆ an yˆ e jk linearly x polarize If an linearly y polarize If an linearly polarize at the angle : - tan z, both real RCP LCP If j, that is j RCP zˆ If jk z xˆ j yˆ e j, that is j LCP zˆ xˆ j yˆ e jk jkz xˆ j yˆ e jkz xˆ j yˆ e z 5

26 nergy an Power egya owe vector ientity vector ientity s M s J j Maxwell s equations Maxwell s equations s v V v M J v j v V s s V V theorem : Poynting's s P o P V V s s v s v M J theorem : Poynting s P V V v j v 6 P l

27 Plane Wave Reflection ect ˆ jkz i x e i jk z z yˆ e t x Te T z t yˆ e ˆ ˆ jkz r x e r ˆ jk z y e T Figure. (p. 7) Plane wave reflection from a lossy meium; normal incience. 7

28 Oblique Incience ce nell' s laws : k sin i k sin r k sin t Figure.3 (p. 35) Geometry for a plane wave obliquely incient at the interface between two ielectric i regions. Parallel Polarization cost cosi cos cos cosi T cost cosi Brewster angle : sin b t Perpenicular Polarization i cosi cost cos cos T i cosi cos i cos t i t 8

29 The Reciprocity Theorem e ec p oc ty eo e s v V v M M J J V s s v M J Figure.5 (p. 4) Geometry for the Lorentz reciprocity theorem. v M J V V 9

30 Image Theorem e Original Geometry Image quivalent Original Geometry Image quivalent Figure.7 7 (p. 44) lectric an magnetic current images. (a) n electric current parallel to a groun plane. (b) n electric current normal to a groun plane. (c) magnetic current parallel to a groun plane. () magnetic current normal to a groun plane. 3