Wave Incidence. Dr. Cruz-Pol. Normal Incidence. Ex.1. Light traveling in air encounters the water; another medium.

Transcription

1 D. Cu-Pol Ex.1. Light taveling in ai encountes the wate; anothe medium. Wave Incidence [Chapte 10 cont, Sadiku] D. Sanda Cu-Pol Electical and Compute Engineeing Dept. UPR-Maagüe Ex.1. Light encountes atmosphee, clouds, gound, oceans. Ex. 3. Wave encountes skin tissue, muscle mass and bones Cellphone adiation Adult 10 s old 5 s old* *Kid s skull is not et developed Ex. 4. Cance teatment Wave incidence Fo man applications, [such as fibe optics, line powe tansmission], it s necessa to know what happens to a wave when it meets a diffeent medium. How much is tansmitted? How much is eflected back? Nomal Incidence 1

2 D. Cu-Pol We will look at Vital Definition I. Nomal incidence Wave aives at 0 o fom nomal Standing waves II. Oblique incidence Wave aives at anothe angle Snell s Law and Citical angle Paallel o Pependicula polaiation Bewste angle Plane between mediainteface Plane of incidence- (what ou daw) H i Reflection at Nomal Incidence H i x Medium 1 e 1, s 1, µ 1 E t e 2, µ 2, s 2 Now in tems of equations E H H t Tansmitted wave =0 H i Tansmitted wave E t It s taveling along axis E H H t Tansmitted wave Nomal Incidence 2

3 D. Cu-Pol Sum to get TOTAL field Look at E fields At medium 1 and medium 2 Tangential components must be continuous at the inteface Define Reflection coefficient, G Tansmission coefficient, t Note: 1+ G= t Both ae dimensionless and ma be complex 0 G 1 Example: PE 10.8 A 5GH unifom plane wave s =10e -jb a x in fee space is incident nomall on a lage plane, lossless dielectic slab (>0) having e = 4e o and µ=µ o. Find: uthe eflected wave E s and Answe: uthe tansmitted wave E ts e jb1 x V/m, SEE ell/demos/eflect/eflect.html 6.67 e -jb2 x V/m whee b 2 = 2b 1 = 200 p/3 SEE os/eflect/eflect.html Toda we ll see 3 Cases and the Standing waves fom on each case 1. is pefect Conducto 2. is pefect Dielectic uh 2>h 1 3. is pefect Dielectic h 1>h 2 Nomal Incidence 3

4 D. Cu-Pol Case 1: Conducto(2) Medium 1: pefect dielectic, s 1 =0 : pefect conducto, s 2 = Find intinsic impedance Coef. Of eflex & tansmission & E1 field The EM field foms a Standing Wave on medium 1 2Eio E 1 sition.html Conducting mateial Case 2: Dielectic 2 h 2 >h 1 umedium 1: pefect dielectic s 1 =0 u: pefect dielectic s 2=0, h 2>h 1 Standing waves due to eflection Lossless Medium 1 E 1 o (1+ G ) 0 Lossless ***At eve half-wavelength, evething epeats! *** Case 3: Dielectic 2 h 1 >h 2 Standing waves due to eflection umedium 1 = pefect dielectic s 1 =0 = pefect dielectic s 2=0 h 1>h 2 Lossless Medium 1 E1 o (1+ G ) o (1- G ) 0 Lossless At eve half-wavelength, all em popeties epeat Nomal Incidence 4

5 D. Cu-Pol Standing Wave Ratio, s umeasues the amount of eflections, the moe eflections, the lage the standing wave that is fomed. uthe atio of E 1 max to E 1 min Ideall s=1 (0 db) No eflections Ex. Given a wave tavelling in F.S. and hitting dielectic Lossless dielectic at 10MH has e =16, nonmagnetic Find SWR on ai o Powe Flow in Medium 1 The net aveage powe densit flowing in lossless medium 1 Powe Flow in Tansmitted wave The net aveage powe densit flowing in lossless medium 2 Ei Et Ei Et Hi ak E ak H =0 Ht ak Tansmitted wave Hi ak E ak H =0 Ht ak Tansmitted wave Medium 1 Medium 1 Powe in Loss Media Ex. Antenna Radome whee A 10GH aicaft ada uses a naowbeam scanning antenna mounted on a gimbal behind a dielectic adome. Even though the adome shape is fa fom plana, it is appoximatel plana ove the naow extent of the ada beam. If the adome mateial is a lossless dielectic with µ =1 and e =9, choose its thickness d such that the adome appeas tanspaent to the ada beam. Mechanical integit equies d to be geate that 2.3 cm. Answe: l/2=.5cm, d=2.5cm Antenna with adome Antenna with no adome Nomal Incidence 5