Lossy Medium EE142. Dr. Ray Kwok

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1 Lssy Mdium EE4 D. Ray Kwk fn: Fundamntals f Engining Eltmagntis, David K. Chng (Addisn-Wsly) Eltmagntis f Engins, Fawwaz T. Ulaby (Pnti Hall)

2 Lssy Mdium - D. Ray Kwk Ohm s Law A E V V El IR ( JA) E Jρ J E ρ J E ρ l A sisitivity ndutivity Lw sistivity > ndut ~<0-5 Ω- m ( T ) High sistivity > insulat ~>0 0 Ω- m Intmdiat sistivity > smindut typial ~0-3 t 0 5 Ω- m ( Eg/kT ) unit f ndutivity S/m Simns/mt mh/m (Ω- m) -

3 Lssy Mdium - D. Ray Kwk EM Wav thugh mdium E ρf H E t H 0 E H Jf t (hmgnus, lina, istpi) ρ 0, J 0 E 0 E H H 0 H J E f H ( ) E ' " E E finit mans mpl

4 Lssy Mdium - D. Ray Kwk Lss Tangnt tan δ " ' gd ndut >> gd insulat << Lw tanδ lw dilti lss th small, th btt!!!

5 Lssy Mdium - D. Ray Kwk Eampl A sinusidal E-fild with amplitud f 50 V/m and fquny GHz ists in a lssy dilti mdium that has a.5 and lss tangnt f Find th avag pw dissipatd in th mdium p ubi mt. tan δ S/m π ( 9 π 0 ) (.5) Th avag pw dissipatd p unit vlum is P V P V av av J E 4.34 E W/m 4 (.39 0 )( 50) Nt: P av V R ( El) ρl / A E ( la)

6 Lssy Mdium - D. Ray Kwk Wav Equatin H E t E H t E E t ( E(, t) E γ k tk plan wav quatin still hlds with mdifiatin f ) E t β γ attnuatin nstant ppagatin nstant allw k b mpl sin is phas nstant

7 Lssy Mdium - D. Ray Kwk Cmpl Ppagatin Cnstant γ " ' ( tan δ) β Th phas E() E γ E β attnuatin -

8 Lssy Mdium - D. Ray Kwk db sal pw intnsity ati in lg sal, nt a unit!! (db) 0lg I I 0lg P P V 0lg V > 0 gain < 0 lss sund intnsity pw vltag 0 lg() 3, 3 db dubl 0 lg(/) -3, -3 db half 0 lg(0) 0, 0 db 0 0 lg(00) 0, 0 db 00 0 lg(0.) -0, -0 db /0 What is 6 db? 9 db? 7 db? 44 db? 4 /

9 Lssy Mdium - D. Ray Kwk dbm & dbw dbw 0lg dbm 0lg P W P mw bm al units 0 dbm mw 30 dbw kw -30 dbm W What is 40 dbw? -7 dbm? -6 dbm? dbm? 0 kw 0. mw.5 W /8 W

10 Lssy Mdium - D. Ray Kwk Eampl Istpi 00 W Hw muh ltiity gnatd by th sla ll? What if a 40 W bulb is usd? 00 W bulb? Intnsity pw/aa 00 4πR 00 4π 7.96 W m ( ) 00 W bulb? m sla ll 0 0 m 40% ffiiny 35 0lg Pw f ltiity gnatd 63. mw Pw gnatd in sla ll W 7.96 ( 00m )( 40% ) 3.8mW m 0.038W In tms f db 0lg 35dB 00W P W bulb? P 35 0lg 40 Pw f ltiity gnatd.6 mw systm gain

11 Lssy Mdium - D. Ray Kwk Attnuatin E() A()[dB] lg a E (b) γ E E() 0lg E(0) lg lg (b) (a) β 0lg 0 A()[dB] ln(0) F ampl, if th lti fild intnsity ging thugh a mdium attnuats at a at f 0.4 db/m, what is? -0.4 db ( m) 0.4/ nps/m Nt: nps (np) is nt a al unit. simila t adians!!! Nt als is a psitiv numb f attnuatin. [db/m] [np/m]

12 Attnuatin tm y ) y s ( sin y y y y y ys sin ŷs sin ˆ kˆ θ θ θ θ θ θ k y θ Sam? Ys, Q.E.D. Hw t pss - tm?? Can think f : ( ) ) s sin ( s sin ˆ y y y k θ θ θ θ

13 Lssy Mdium - D. Ray Kwk Lw-lss dilti ( << ) (<<) ( ) η β β γ δ γ ' " ' " ) ' "/ ( v / ' " ' " ' " n ) (... ) n(n n k)! k!(n n! ) ( tan ' " / / n k n n 0 k n f small small

14 Lssy Mdium - D. Ray Kwk Gd Cndut (>>) ( ) ( ) η β β γ γ π π ) / ( ) ( 4 / /

15 Lssy Mdium - D. Ray Kwk Skin Dpth δ δ δ β E At δ, E dass t / ( 63% dp). E() s (NOT lss tangnt δ!!!!!) A()[dB] 0lg E() E(0) 0lg At δ, E dass by -8.7 db. At δ, E dass by -7.3 db.

16 Lssy Mdium - D. Ray Kwk 4 Gnal Matial γ γ ' " β β 4 4 " ' 4 ' ± ' ' ( ' ") β ( ' ") β ' ( ") 0 ( 4 ' ) 6( " ) 8 ( ) ± tan δ ( ) tan δ β al imaginay β ' β β β β η η " ( ) tan δ ( ) ( tan ( ) ) ' tan δ δ tan δ tan δ ( ) ' tan δ tan δ ' ' ( tan δ ) ' tan ( ) tan δ ' ( tan δ) / ( tan δ) δ

17 Lssy Mdium - D. Ray Kwk Summay

18 Lssy Mdium - D. Ray Kwk Eampl - Th skin dpth f a tain nnmagnti nduting matial is m at 5 GHz. Dtmin th phas vlity in th matial. What is th attnuatin (in db) whn th wav pntats 0 m int th matial? phas vlity v /β f ndut, β /δ v δ (π)(5 0 9 ) ( 0-6 ) m/s E() A()[dB] 0lg E(0) 0lg A()[dB] / δ 8.686(0 / ) 43.4dB in ust 5 skin dpth. ( 43 db / 0,000!!!) Only sufa unt n nduts.

19 Lssy Mdium - D. Ray Kwk Eampl (a) Calulat th dilti lss (in db) f an EM wav ppagating thugh 00 m f tfln at MHz. (b) at 0 GHz? Tfln:.08, tanδ at 5 C assuming fquny indpndn. (a) tan δ tan δ η ( π 0 ) (.08)( ) 8 ( )( 377).08 A(dB) (b) 36 π ( 0 )( 00) tan δ η np/m Caial abl wks wll at lw fq (TV t antnna) but nt s wll at high fq.!! 8 db S/m ( π 0 ) (.08)( ) 4 ( )( 377).08 A(dB) π ( 0 )( 00) np/m db 4 S/m

20 Lssy Mdium - D. Ray Kwk Eampl In a nnmagnti, lssy, dilti mdium, a 300-MHz plan wav is haatizd by th magnti fild phas Obtain tim-dmain pssins f th lti and magnti fild vts. What is th plaizatin stat f this wav? H H, β 9 { } " ' η η ' ' " β β β ' β β H y ( t9y) (, t) R ( ˆ 4ẑ) y y (, t) ˆ s( t 9y) ẑ4 sin( t 9y) E ẑη E ẑ57 y y 9y ( ˆ 4ẑ) A/m. ( ) / tan δ ( tan δ) / ( 0.468) 57.5 s( t 9y) ˆ 4η y ()(9) s( t 9y 0.) ˆ08 y tan δ (3 0 ) (π η sin( t 9y) y sin( t 9y 0.) 6 ) t 0 y, k t 0 LHEP z /

21 Lssy Mdium - D. Ray Kwk Eis (hw t wit th attnuatin?) Givn E at th igin has a amplitud f V/m alng th y-ais in a nn-magnti mdium, with th ppagatin givn by: ~ sin( t 30 5z) (4 0.0) Wit H (, t)?

22 Lssy Mdium - D. Ray Kwk Sufa sistan f nduts δ δ Z w L Z w L I V Z L J L E V s s J L w J δ/ w ( ) 4 / 0 )z / ( )z / ( z z w J w J dz w J da J I J J E J π δ δ β δ δ n sufa sufa impdan (Ω) simila t R & ρ

23 Lssy Mdium - D. Ray Kwk Hmwk. Dtmin th fquny at whih a tim-hamni lti fild intnsity auss a ndutin unt dnsity and a displamnt unt dnsity f qual magnitud in (a) sawat with 7 and 4 S/m, and (b) mist sil with.5 and 0-3 S/m.. Calulatins nning th ltmagnti fft f unts in a gd ndut usually nglt th displamnt unt vn at miwav fqunis. (a) Assuming and S/m f pp, mpa th magnitud f th displamnt unt dnsity with that f th ndutin unt dnsity at 00 GHz. (b) Wit th diffntial quatin in phas fm f magnti fild intnsity H in a su-f gd ndut.

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