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Tansmiss Thy Micwav Engg EE 7 D. Ray Kwk

Tansmiss - D. Ray Kwk RF Spctum km mm µm Å Advancd ight Suc Bky ab

Tansmiss - D. Ray Kwk RF / Micwav icuit wis GND pt ntwk put suc pt ntwk utput ad

Tansmiss - D. Ray Kwk Sis cnnct w f A B RF A B

Tansmiss - D. Ray Kwk Paa cnnct w f A B RF A B

Tansmiss - D. Ray Kwk mmn tansmiss s mst cct schmatic twistd pai F ssy & nisy paa wi F - HF nisy & ssy caxia cab n distt wid fq ang micstip () n distt wid fq ang wst cst c-pana wavguid w cst fip chip accss cmpx dsign wavguid wst ss fq bands

Tansmiss - D. Ray Kwk Equivant cicuit (,t) i(,t) i(,t) (,t) da tansmiss Kichhff s aw: (, t) ( ) i(, t) (, t) t i(, t) (, t) t Tay (, t) (, t) Junct u: i(, t) i(, t) ( ) (, t) t i(, t) Q dq/dti d/dt (, t) t i(, t)

Tansmiss - D. Ray Kwk upd quats ( i) t) (, t t) i(, t) i(, t t) (, t i i i i t t i cunt wav t t i t simiay vtag wav

Tansmiss - D. Ray Kwk Wav quat f (x ± vt) f (u) vs / fwad tavg wav f u f '(u) f '(u) x x f u f"(u) f"(u) x x f u f '(u) ± vf '(u) t t f u ± vf"(u) v f"(u) t t f f x v t wav quat nt: x ± vt k k ( kx ± πft) ± ( t ± kx) k f (x ± vt) f ± f ( t k ) π λ x ± π λ ( t kx) (3D) vt

Tansmiss - D. Ray Kwk tag & unt Wavs (, t) i(, t) i i ± ( t) ( t) wh λ t ± ( t) ( t) ( t) [ ] ( t) ( t) why -? ± ( t) ± ± π λ v fλ (πf ) π v

Tansmiss - D. Ray Kwk Fids and cicuits ) k t ( ) k t ( i ) k t ( ) k t ( i i i H H t) H(, E E t) E(, H E t H E µε ) t ( ) t ( ) t ( ) t ( t) i(, t) (, i t i ε µ η µε v v

Tansmiss - D. Ray Kwk What is? haactistic mpdanc. 50 hms f mst cmmunicats systm, 75 hms f T cab. Masu 75 hms with a hmmt? Tw 75Ω cabs tgth ( sis) maks a 50Ω cab? 75 75 75!!!! What ds psnt?

Tansmiss - D. Ray Kwk Rfct at ad x x x x i(x) (x) ( ) ( ) ( ) ( ) ( ) i(0) (0) Γ x 0 x at th ad Df nmaid impdanc Γ fct

Tansmiss - D. Ray Kwk Examp ds it wk? 75Ω 50Ω 75Ω

Tansmiss - D. Ray Kwk mpdanc at nput x x x x i(x) (x) x 0 x ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( ) ( ) Γ Γ tan tan tan tan tan tan tan tan tan tan tan tan tan tan ) i( ) (

Tansmiss - D. Ray Kwk Excis 50 Ω 00Ω? x x 0 F ngth λ/8? λ/4? λ/? tan tan What if 50Ω? Wud th ngth mak any diffnc? tan tan 50Ω (-37 ) 5Ω 00Ω

Tansmiss - D. Ray Kwk Tansmiss mpdanc cas : 0, 0 tan 0 x x 0 tan tan tan tan cas : π, λ/ tan 0 cas 3: π/, λ/4 tan / Quat-wav tansfm (impdanc), a-t-a, cmpx-t-cmpx. nt: at w fq, 0, gadss f ngth impdanc.

Tansmiss - D. Ray Kwk Rfct at nput Γ x x 0 Γ tan tan ' ' tan tan ' ' n gna Γ ust hav t knw what t us

Tansmiss - D. Ray Kwk Excis Γ tan tan ' ' 50 Ω Γ x tan tan ' ' x 0 50 Ω 00Ω ngth λ/8 Γ? Γ? What if is 75 Ω? /3 /3 (-90 ) ny chang phas!?! 0.388 (35 )

Tansmiss - D. Ray Kwk tag wav tansmiss (x) (x) x x x ( Γ ) x Γ x x x 0 Γ ρ θ ρ ( θ x) ( ρcs( θ x) ) ρ s ( θ x) m whn s m max whn s 0 max ( ρ) 4ρ ( ρ) ( ρ) ( ρ) ρcs( θ x) ρ ( ρ) ρ( cs( θ x) ) θ x ( ρ) 4ρs

Tansmiss - D. Ray Kwk tag Standg Wav (x) x x m max standg wav f, Γ ρ ± pfct standg wav with nds x x 0 θ x ( ρ) 4ρs m whn (x < 0) θ x x θ (n ) π ± λ [ m (n ) π] 4 π max whn θ x ± nπ λ x θ [ m nπ] 4 π

Tansmiss - D. Ray Kwk SWR (tag Standg Wav Rati) m max m θ x ( ρ) 4ρs ( ρ) 4ρ ( ρ) x x 0 max ( ρ) ( ρ) SWR max m ρ ρ Γ Γ pfct match: ρ 0, SWR.0 pn / sht: ρ, SWR t is an dicat n hw w th ad matchs th. SWR is th standg wav pattn NSDE th. Ony Γ at th fctd unct that cunts

Tansmiss - D. Ray Kwk Excis 50 Ω 75 Ω Γ 00Ω x x 0 ngth λ/8 SWR? Γ /3 SWR

Tansmiss - D. Ray Kwk Rtun ss R 0 g ρ (db) pfct match: ρ 0, SWR.0, R pn / sht: ρ, SWR, R 0 db SWR ρ ρ Γ Γ ρ Γ SWR SWR Typica SWR. t ρ 0.048 t 0.33 R 6 db t 9.5 db

Tansmiss - D. Ray Kwk db sca pw tnsity ati g sca, nt a unit!! (db) 0g 0g P P 0g > 0 ga < 0 ss sund tnsity pw vtag 0 g() 3, 3 db dub 0 g(/) -3, -3 db haf 0 g(0) 0, 0 db 0x 0 g(00) 0, 0 db 00x 0 g(0.) -0, -0 db /0 What is 6 db? 9 db? 7 db? 44 db? 4x /8 5x 4 x 0-5

Tansmiss - D. Ray Kwk dbm & dbw dbw 0g dbm 0g P W P mw bcm a units 0 dbm mw 30 dbw kw -30 dbm µw What is 40 dbw? -7 dbm? -6 dbm? dbm? 0 kw 0. mw 4 µw /8 W

Tansmiss - D. Ray Kwk Examp stpic 00 W Hw much cticity gnatd by th sa c? What if a 40 W bub is usd? 00 W bub? ntnsity pw/aa 00 4πR 00 4π 7.96 W m ( ) 00 W bub? m sa c 0 x 0 cm 40% fficincy 35 0g Pw f cticity gnatd 63. mw Pw gnatd sa c W 7.96 ( 00cm )( 40% ) 3.8mW m 0.038W n tms f db 0g 35dB 00W P 00 40 W bub? P 35 0g 40 Pw f cticity gnatd.6 mw systm ga

Tansmiss - D. Ray Kwk Stub Tansmiss cnnctg nwh(?) Opn stub Sht stub (sht) Sis stub Shunt stub (sht)

Tansmiss - D. Ray Kwk Opn Shunt Stub -Band

Tansmiss - D. Ray Kwk Sht Shunt Stub 0 GH ntdigita Fit

Tansmiss - D. Ray Kwk Radia Stub 8 GH Rat Rac

Tansmiss - D. Ray Kwk Tung stub (pn)

Tansmiss - D. Ray Kwk Sht Stub ( 0) Y sh sh tan tan tan sh ct ci π/ π 3π/ π pid f π cap -/ ss ps

Tansmiss - D. Ray Kwk Opn Stub ( ) p tan tan ct Y p tan cap -/ π/ π 3π/ π pid f π ci ss ps

Tansmiss - D. Ray Kwk Excis 75 Ω, λ/8 Fd & Γ. 50 Ω λ/ 00 Ω 0.λ sh tan() 75 tan(45 ) 75 Ω p - ct() - 00 ct(36 ) - 38 Ω 50 Ω λ/ Y /75-0.033 Y /38 0.0073 50 Ω λ/ Γ /Y /(-0.006) 66 Ω tan tan 66 50 66 Ω (07 73 ) 34 66 50

Tansmiss - D. Ray Kwk Tansmiss with ss i(,t) i(,t) (,t) R G (,t) Kichhff s aw: (, i(, t) t) ( ) t (R )i(, t) (, t) i(, t) (, t) Ri(, t) t (, t) (R )i(, t) i( Junct u:, t) i(, t) ( ) (, t) t ( G ) (, t) (, t) i(, t) G(, t) t i(, t) (G )(, t)

Tansmiss - D. Ray Kwk Ppagat nstants ) )(G (R () ) )(G (R ) (R ) (R ) (G γ γ γ ) (G ) (R ) )(G (R ) (R ) (R ) (R ) (R ) )( (R ) (R () () γ γ γ γ γ ± ± ± ± ± γ γ γ γ γ γ γ γ

Tansmiss - D. Ray Kwk ssss imit ± γ λ ± γ γ f v ) )(G (R ) (G ) (R () () () () γ γ R 0, G 0

Tansmiss - D. Ray Kwk Tansmiss Equat x x 0 tanh γ tanh γ tanh tanh γ γ which duc t ida tansmiss quat whn γ. tanh(x) tan(x)

Tansmiss - D. Ray Kwk w ss G R G R G R ) ( G R ) ( ) )(G (R γ γ γ γ γ v G R G R ) (G ) (R α γ α phas cnstant attnuat cnstant ppagat cnstant disttss

Tansmiss - D. Ray Kwk Disttss v R α R R R ) ( G R ) ( ) )(G (R G R γ γ γ γ γ fquncy dpndnc

Tansmiss - D. Ray Kwk Attnuat () () () (0) 0g α α 0 0 α () (0) ( α α db γ α db / 0 / 0) 0g ( α ) fwad vtag wav attnuat & ppagat A() α db A attnuat db α db attn. db/m α /m nps/m

Tansmiss - D. Ray Kwk Examp α 50 Ω 5 cm 0 α db / 0 0 ( 0.04/ ) 9 π( 3 0 ) π α n 0 0 8 v 3 0 α 0.04 db/m? at 3 GH A (0.04 db/m)(0.5m)0.006 db (vy w ss) 0.04 db 8.868 α α 0.0046 /m ( Np / m) 6.8 /m ( ad / m), 5 cm 3λ/!! sh sh tanh γ tanh γ tanh γ tanh( α ) tanh( α) tan( ) tanh( α) tan( ) sh sh sh tanh(0.00069) tan(3π ) 50 tanh(0.00069) tan(3π ) 0.00069 0 50 0 0.0345 hms tanh(x) x f sma x

Tansmiss - D. Ray Kwk Examp sh p tanh γ tanh γ 4 m tanh γ tanh γ p sh sh p tanh( α 50 360 30 360 70 50 pn 50 (-50 ) Ω sht 360 (0 ) Ω What is, α,? As R,, G,? cmpx sht / pn ssy!! 300 5. 35 tanh α tan ) tanh α tan 0.983 4m, α 0.39 Np/m, 0.35 ad/m (90 0.688 0.983 78) Ω 0.688

Tansmiss - D. Ray Kwk Examp - cntu 4 m What is, α,? As R,, G,? γ γ γ R G ( R )( G ) R G 90 78 γ α 0.39 0.35 v (0.35)(3 0 8 ) 0.705 0 8 4 quats, 4 unknwns R 58.6 Ω/m, 0.8 µh/m G 0.46 /Ωm,.4 pf/m

Tansmiss - D. Ray Kwk Fid Equivanc.g. TEM - caxia ds E " G d H R R ds E ds H S s S S ε ε µ d c m G P R P 4 W 4 W tim avag R s /σδ s ε ε ε ε ( tanδ)

Tansmiss - D. Ray Kwk axia ab - π µ π µ Φ π µ Φ φ φ π µ Φ φ π µ a b n h ' a b n h ' a b n h ˆhd ˆ da B ˆ B H d H b a f π µ π µ π π µ µ a b n d d ds H b a b a S

Tansmiss - D. Ray Kwk axia ab - ( ) a) n(b / h ' a) n(b / h Q ' a b n h Q d E ˆ h Q E Q h E Q ds D a b f πε ε π ε π ε π π ε a) n(b / d a)] [n(b / d a) n(b / / d h Q ds E b a b a b a S πε πε π ε π ε π ε ε a b - -

Tansmiss - D. Ray Kwk axia ab R & G π ϕ π ϕ π b a R R bd b ad a R R d H R R s b a s s a b - - a) n(b / " G d a)] [n(b / " G d a) n(b / / " G d h Q " G ds E " G b a b a b a S πε πε π ε π ε π ε ε

Tansmiss - D. Ray Kwk Summay - axia ab w ss caxia R G µ b n π a πε' n(b / a) R s π a πε" n(b / a) b v v η π µε ε µ π n n b a b a π µ n(b / a) EM wav mdia n(b / a) πε (η 377 Ω) n(b / a) πε'

Tansmiss - D. Ray Kwk tan Y Y tan Y Y Y Y tan Y tan Y Y tan Y / tan ) Y (/ Y tan tan Y tan tan Y Y Y Y Y Y Y / Y / Y / Y / Γ Γ Γ Y Y Y Γ Y usfu f shunt cicuits Admittanc (Y /)

Tansmiss - D. Ray Kwk Eai xcis 75 Ω, λ/8 Fd & Γ. 50 Ω λ/ 00 Ω 0.λ Y sh - Y ct() - (/75) ct(45 ) - 0.033 Y p Y tan() 0.0 tan(36 ) 0.0073 Ω 50 Ω λ/ Y - 0.033 Y 0.0073 Y - 0.006 50 Ω λ/ Γ Y Y Y tan Y Y tan / 50 0.006 Y Y - 0.006 66 Ω (7 7 ) 34 Y Y / 50 0.006

Tansmiss - D. Ray Kwk Eai Excis pw cnsidat Γ Γ x tan tan ' ' tan tan ' ' x 0 Pw fctd? 50 Ω 50 Ω 00Ω ngth λ/8 Γ? Γ? Pw divd? /3 /3 (-90 ) Γ ny chang phas Γ 89% 3 % Dn t dub cunt fct. Γ & Γ Rtun ss (R) - 0 g ρ 9.5 db

Tansmiss - D. Ray Kwk Pbm.6 (put vtag) Γ Γ Γ Γ Γ Γ i i i ) ( ) ( R R () R R i λ/4 Wit & - tms f i

Tansmiss - D. Ray Kwk P Max Pw Divy (atd t pbm.) dp d 0 g d P d g g g g > 0 g g g g max g 3 g g g Max pw div whn g & ½ suc pw. Why?? P P max g g g g g (assumg a) assum s & s a a a f simpicity P P suc max P g suc g g g g 8 g 4 g g g

Tansmiss - D. Ray Kwk High f cicuit mnts GH umpd mnt Band pass fit.... AP NDAP AP D 3 D ND D D 4 D AP 3 4 6 ND pf D pf nh 5 pf D 7 pf nh nh pf GH umpd mnt w pass fit much sma.... ND AP AP ND AP D D D D 3 4 4 7 6 nh pf pf nh pf A sma p f th wi is an duct!!

Tansmiss - D. Ray Kwk High- as duct Γ tan tan >> ngth << λ/4 (π/) ~ a Ψ b ϕ θ has a psitiv phas duct-ik!!!

Tansmiss - D. Ray Kwk w- as capacit Γ tan tan << ngth << λ/4 (π/) ~ a ϕ b Ψ θ has a ngativ phas capacit-ik!!!

Tansmiss - D. Ray Kwk w pass fit 5 GH w pass fit.... ND AP AP ND AP D D D D 3 4 4 7 6 nh pf pf nh pf 4 GH w pass fit high-w impdanc s wavguid high pw w ss

Tansmiss - D. Ray Kwk High-w- s 0 GH band pass fit high s ducts Sht shunt stubs λ/4 snats.... ND ND ND D D ND AP D D ND 6 3 4 D D 7 6 4 nh pf 5 nh nh nh pf nh 3 GH cup Tung with stubs (shunt pn) Thk f thm as shunt capacits w s

Tansmiss - D. Ray Kwk Hmwk h. #, 3, 6, 8, 9, 0 h. # -4, 7, 8