ONIT- | MICROWAVE TRANSMISSON LINES. | Igtraduction: ¥ MiCOWaVeS aye electvomagnetic waves whose frequencies nange F10M [GHz 10 1000GHZ Microwaves Ave So cated since they defined interms of thein Wavelength in the Sense thal Micro nefers to tinyness ' tiNyness neferring to the Waverength and the period of cycle ofem | wave: | NQte: A Microwave is a signal that has a wavelength oF | 4004 oy less iS that Az30-Scms -This is converted 10 a Frequency of Q8yMHZ approxi Mateiy = Ganz Bands and Spectrum: The higher frequency edge of microwave bonders on the infrared and visible light negions or spectrum. | This explains why Microwaves behave Move like vays Of light than ordinary xadio waves: Bue to this unique behaviour the micro- | ‘wave freq's are classified seperately from nadio waves | Eur |scr | ver [ce-| me] ae [vnr]one| Bue [ene] indrared [Aight |x-vays | yng [osm || | 300HZ B0KHZ BKHz) 300m 30GHX Ygoraz lolsT HZ ode | ELF - Exieremely row frequency | (SUP - Super low frequency lvLF - very tow fyequency | Fuecwgmoaanetic Frequency Spectyyin | Microwave band Millimeter | & |s [ec [x|eu[k [ka | submillimeter | | | SoHe | gone] iBaAZ 4YOGHZ GHZ z IGH. Yow GHZ = 29GHZ 9 .300THZ 2SS eS ee ee [Advantages of microwaves: dee . Theve ave Some unique advantages of microwaves over iow ! frequencies: |) i Toceased Bandaiaih AVAIAB ty: Microwaves have lavge bandwidih compared to common bands Microwave negiON contains thousand Sections of the frequency band 0-107 Hz and hence any one of these thousand sections may be used | 40 transmit all the Tv, radio and other Communications & enproved Directive proper es: AS frequency incveases, divectivity incyeases and beamwidth decye- ases. Hence the beamwidth of nadiation 6 is propoytional 10 Ya For @ payabolic antenna 8 = !40" (ra) ushere 8- Hiameier of an antenna in cm | A~ waverength in cm | | B- Beamwidth in degrees | AS frequency increases ,4 decreases hence power gadiated and | gain increases seeding ailet ane feulehulty Fading eect due 10 vavialion in the transmission medium is lmore effective at lower Frequencies Due to line of sight propagation land high frequencies there is 15s fading effect and hence microwave | {communication is More seliabie | Fading def: A Signal experiences multipaih propagation vahich Causes lnapid Signal (ever fiuctuations in time caied Fading Hepower Requirement: avansMittey /Receiven powen nequinement aye pretty row at micaowave frequencies compaye tO that of short Wave bands1: Vxne TH Ba > Ampere's haw (Moditred) . B.Jxes - 38 ~> Faraday's haw of Enduceron, 3. V-0= Py = Gauss hawfor slectrestatic. 7? V-G-0 —Gauss raw of Magnetisry . * The above Zquations describe how Llectric charges + Electric Current Creat Sleceric # Magnetic Field, V2 Nabla > Zndicate Partial derivative = Vector aradrene - * EF - Electric Field: * P= Free Lleerric Chage Density. J = Current Pesity, * GB > Slagnetic Hax Density 1 _ elegerre Displacement # H —> Magnetic Fires. Re Divergence FJ > graaient- freld. Wx —Curl oes Eine Sirgre Mm}. eee z z & Three dimensional] i x y: . y 2 2 a fax t Sa ta Doe 1 oy te aeRylindzical Loordinate Biysrem*: Reordinate z ye Radial Distance og = Azinuthal Angle (Nf ®) Z = Height: a = ay + 24 3 +542. ay y2¢e os z K Cylindtical To Caxeesiah oe apa cence cosf= > sings & a : Z-z x aves g y = vsing Lylinazical : aaa # Cartesian To ae ee * o Ete| p . ; a. Ethericl Coordinate Fysten ! 6 = polar Angle id Yr Radial Distance Gz Azimuthal Angle: | r (8/9) | a | | Cb ge et “ Y | | aA Dart dae 2¥ x06 | eles non 5 | ysihe | | | | F ehencal Kovrdinate iysrem 15 Loartesian. | TN I ne Re | Fron Triangle a From Triangle = 4 | | > 2-4 ce. = & i y = xCcoS 6 g= aa : Xa ‘ =e Lie a cos ine y a2 a = xYSsIhe eo he From Triangle A sing = ms oe Yrasing OME xe ye = Bihosih g HWieT From Triangle B= ¥ te ghyar tee xXMSyhb2* v sige oo A : yee! a oY Tata .From trangie 6 ee COS B= cose = ayer iy ———— Or CoS (FS) gb? m1 Triangle A Fro tang a * Gr tan! ) : | * have Equations :- * The chavacrerisrics of the Medium in which the fields enrse ave needed te. specify the flux | * 0-22 * B=MH | x eeJ=o-E * E=LxES + A= Ly, * With the above Equatrons. Vx = T4222 rete dk De DE- VxE = —-%8 -~ 498 De we Th terms of the fields in a specific Mediurm-Hearc.et ISE actamed phar gine elewsic & Magnetic Follow an Exponential form of Lime Variation , we freids can write Twt E= ee a CeosusteTsinwe) * Tn the above Lanation real pare is Considered 4 Tmaginasy Part is Retained for Sinusoidal Varia tion Jue: PE=AE,e #% Partial differential Equation. Ee Tuk OF = 3 E,e de De Tur = £0 (me DE. esw DE Es JWE VE Partial djfferential Equation OK : x 5 —— Tue we DE Sa RHoe = Hols) e7Vxn = (— + Iwe)eE VxE = - adn 7 - MIwH * Apelying Carl to above Equation. VXE = — JWHH YXUXE = - Iw (yxn) Wve) - Ves -TwM(ce + swe) BT TWMT ER + ~The - VES -INMeR TUE * Free Charge akfzo vies L 6 oe -G V-D=Me6 k Using above Equations. UME) = Oo = (-1u Ee ~NVCE) = wraee Vee] Soe > Lleciric Wave Equaroh Similarly 2 aa VOH =~ a cH Magnetic Wave Lquahes *In time domain, ElecwedMagnetig Wave Equations ave L, 1 mn vz a £equide: ® frog's highey that 3GHZz , transmission of En waves along Lransmission lines and cables becomes difficult Mainty due to 105Ses Ahad OccUM both iM ANAM Solid diolectric Needed io Support the conducion hervefove, A metallic tube i Can be used’: te" ~ transmit electromagnetic wave at these freq's A HONOW Metallic {Ube OF UNITOYM CYOSS- SECLION For AYaNSsMilting EP) waves by SUCcessive mefIeCLONs from innen walis Of the tube iS cayied @ Y Waveguide’: Comparison Qf Waveguide With 2 wine TWANsMiIssion Anes: | wave travelling in a waveguide has a phase velocity and will be aitenuaied as a transmission line. 2 when the wave neaches the end of ihe wavequide i is neflected uniess the load tmpedance 1S Adjusied 10 absevve the wave. 2 ANY invequidvity iN @ Waveguide produces meflecion just like an inaeguianity in a lyansmission tine JOR OF waveguides: Any shape of cross-sectional of waveguide can support EM Waves But Since inneguian shapes ave difficult 10 ANatyxe and aye rarely used, rectanquiay and ciyculay wave guides have become move common. recianquiay wave quide is MOS common C/4i9: OP Wen = (6) Cifeulay wave (C) Elliptical Wave Copper wails | | | quide pulde inner Surdace hin tining of AU and Ag.(ei @) Single kidged (©) Bouble Ridged Crculay wave guide iends 10 twist the Waves as these travel ibyough dhom. civcwlan Wave quides ave used With nolating antennas as in nadars Propagation of Waves in Reclanguian wave Guidescewa) Consider A RWh SitUaied FM the Nectanquian coondinaied system with 18 breadth along x axis Width aiong yanis and the wave is assumed 10 Propagate along the z direction wave vide is filed . . Hive ction) with ain as dielectric q i The wave eqn fon 7E and 7M Waves on. are given by To width Viz =-usuenz for 1E Wave (éz=0) | = air -—3% 2 i oO a Wey = -us ek, 101 TM WAVE (Hz =0) %— breadih —} \Expanding vtéz in nectanguian coondinate sysiem P | Oke , Okey Er . uw peke Ou oy On | Since the wave is propagating in z direction we have operate — O24 one | | substituting | > Pee, tesa ox yt - OSU BE Oke 4 ke 4 Pru eyk, = 0 ou OgPrutue- be a constant then @ zi dkeyRe, -0 for 7M wave ay emidiy GAR 4a Az yh Hy=0 for T£ wave on Oy oidal EM wave = Mt riNsic propagation (Measure of changes ina Sinus ‘ough a medium) sorms of amplitude and phase while propagating thr from marwol's frst eqn Vx i= jusee | expanding gx,t § &- unit vectors along a1 yz direction 2 2 S|, jue[teatdeytRer] Rea jek 6 @ 3] = j Oey dey noi 3 juse [PEx 4) Eytk Ec] Hy Hy Az ip On ap az riba} +h { Sty 3h] . jue [teaad EythE Rp Oke + any) 3 [ Gt ajre fp ha at). juse [Tend &y 2] equating coeH's of *,F,k am +dHy = Jwelx 90 OHz 4 5ny = -jwefy 9@ rt dHy da. jwetz a@ On BY similaviy drom maxwen's a4 eqn gre = -juspt £xpanding vxeE«Tai ¢ “0 3fe 43 c{aey -o€ [oe veg] 3p 8 13ex) RLY aa Equating coefficients of 7, and & Okz, dky = -jophy 3 “< dE pak, = jWUKY AO 3 aéy - dk ~ -jupnz 9© “oxy subsiituling Hx from ean @ in eqn @ we get £y Hy > -1 Oke - 3 £y JOP OY jsp Sub Hx iN eqn@® | 2 ax jus oy Jwp de _ 4 ox | | L | sunstituring Hy from eqn® in eqn® we get Fy Hy = 1 Oke 4a gy | | | Just Ox — wo | Sub Hy in @ | BHe, 2 akea FP kx 2 huey jue GHz 4» 3 Bee 4 (344 usWe)Er =0 8y Oe ~jup (Ta F hy sh He]he ox Sub Fx eqn > in > eqn® we gel Hy f,- 2h Ole 4 jue OY jwe gub in ® 2 GHz 43° vy = fuouH ine OY juve ee) jure Gk 43 die 4 PHyTUPMEHY =0 a b> dy | substituting £y fom egn@® in eqn@ Hx from eqn® fys -+ He -3 py jwWe OX Swe sub £y in @ kz 3 OHe ~ a py = -jwylle 3 jue OX use juse O42 ~ 3 Hz _9%yy - wea = 0 ay ox | || juse OF adhe phy | ay Ox + quse fe these agns gives a TeLAtionship bIw dietd components within ie wave guide: : | Propagation 2 TM wave ia wave quide: | For 7M Wave, Hz=0 and £240 2 Bee, Ok abr ex 20 ovr ay det US consider a Solution &z=xY where x > pure function of 2, ¥> pure dunttion of y |1 POY) speyy=0 a Op | VOX 4 xPy shy -0 or ay Divide the entise eqn by xy’ SA Pe LAY she Xow Y oy LOV Lop Vv ay =) - Be M4b 20 =) phe A248? b= JAB 10 Solve the eqn we have to use seperation Method det us CONSidey, 1 BX 2-9, x or X= (C,COSBX 4 Cy SIN BA) Y= (CgC0SAY + Cy Sin AY) Herve Ci,G,&, cy ave constants Boundary conditions: For TM wave, 2=0 along the walls ISt boundary condition (bottom Walls): : | Fz =0 at YrOVxX FO10a 20! Be Cleft side wan): 42 | Fz=0 at 1-04 y 4 010b aid Be (top wain: fz=0 al Y=b¥ 19014 ath Bc C Right Side wars | &zg-0 al x2a¥Ys0tob | NOW CONSider £7 =xy ee F = (C1COSBX4 G SINBX) (63. COSAY 4¢y Sub iSt boundary and in® 2-0 aly-o¥ 00a0 = [COS B1 46) SiN Bx] C3 AS X varies from 0 t0a Xt0 370 i010 | Ez = [cc0sBa4 G sin6x) éy sinay [> Q Sub aNd bouNd-cond in © =0 at X=0 VY Otob 0 = Ci [Cy Sinay} | | C120 in@ | | [e=lesnadiqsmyt | @ | Sub 3'd Bc in@ | | he £20 at y=b ¥ x 50000 0=[ 4 SIN Bx] [Cy sin ab) i SiN Ab=0 =) Ab= SIN) = AT A- on b | 3Ub yth B-cin @ ie kz=0, at ta ¥y70 0b 0 = G CySiNBASINAY = SINBA=0 =) Ba=SiM'ol=MN 8= (mn) in® Fz = Gcy sin [ MJx sin (al) y | ey considering divection of propagation te &*? and vaviation with time Wt and consider qty =¢ Kz = ¢ sin (HP) xsin (O8 )y. 9 iut 32 we have ~4 dk - jw ote wh On nm Oy - Sy) 4G SIN BY] [G,COS(.0)4 Cy SiN} ®= | fOr IM Wave Hy=0 ky = -3 Ok Wax Sub kx eqn in above eqn Ey: -i 8 [c sin (mn) x sin (OM Jy put a) cach! BU Pe ei an | Re ic (ej cos (Ma si0( AN) elit 34 a ON es a now take ky Ry> 2 dks 1 jun oe hoy be 0 fut Hz=0 =) ky> -2 Okx boy oe Hz=0 and Sub Az | y= Jue can on Ty x eiust-a f= Le & (OP) C08 OB): im UT) NoW Hy= -2 OHz _ Jue oke OY pe OF Hz=0 and Sub kz era esa) Hy = Jue ¢. (mm A Jude -3Z, qe “208 c- (enn nn) ete (2! )a- sin (OB )y @ [oe Sh ed TM modes for a RWG: WE ARO ow ~ the modes of 7M WAVeS AYe eperesenied as IMmn | | ky 4 c( (a) Cos (MMM) x sin (22 )y. ela Eyes ae {ott Sin (OP yx C05 ( (an)y-e oiuot- az 1-3 Mg IME c Of) Sin (OT )x cosa yee iz. “UWE ¢. (MT) cos (BM)x sin (OT )ye oles befor M=0 aNd N=O Subst 19 &,£y, Ha, Py =) £,=£y =Ha=hy=0 TMoo Mode does NOL exists. case wis for m=O and n=! we 2) Ey = Fy = Ha = Hy 20 <-TMp; mode doesnt exisis MMSE Nis fOr Mel and n=0 =) £y ys Hn = Hy 20 “= 7M 19 Mode doesn't exists case ve for Mz! ANd N= =) Eye kyr Ha By #0 TM y MOde exists Propagation of TE wave in B:W-6: For 9€ Wave: &x=0 and Hx +0 Sz 4 DH she 20 om byt | ket Hx 2xy | BY 4 OKY +iry =o | av oy YOK 4 xd thhxy 20 me Oe BAe hs 0 =) hs A486 7 Soe the above eqn we have to use seperation meth ave WO solutions of this MOde. od, theseX = [Gc05B4 4 G sin Ba) Y= [escos Ay + cysin ay) Beexy Hz = (QCOSBA 1G SIMBA) (C3 COS AY +y SiDAY) AO From 4 sield components Ez, = Jug Bz +@ he OY Fy jw ane 5@ h> Ox Hy>-2 . he | a Boon 26 | Hys-a die a 34 3@ ‘Bouedary codivions |) Botlom wal: | £420 at Yeo¥1 30 toa R. zefl side wall: [OKAY AAS TA Ky=o at x0 ¥y 2010b #70 wal" Ay=0 at Yeb¥x 30100 i, RiQDE Side WAI ky20 at WA ¥Y 40t0b ee 4mM £4 = -—jusu OH bh? Oy = -JwH 2 [a cosex+gsinay) [cacosays cysinay] we Oy Ey = eee he Subst ISt bound-cond Oo = ae [cicos6x4 G8inbx) [ACU] 7 cy Subst in © Hz = [c:C0SBX + GSiNBx] C,C0SAY 7O | from £ys juss ate pe Ox 3 Just 9 ar be & (Hz) 0 = jus not jee [- c1Qin8-B +GCOSBa 8) [¢3cosAy 4Cy SiMAY J SUbSE- aNd bound cond O = jut BG [C3COsAY 1 Cysin AY] he G=o] in® =) Hz =((iC0SB1) (GCOSAY) | om Ka > -JUS atte be ox av Fy= jus . = ee (cveqsinex. 8) [ %3C0sAg] | Subst 31d bound-cond | | €x=0 at yeb¥ 2 a0tob =) O= jwp [ersinx-8][ cos Ab)- OO COS Abs0 =) Ab=fn =] A = aio 8 6 Hz= C3 COSBx- cos at .y aM 6 From £y = jw Bx hr Ot ys JUast cj¢3 sina. 6: COSA )Y fe b subst uth pound. cond fy =0 aixrzav¥yrotob SiNBI=0 =) Gen n@ : Moh \ x= c0$ (00 \Y - Ha = CiC3 COS( mE) cos(E\¥ By considering the divection Of propagation 6 and variation wrt time elut Tr ar Ha= Cr 63 cos(") a cos(O)y Sub I Arby Crd pr =Ey = J mi) 1.510 (OH piugt 3% | Ex jak rey (0m )eos( Bt) * (Bi)y-e . -. pit -8Z bayey = TWH acs (i) sin (220) x-cos (AE) 9 é ; d | Hy = jus t-32 Jt : on 4 juot~ tye 2 4G (mr) sin can) 1-208 22) 4 e ) ° O03 os Cos (Gt Si ( casey: M=0, N20 Subsi above eqns ihe mode is TE) =) x= Fy= Ay= by =0 T£oo Mode doesn't exist-( ' jQgsedle mo, n=! | Kxchy go ithe Mode Teo: exists case ditt M=1,N=0 | RRS a Ky Ha #0 The mode 1Ei9 exists | case iv! m=, n=l Ea, ky, Ha, Hy $0 The mode is 7, ANd it exisis which ais0 get higher order modeys UU! frequenry oy Cu oty dregs From Nodal analysis p= Ar+B> he Prusue -/onyy 2 je Pere = (og Pacey At lower fveq’s ine 2 (BE OL) > utue JF becomes neal and dinite and attenuation constant x exists, because 3-a4j)p ANd phase CONSt becomes xC10 The wave will NOL propagate through the wave guide AL bigher freq's Y mm), (OT \* use > (M0) + (22) NOW 9 iS IMaginary and finite aNd phase const exists, attenuation ipecomes evo The 41¢q at Which w-0 aNd 3 becomes o al ffe aNd us=We is | KNOWN as critical freq oy Cut off freq aleGuides woaye length (9): ithe disiance tvavelled by the wave 10 undergo a phase Shift OF fan nadians iS KNOWN as Guided wavelength (Ag) | 1. ; phase youoctty (yer Wk Upe dg |Multedivid by am a ee [2 at .p som az 20] [vps fdg al =) Wedge q a | an amr Mag jhe vate at which the wave change its phase inierM of its guided wavelength ag. (Aagup veudity (gr |the yale ai which wave propagates thyvough @ wave quide jusith certain velocity will be reymed as group velocity (vg) |: n for rigse velocity: —@] we have, 9- (mn)? ONY. as, = (my ) 1 (2°) usue 20 For wave propagation , at cnitical freq al f= 4c 1Ud= We and 3-0 miry? 4 /ony i 0 (ary vay Ue ME tue = (Mmy?y (OM | Ue WE (a) 4 (LY +e for wave propagation =o =) aejp ind | c) Bt L Load ; yjet= (DE)* + (DE)*- use from @} apt = usdpe -udue = pe [usc v9") aan eae B= (Hel use) Subst Bin Vp =) vp = Us wy - Jeo we] usyae [fi S| in critical WAvele Agth , iEaparssion for qigup yogeity: Nike Vg= qe a ae dB dw - fs [etewe )- gue = dye Sue . Jie 2M3: cf C5) Reiation Blw Ng ane and Mpi- Vp-Vq = 2 x € 1 be ——— JT epg)? | Relation b/w blw 4gido and Act weke7 phase veloc ty Vp = Fg = & al 40 Ue . p= —L_— 3@ in tems of A I Aa) From © and © Qe et Foe Io? AeA » sy 0, ACAD. I= Ak =) ah 4 d= gr Adcave impedance ip @ RWS Gri, oe = Oe qhe wave impedance in a RWG is defined as the natio of Istvengih of electric field 19 one transverse dine ction 10 the styength | £ magnetic Field in Other tyansverse dinectiOn. zz - Ver vey ra ae ov Ky Hx we have the dieid component varues | a> 3 Ok — jut ane and Hy = 3. dhe ie ok Wh ox Ar OY he dy Dx Kee Fa 2 -3fpr OKs - jw, Hy ox 3 pe bHz ay For T™M,Hz=0 and 3= jp -d Oke oc aura py dd | ~juse aée «Ewe | “he OL | Zr coh ee pe (Us We?) oe we | | Zz: OEJAI-M) 1-{ies)? eae . - eve dee Bn | Ze (amy? WEY \for TE , £2=0 and a= jp Zz - SwL. dhe Se Te a du. wn i. Obl Tee | eB A ogie “Etre JEU-&) power Transyited in Awe the power txed in a RWH IS defined as the powen at a freq greater than 4c critica req. Pir Gx ids [Pure Eg CEI as Also power transmitted [irs ae [eras Ba) pur tyed from TM Wave With the Consideration of dimensions a+b Payerm) = ae at re!" elt ds bw t OF ogy be ole on "CM ap Te f ft (Ex? 4leyfrdady For 1& wave | | | | oe Perv (ne) => I~ fs) fof teat Legh dady | 0 4 Power L0S50S in @ Rw: [ihe Pwr (05525 IN a RWh due to attenuation , below the cut-oH | freq, fe due 10 dissipation within a wave quide wats and 105ses due i the dielectric within the waveguide.a + At fiveq 125s than fe % becomes yeat and B becomes imaq Equating x and iMag value OF B is given as jp: at + dg = do (cet) | Ag Jt Co fag | | jee Jani fi- @o%ac)*, an Ji- Geac)t . ant fr-fe ye ip ee diatiei) : le 0 f Equating « and p a= ant fi =) Ar AC «= 546 [T-Eep apjiength | We @ } ae] "9 ‘Ablenuadion due £0 lapartRst CONAUCHNG HABEAS: walls: ae is given as a&e = I+ 82 (#)* aanengih for TEI | [-feye | I) “Avenuation due to imperfect diectre: | aq > 233 Jer 448 4p) ength do Ire) dominant and gegeneyate modes: BALA BAS Anda A ‘he Mode of plopagation ¢on which the field components exist |4vom lower cut off freq IS Calléd a8 Hominant Mode | For TE wave, a7b | | dhe dominant mode in TE wave is TEIo | for 1M wave, the dominant Mode is tmy, | prom, ac = —22b | Jo Penta | |the dominant Modes are TED he M=t N=0 [4c =2a] | TMy be menzt dee AAb Jartb* For higher modes any & values Of TE and TM ane equal in tems of Ac that Pain IS called degenerate Modes the degenerate Mode in 1& wave is TE}. TM wave 1s TMi Met Met =) Ac= aab Jat -TEmn ANd TMmp are degenerate modes for NFO and m #0 Here TEy and Tmy ave degenerate modes. pagbyerns a 1) Caicuiaie the dominant mode cut-off freq Waveiength in RWG Of dimensions qycm xacm | | Jim? brane [ROY REND des Ax x2 | Jaa 1 | | por TEIp Ac= Ad= 3CM a] A Wave IS propagated iN KWH At 6HHZ- Cali Ac for dominant [MOde- ik Ac IM & guide Ag for dominant Mode sir. Vp aNd Vg given, | a= 30m | sd Given a= 3m | Here dominant Mode is 7Ej9 M=1,020ce 8a 60M = 6xIO-M ag? Jo = 005 = g.09m | a | T(r)? fr- (@05\* | Vi= Go/Ac) ey | sii Vp = 2s Gs sey axioms Vi Goyac)® 0-882 1Vg= Jim Aoyy)r= ¢x0°55 = 165x io M/S 5) A RWG has a=acm and Cayries dominant Mode of a signal oF | ~ | 4:63 GHIE: Find Zz | sh Given a>3cm, f= 7-63GHE Pov TE) zz = n £ Ac =~ ab Ji fon oF + 00)- For Tin 1 dc= Q0b 22a pe | de = ax3= ecm | az & 2 3x10. 9.939m = 3:9em 763x109 Z el Zz = 493-8 y)| For an ain filed RuDh Of ex1CM-CAIC Ac for TEI and TMn Modes jaiso caicuiate dg at (0H | sd Given dimensions - acmx1a@ For TElor Ac=@a= YOM bo. awa) : For 1M; dez ROb = BOP = 8) Ly Lj gem | Voie: PHO TG & |uided wavelen Hb Ag: q ge fo T= Co /ac)* 2 3xip® -9.03¢m= 3CM to x109 es dow $ Ags 3 - yssem “ay 5) AD ain filled RWh has dimensions of 6emx4ucM propagates Signal at aGHz for TE{o Mode Cal Ade ding aly B iv, Vp Mg Mu TE st given a= 6cm, b=YCM, f= 3GHZ re Flere" For 1&0 , de> £ [) Jor) aa = Bxtol?. a5 GHZ aa axe dg = _do I> be /ag)* doz = 3x10!0. (gem F 3x04 Acz= aa a @) =1acm | s ' dg= HO = 10 , 10. 78-050 RB)’ froey reve. > Bx1!9 | 5.y2x10!cmis a Ts lo\ Vt @orac)* J(R)ye - = 3. gai-ay ‘Ag \2 1/10) x) () eldhe dimensions of WG ave a-ScmxicM ,the 410g iS B6GHZ -Caiculcde + possible Mobe Ji cul off freq Jil aq J Dominant Modes: wee fe § (UB) ay) | [et fre ( 30x10" 770. )* B6GHZ 7 sb (ee) + (2). Bb > ovens (BL) Bbxa5 M \t qr ans Py ph L BERR? af yyar - 8b5 > mPenrcasy® - | | pos gs) 9 ras | sh Given as aSlm ,b= tem ,f2 86GHK | | 19333, paren (a-5)* 8705 vi04 >M*4N* (a-5)> | | check* | [ [a condition | TEo} 0 1 doesn't eaist | TEl0 i 0 exist | El TeM I ! doesn't exist AT | \ doesn't exist TM) & ' doesn't exist ™ eet es doesn'texistFE(o 1S possible mode Wh fe= (BYE coy) : SHI" [ gzim \+) = 6aHz die dg = _4o Ut Aoyag? f Scat doe 3:48 2 y.eyem Trey 7 S 4) Tn a RW axIcM Operating at a freq Of GGHZ in TE[p Modes. Calc the MAX pwr handling capacity of WG If max potential qvadient of asignal is SkvicM sf pwn handting capacity , p= (6:63x10%) yay (061 (4) fC. £ 2 0:03m= 8-3CM °F 4G | | ag= for 1€10 dc= aa= Gem | Ag La | q= res 395M = Y ie P= (63x (03k) (30M x ICM) (32 3) = 1y.46 kw a] the TEip Mode iS plopagating in a RWh OF dimensions 6xuCm iby means of travelling detection , the dist bw max and min Is dound 40 be Yy.ASEM-FINd Freq of wave. si dhe successive seperation bw max and min in a WH is a 7iQ . y.s5(m =)dg= u 1 1a-Rom - For Tip Ac= aa =(acm ee a He bey al “a at a) 3 Be ke a ap ae ee Av*= 100-36 =) do=l0cm ; freq f=lications of microwaves: | MicvoWaves have a broad yange Of applications in Modern dechnology. iJelecommunication: mtercontinental tetephone and F-v space communication (karth 10 space and space to earth) telemetry comm- uNication tink for airways etc Radars: Detect aincratt ,tvatk/guide supensonic observe and ack weather patterns , Air traffic Control (ATO etc s-commerciar and ingustrian appucatos: These applications use heat property of microwaves Microwave OVEN (a-4aHZ, B0W) a Oty ing Machines 3)FO0d processing industry W Rubber induStry pias tics | chemical 5) MINING / Public WOTkS §) Biomedical applications muna and peace Lime Armen ions: Ra All the above 3 forms of applications ave peace time applications ipnticrowave weapon sustenns: AN EriCssions PYoduct Known as MINIS 1s Q highty moduiay and | multifunctionar detensive information System thai meets requirement for situation awareness, survivability and sensor fusion in {omorouwg dense and complex Signal environment aphase quay gaday: This WAS aN impor lant development in Military rarge 10 Make MQ battle there May be no time to wait for a large, slow dish antenna t0 Move -A phased array is a set Of huNdreds or thousands of little yadar sets thai al emit Microwaves. | seen ee ee---— Magnetic Pied Electotc freld a | e Entering Plane |_| i EnoVrew | x Leawrg plane. | ——|-—- Field ; ; Hacles Pater MOE TE | In a RWG Side view Topview poorTE agp Stde vrew Top view End view TE20 Side view Top viey